Chimera: A hybrid numerical approach for isotropic loop quantum cosmology
NASA Astrophysics Data System (ADS)
Diener, Peter; Gupt, Brajesh; Singh, Parampreet
2013-04-01
Loop quantum cosmology (LQC) is one approach to the resolution of the problem of singularities in classical cosmologies. The evolution of a cosmological model in LQC is governed by a set difference equations. In the isotropic cosmology (1+1 dimensions) the discretization is uniform in the spatial dimension. The stable simulation of a widely spread semi-classical state requires a very large computational domain and would therefore be computationally very expensive. In this talk we present an efficient hybrid numerical scheme based on the fact that the difference equations can be approximated by a set of partial differential equations (PDE's) in the limit of large spatial volume. We therefore introduce a hybrid scheme where we solve the LQC difference equations in the small volume and the PDE's in the large volume regime. By a simple change of coordinates in the large volume regime, we can significantly reduce the computational cost and explore regions of parameter space previously unachievable. We will describe the numerical implementation, present selected results and discuss the extension of the scheme to other models.
Higher dimensional loop quantum cosmology
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong
2016-07-01
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n+1 dimensional model and the 3+1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology.
Loop quantum cosmology in 2 +1 dimension
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong
2014-12-01
As a first step to generalize the structure of loop quantum cosmology to the theories with the spacetime dimension other than four, the isotropic model of loop quantum cosmology in 2 +1 dimension is studied in this paper. We find that the classical big bang singularity is again replaced by a quantum bounce in the model. The similarities and differences between the (2 +1 )-dimensional model and the (3 +1 )-dimensional one are also discussed.
Testing loop quantum cosmology
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2017-03-01
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the tensor-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop quantum cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop quantum cosmology: its relation to loop quantum gravity, the trans-Planckian problem, and a possible transition from a Lorentzian to a Euclidean space-time around the bounce point.
Loop quantum cosmology and singularities.
Struyve, Ward
2017-08-15
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
NASA Astrophysics Data System (ADS)
Chiou, Dah-Wei
2015-12-01
This paper presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) — a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and systematic derivations, it aims to provide a general picture of LQG, placing emphasis on the fundamental ideas and their significance. The canonical formulation of LQG, as the central topic of the paper, is presented in a logically orderly fashion with moderate details, while the spin foam theory, black hole thermodynamics, and loop quantum cosmology are covered briefly. Current directions and open issues are also summarized.
Bojowald, Martin
2008-01-01
Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.
Bojowald, Martin
2005-01-01
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time.
Isotropic quantum scattering and unconventional superconductivity.
Park, T; Sidorov, V A; Ronning, F; Zhu, J-X; Tokiwa, Y; Lee, H; Bauer, E D; Movshovich, R; Sarrao, J L; Thompson, J D
2008-11-20
Superconductivity without phonons has been proposed for strongly correlated electron materials that are tuned close to a zero-temperature magnetic instability of itinerant charge carriers. Near this boundary, quantum fluctuations of magnetic degrees of freedom assume the role of phonons in conventional superconductors, creating an attractive interaction that 'glues' electrons into superconducting pairs. Here we show that superconductivity can arise from a very different spectrum of fluctuations associated with a local (or Kondo-breakdown) quantum critical point that is revealed in isotropic scattering of charge carriers and a sublinear, temperature-dependent electrical resistivity. At this critical point, accessed by applying pressure to the strongly correlated, local-moment antiferromagnet CeRhIn(5), magnetic and charge fluctuations coexist and produce electronic scattering that is maximal at the optimal pressure for superconductivity. This previously unanticipated source of pairing glue opens possibilities for understanding and discovering new unconventional forms of superconductivity.
Elastic field of approaching dislocation loop in isotropic bimaterial
NASA Astrophysics Data System (ADS)
Wu, Wenwang; Xia, Re; Xu, Shucai; Qian, Guian; Zhang, Jinhuan
2015-10-01
A semi-analytical solution is developed for calculating interface traction stress (ITS) fields due to elastic modulus mismatch across the interface plane of isotropic perfectly bounded bimaterial system. Based on the semi-analytical approaches developed, ITS is used to correct the bulk elastic field of dislocation loop within infinite homogenous medium, and to produce continuous displacement and stress fields across the perfectly-bounded interface. Firstly, calculation examples of dislocation loops in Al-Cu bimaterial system are performed to demonstrate the efficiency of the developed semi-analytical approach; Then, the elastic fields of dislocation loops in twinning Cu and Cu-Nb bimaterial are analyzed; Finally, the effect of modulus mismatch across interface plane on the elastic field of bimaterial system is investigated, it is found that modulus mismatch has a drastic impact on the elastic fields of dislocation loops within bimaterial system.
Rovelli, Carlo
2008-01-01
The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
Uniqueness of measures in loop quantum cosmology
Hanusch, Maximilian
2015-09-15
In Ashtekar and Campiglia [Classical Quantum Gravity 29, 242001 (2012)], residual diffeomorphisms have been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). We show that, in the homogeneous isotropic case, unitarity of the translations with respect to the extended ℝ-action (exponentiated reduced fluxes in the standard approach) singles out the Bohr measure on both the standard quantum configuration space ℝ{sub Bohr} as well as on the Fleischhack one (ℝ⊔ℝ{sub Bohr}). Thus, in both situations, the same condition singles out the standard kinematical Hilbert space of LQC.
Unstable anisotropic loop quantum cosmology
Nelson, William; Sakellariadou, Mairi
2009-09-15
We study stability conditions of the full Hamiltonian constraint equation describing the quantum dynamics of the diagonal Bianchi I model in the context of loop quantum cosmology. Our analysis has shown robust evidence of an instability in the explicit implementation of the difference equation, implying important consequences for the correspondence between the full loop quantum gravity theory and loop quantum cosmology. As a result, one may question the choice of the quantization approach, the model of lattice refinement, and/or the role of the ambiguity parameters; all these should, in principle, be dictated by the full loop quantum gravity theory.
Ekpyrotic loop quantum cosmology
Wilson-Ewing, Edward
2013-08-01
We consider the ekpyrotic paradigm in the context of loop quantum cosmology. In loop quantum cosmology the classical big-bang singularity is resolved due to quantum gravity effects, and so the contracting ekpyrotic branch of the universe and its later expanding phase are connected by a smooth bounce. Thus, it is possible to explicitly determine the evolution of scalar perturbations, from the contracting ekpyrotic phase through the bounce and to the post-bounce expanding epoch. The possibilities of having either one or two scalar fields have been suggested for the ekpyrotic universe, and both cases will be considered here. In the case of a single scalar field, the constant mode of the curvature perturbations after the bounce is found to have a blue spectrum. On the other hand, for the two scalar field ekpyrotic model where scale-invariant entropy perturbations source additional terms in the curvature perturbations, the power spectrum in the post-bounce expanding cosmology is shown to be nearly scale-invariant and so agrees with observations.
Classical Physics and Quantum Loops
Barry R. Holstein; John F. Donoghue
2004-05-01
The standard picture of the loop expansion associates a factor of h-bar with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss examples wherein classical effects arise from loop contributions and display the relationship between the classical terms and the long range effects of massless particles.
Characterizing error propagation in quantum circuits: the Isotropic Index
NASA Astrophysics Data System (ADS)
Fonseca de Oliveira, André L.; Buksman, Efrain; Cohn, Ilan; García López de Lacalle, Jesús
2017-02-01
This paper presents a novel index in order to characterize error propagation in quantum circuits by separating the resultant mixed error state in two components: an isotropic component that quantifies the lack of information, and a disalignment component that represents the shift between the current state and the original pure quantum state. The Isotropic Triangle, a graphical representation that fits naturally with the proposed index, is also introduced. Finally, some examples with the analysis of well-known quantum algorithms degradation are given.
Effective scenario of loop quantum cosmology.
Ding, You; Ma, Yongge; Yang, Jinsong
2009-02-06
Semiclassical states in isotropic loop quantum cosmology are employed to show that the improved dynamics has the correct classical limit. The effective Hamiltonian for the quantum cosmological model with a massless scalar field is thus obtained, which incorporates also the next to leading order quantum corrections. The possibility that the higher order correction terms may lead to significant departure from the leading order effective scenario is revealed. If the semiclassicality of the model is maintained in the large scale limit, there are great possibilities for a k=0 Friedmann expanding universe to undergo a collapse in the future due to the quantum gravity effect. Thus the quantum bounce and collapse may contribute a cyclic universe in the new scenario.
Classical physics and quantum loops.
Holstein, Barry R; Donoghue, John F
2004-11-12
The standard picture of the loop expansion associates a factor of variant Planck's over 2pi with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss counterexamples wherein classical effects arise from loop diagrams and display the relationship between the classical terms and the long range effects of massless particles.
Loop quantum cosmology: Anisotropies and inhomogeneities
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
In this dissertation we extend the improved dynamics of loop quantum cosmology from the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-times to cosmological models which allow anisotropies and inhomogeneities. Specifically, we consider the cases of the homogeneous but anisotropic Bianchi type I, II and IX models with a massless scalar field as well as the vacuum, inhomogeneous, linearly polarized Gowdy T3 model. For each case, we derive the Hamiltonian constraint operator and study its properties. In particular, we show how in all of these models the classical big bang and big crunch singularities are resolved due to quantum gravity effects. Since the Bianchi models play a key role in the Belinskii, Khalatnikov and Lifshitz conjecture regarding the nature of generic space-like singularities in general relativity, the quantum dynamics of the Bianchi cosmologies are likely to provide considerable intuition about the fate of such singularities in quantum gravity. In addition, the results obtained here provide an important step toward the full loop quantization of cosmological space-times that allow generic inhomogeneities; this would provide falsifiable predictions that could be compared to observations.
Loop quantum cosmology gravitational baryogenesis
NASA Astrophysics Data System (ADS)
Odintsov, S. D.; Oikonomou, V. K.
2016-11-01
Loop quantum cosmology is an appealing quantum completion of classical cosmology, which brings along various theoretical features which in many cases offer a remedy for or modify various classical cosmology aspects. In this paper we address the gravitational baryogenesis mechanism in the context of loop quantum cosmology. As we demonstrate, when loop quantum cosmology effects are taken into account in the resulting Friedmann equations for a flat Friedmann-Robertson-Walker Universe, then even for a radiation-dominated Universe, the predicted baryon-to-entropy ratio from the gravitational baryogenesis mechanism is non-zero, in contrast to the Einstein-Hilbert case, in which case the baryon-to-entropy ratio is zero. We also discuss various other cases apart from the radiation domination case, and we discuss how the baryon-to-entropy ratio is affected from the parameters of the quantum theory. In addition, we use illustrative exact solutions of loop quantum cosmology and we investigate under which circumstances the baryon-to-entropy ratio can be compatible with the observational constraints.
Fermions in hybrid loop quantum cosmology
NASA Astrophysics Data System (ADS)
Elizaga Navascués, Beatriz; Mena Marugán, Guillermo A.; Martín-Benito, Mercedes
2017-08-01
This work pioneers the quantization of primordial fermion perturbations in hybrid loop quantum cosmology (LQC). We consider a Dirac field coupled to a spatially flat, homogeneous, and isotropic cosmology, sourced by a scalar inflaton, and treat the Dirac field as a perturbation. We describe the inhomogeneities of this field in terms of creation and annihilation variables, chosen to admit a unitary evolution if the Dirac fermion were treated as a test field. Considering instead the full system, we truncate its action at quadratic perturbative order and construct a canonical formulation. In particular this implies that, in the global Hamiltonian constraint of the model, the contribution of the homogeneous sector is corrected with a quadratic perturbative term. We then adopt the hybrid LQC approach to quantize the full model, combining the loop representation of the homogeneous geometry with the Fock quantization of the inhomogeneities. We assume a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger equation for the quantum evolution of the perturbations, where the role of time is played by the homogeneous inflaton. We prove that the resulting quantum evolution of the Dirac field is indeed unitary, despite the fact that the underlying homogeneous geometry has been quantized as well. Remarkably, in such evolution, the fermion field couples to an infinite sequence of quantum moments of the homogeneous geometry. Moreover, the evolved Fock vacuum of our fermion perturbations is shown to be an exact solution of the Schrödinger equation. Finally, we discuss in detail the quantum backreaction that the fermion field introduces in the global Hamiltonian constraint. For completeness, our quantum study includes since the beginning (gauge-invariant) scalar and tensor perturbations, that were studied in previous works.
Quantum reduced loop gravity and the foundation of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Alesci, Emanuele; Cianfrani, Francesco
2016-06-01
Quantum reduced loop gravity is a promising framework for linking loop quantum gravity and the effective semiclassical dynamics of loop quantum cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.
Quantum Monte Carlo with directed loops.
Syljuåsen, Olav F; Sandvik, Anders W
2002-10-01
We introduce the concept of directed loops in stochastic series expansion and path-integral quantum Monte Carlo methods. Using the detailed balance rules for directed loops, we show that it is possible to smoothly connect generally applicable simulation schemes (in which it is necessary to include backtracking processes in the loop construction) to more restricted loop algorithms that can be constructed only for a limited range of Hamiltonians (where backtracking can be avoided). The "algorithmic discontinuities" between general and special points (or regions) in parameter space can hence be eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg antiferromagnet in an external magnetic field. We show that directed-loop simulations are very efficient for the full range of magnetic fields (zero to the saturation point) and anisotropies. In particular, for weak fields and anisotropies, the autocorrelations are significantly reduced relative to those of previous approaches. The back-tracking probability vanishes continuously as the isotropic Heisenberg point is approached. For the XY model, we show that back tracking can be avoided for all fields extending up to the saturation field. The method is hence particularly efficient in this case. We use directed-loop simulations to study the magnetization process in the two-dimensional Heisenberg model at very low temperatures. For LxL lattices with L up to 64, we utilize the step structure in the magnetization curve to extract gaps between different spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the transverse susceptibility in the thermodynamic limit: chi( perpendicular )=0.0659+/-0.0002.
Compatible quantum correlations: Extension problems for Werner and isotropic states
NASA Astrophysics Data System (ADS)
Johnson, Peter D.; Viola, Lorenza
2013-09-01
We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global N-partite quantum state. Intuitively, we say that the multipartite state “joins” the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible N-partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in d dimensions and focus on two specific versions of the quantum marginal problem which we find to be tractable. The first is Alice-Bob, Alice-Charlie joining, with both pairs being in a Werner or isotropic state. The second is m-n sharability of a Werner state across N subsystems, which may be seen as a variant of the N-representability problem to the case where subsystems are partitioned into two groupings of m and n parties, respectively. By exploiting the symmetry properties that each class of states enjoys, we determine necessary and sufficient conditions for three-party joinability and 1-n sharability for arbitrary d. Our results explicitly show that although entanglement is required for sharing limitations to emerge, correlations beyond entanglement generally suffice to restrict joinability, and not all unentangled states necessarily obey the same limitations. The relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed.
NASA Astrophysics Data System (ADS)
van de Ven, Anton E. M.
1992-07-01
We prove the existence of a nonrenormalizable infinity in the two-loop effective action of perturbative quantum gravity by means of an explicit calculation. Our final result agrees with that obtained by earlier authors. We use the background-field method in coordinate space, combined with dimensional regularization and a heat kernel representation for the propagators. General covariance is manifestly preserved. Only vacuum graphs in the presence of an on-shell background metric need to be calculated. We extend the background covariant harmonic gauge to include terms nonlinear in the quantum gravitational fields and allow for general reparametrizations of those fields. For a particular gauge choice and field parametrization only two three-graviton and six four-graviton vertices are present in the action. Calculational labor is further reduced by restricting to backgrounds, which are not only Ricci-flat, but satisfy an additional constraint bilinear in the Weyl tensor. To handle the still formidable amount of algebra, we use the symbolic manipulation program FORM. We checked that the on-shell two-loop effective action is in fact independent of all gauge and field redefinition parameters. A two-loop analysis for Yang-Mills fields is included as well, since in that case we can give full details as well as simplify earlier analyses.
Singularities in loop quantum cosmology.
Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David
2008-12-19
We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.
Loop expansion and the bosonic representation of loop quantum gravity
NASA Astrophysics Data System (ADS)
Bianchi, E.; Guglielmon, J.; Hackl, L.; Yokomizo, N.
2016-10-01
We introduce a new loop expansion that provides a resolution of the identity in the Hilbert space of loop quantum gravity on a fixed graph. We work in the bosonic representation obtained by the canonical quantization of the spinorial formalism. The resolution of the identity gives a tool for implementing the projection of states in the full bosonic representation onto the space of solutions to the Gauss and area matching constraints of loop quantum gravity. This procedure is particularly efficient in the semiclassical regime, leading to explicit expressions for the loop expansions of coherent, heat kernel and squeezed states.
Loop Quantum Cosmology: holonomy corrections to inflationary models
Artymowski, Michal; Lalak, Zygmunt; Szulc, Lukasz
2009-01-15
In the recent years the quantization methods of Loop Quantum Gravity have been successfully applied to the homogeneous and isotropic Friedmann-Robertson-Walker space-times. The resulting theory, called Loop Quantum Cosmology (LQC), resolves the Big Bang singularity by replacing it with the Big Bounce. We argue that the LQC holonomy corrections generate also certain corrections to field theoretical inflationary scenarios. These corrections imply that in the LQC the effective sonic horizon becomes infinite at some point after the bounce and that the scale of the inflationary potential implied by the COBE normalisation increases. The evolution of scalar fields immediately after the Bounce becomes modified in an interesting way. We point out that one can use COBE normalisation to establish an upper bound on the quantum of length of LQG. LQC corrections other than the holonomy one are assumed to be subdominant.
The consistent histories approach to loop quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David A.
2016-06-01
We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on “measurements” to convert unrealized quantum potentialities into physical outcomes that can be assigned probabilities. In the early universe and other physical contexts in which there are no observers or measuring apparatus (or indeed, in any closed quantum system), what criteria determine which alternative outcomes may be realized and what their probabilities are? In the consistent histories formulation it is the vanishing of interference between the branch wave functions describing alternative histories — as determined by the system’s decoherence functional — that determines which alternatives may be assigned probabilities. We describe the consistent histories formulation and how it may be applied to canonical loop quantum cosmology, describing in detail the application to homogeneous and isotropic cosmological models with scalar matter. We show how the theory may be used to make definite physical predictions in the absence of “observers”. As an application, we demonstrate how the theory predicts that loop quantum models “bounce” from large volume to large volume, while conventional “Wheeler-DeWitt”-quantized universes are invariably singular. We also briefly indicate the relation to other work.
Exact mapping between different dynamics of isotropically trapped quantum gases
NASA Astrophysics Data System (ADS)
Wamba, Etienne; Pelster, Axel; Anglin, James R.
2016-05-01
Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or non-equilibrium states prevent exact theoretical treatment. In this talk, we present a class of exact mappings between all the observables of different experiments, under the experimentally attainable conditions that the gas particles interact via a homogeneously scaling two-body potential which is in general time-dependent, and are confined in an isotropic harmonic trap. We express our result through an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics which makes it general. It applies to arbitrary measurements on possibly multi-component Bose or Fermi gases in arbitrary initial quantum states, no matter how highly excited or far from equilibrium. We use an example to show how the results of two different and currently feasible experiments can be mapped onto each other by our spacetime transformation. DAMOP sorting category: 6.11 Nonlinear dynamics and out-of-equilibrium trapped gases EW acknowledge the financial support from the Alexander von Humboldt foundation.
Quantum Kinematics of Bosonic Vortex Loops
Goldin, G.A.; Owczarek, R.; Sharp, D.H.
1999-05-06
Poisson structure for vortex filaments (loops and arcs) in 2D ideal incompressible fluid is analyzed in detail. Canonical coordinates and momenta on coadjoint orbits of the area-preserving diffeomorphism group, associated with such vortices, are found. The quantum space of states in the simplest case of ''bosonic'' vortex loops is built within a geometric quantization approach to the description of a quantum fluid. Fock-like structure and non-local creation and annihilation operators of quantum vortex filaments are introduced.
Loop Quantum Gravity and Asymptotically Flat Spaces
NASA Astrophysics Data System (ADS)
Arnsdorf, Matthias
2002-12-01
Remarkable progress has been made in the field of non-perturbative (loop) quantum gravity in the last decade or so and it is now a rigorously defined kinematical theory (c.f. [5] for a review and references). We are now at the stage where physical applications of loop quantum gravity can be studied and used to provide checks for the consistency of the quantisation programme. Equally, old fundamental problems of canonical quantum gravity such as the problem of time or the interpretation of quantum cosmology need to be reevaluated seriously. These issues can be addressed most profitably in the asymptotically flat sector of quantum gravity. Indeed, it is likely that we should obtain a quantum theory for this special case even if it is not possible to quantise full general relativity. The purpose of this summary is to advertise the extension of loop quantum gravity to this sector that was developed in [1]...
Anomaly freedom in perturbative loop quantum gravity
Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.
2008-09-15
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoiling space-time covariance. Nevertheless, nontrivial quantum corrections do arise in the constraint algebra. Since correction terms must appear in tightly controlled forms to avoid anomalies, detailed insights for the correct implementation of constraint operators can be gained. The procedures of this article thus provide a clear link between fundamental quantum gravity and phenomenology.
Observations on interfacing loop quantum gravity with cosmology
NASA Astrophysics Data System (ADS)
Pawłowski, Tomasz
2015-12-01
A simple idea of relating the loop quantum gravity (LQG) and loop quantum cosmology (LQC) degrees of freedom is introduced and used to define a relatively robust interface between these theories in context of toroidal Bianchi I model. The idea is an expansion of the construction originally introduced by Ashtekar and Wilson-Ewing and relies on explicit averaging of a certain subclass of spin networks over the subgroup of the diffeomorphisms remaining after the gauge fixing used in homogeneous LQC. It is based on the set of clearly defined principles and thus is a convenient tool to control the emergence and behavior of the cosmological degrees of freedom in studies of dynamics in canonical LQG. The constructed interface is further adapted to isotropic spacetimes. Relating the proposed LQG-LQC interface with some results on black hole entropy suggests a modification to the area gap value currently used in LQC.
Cosmological footprints of loop quantum gravity.
Grain, J; Barrau, A
2009-02-27
The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum effects in the early universe. We show that the associated corrections should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of quantum gravity.
Loop quantum cosmology: confronting the hybrid quantization approach with observations
NASA Astrophysics Data System (ADS)
Olmedo, Javier; Martin de Blas, Daniel
2017-01-01
In loop quantum cosmology there are several approaches for the confrontation of the theory with observations. Here, we focus on the hybrid quantization approach. We provide an exhaustive analysis including scalar and tensor perturbations on effective (quantum-mechanically corrected) homogeneous and isotropic cosmologies coupled to a massive scalar field. We compute the primordial power spectrum of the perturbations at the end of inflation for a set of initial vacuum states defined at the deep quantum regime of the cosmological model. We then analyze the tensor-to-scalar ratio and the consistency relation between this quantity and the spectral index of the tensor power spectrum. Eventually, we compute the temperature-temperature, electric-electric, temperature-electric and magnetic-magnetic correlation functions predicted by this approach and compare them with present observations.
Fundamental Structure of Loop Quantum Gravity
NASA Astrophysics Data System (ADS)
Han, Muxin; Ma, Yongge; Huang, Weiming
In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar-Isham-Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to
Onset of inflation in loop quantum cosmology
Germani, Cristiano; Nelson, William; Sakellariadou, Mairi
2007-08-15
Using a Liouville measure, similar to the one proposed recently by Gibbons and Turok, we investigate the probability that single-field inflation with a polynomial potential can last long enough to solve the shortcomings of the standard hot big bang model, within the semiclassical regime of loop quantum cosmology. We conclude that, for such a class of inflationary models and for natural values of the loop quantum cosmology parameters, a successful inflationary scenario is highly improbable.
Recent Advances in Loop Quantum Cosmology
NASA Astrophysics Data System (ADS)
Singh, Parampreet
2007-04-01
Einstein's theory of classical general relativity explains the dynamics of our universe at low energies to an excellent precision. However, it breaks down at the Planck scale before the big bang singularity is reached. Relativity thus fails to tell us about the origin of our cosmos and leaves open various questions which are expected to be answered by a quantum theory of gravity. We will review recent developments in loop quantum cosmology which is a quantization of cosmological spacetimes based on loop quantum gravity -- a non-perturbative background independent quantization of gravity. Because, of fundamental discreteness of quantum geometry underlying loop quantum gravity, novel features arise. In particular, for quantum states representing a large classical universe at late times there is an upper bound on the gravitational curvature, of the order of 1/(Planck length)^2. Thus, non-perturbative quantum gravity effects forbid the cosmological dynamics from entering a regime where curvature or energy density blow up. Evolution in loop quantum cosmology is non-singular. In models studied so far, the backward evolution of our expanding universe does not lead to a big bang but a big bounce to a contracting branch when the gravitational curvature reaches Planck scale. These results which have now been established for various homogeneous spacetimes provide a new paradigm of the genesis of our universe and lead to useful insights on the generic resolution of space-like singularities through quantum gravity effects.
Numerical simulations of loop quantum Bianchi-I spacetimes
NASA Astrophysics Data System (ADS)
Diener, Peter; Joe, Anton; Megevand, Miguel; Singh, Parampreet
2017-05-01
Due to the numerical complexities of studying evolution in an anisotropic quantum spacetime, in comparison to the isotropic models, the physics of loop quantized anisotropic models has remained largely unexplored. In particular, robustness of bounce and the validity of effective dynamics have so far not been established. Our analysis fills these gaps for the case of vacuum Bianchi-I spacetime. To efficiently solve the quantum Hamiltonian constraint we perform an implementation of the Cactus framework which is conventionally used for applications in numerical relativity. Using high performance computing, numerical simulations for a large number of initial states with a wide variety of fluctuations are performed. Big bang singularity is found to be replaced by anisotropic bounces for all the cases. We find that for initial states which are sharply peaked at the late times in the classical regime and bounce at a mean volume much greater than the Planck volume, effective dynamics is an excellent approximation to the underlying quantum dynamics. Departures of the effective dynamics from the quantum evolution appear for the states probing deep Planck volumes. A detailed analysis of the behavior of this departure reveals a non-monotonic and subtle dependence on fluctuations of the initial states. We find that effective dynamics in almost all of the cases underestimates the volume and hence overestimates the curvature at the bounce, a result in synergy with earlier findings in the isotropic case. The expansion and shear scalars are found to be bounded throughout the evolution.
Particle scattering in loop quantum gravity.
Modesto, Leonardo; Rovelli, Carlo
2005-11-04
We devise a technique for defining and computing -point functions in the context of a background-independent gravitational quantum field theory. We construct a tentative implementation of this technique in a perturbatively finite model defined using spin foam techniques in the context of loop quantum gravity.
Loop Quantum Cosmology and the CMB
NASA Astrophysics Data System (ADS)
Agullo, Ivan
2017-01-01
This talk will provide an up-to-date summary of phenomenological explorations in loop quantum cosmology. The possibility of a quantum gravity origin of the anomalies observed in the cosmic microwave background at large angular scales will be discussed. The talk will also provide some background material for subsequent contributions in the same session. NSF PHYS-1403943.
State refinements and coarse graining in a full theory embedding of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Bodendorfer, N.
2017-07-01
Bridging between descriptions involving few large and many small quantum numbers is the main open problem in loop quantum gravity. In other words, one would like to be able to represent the same physical system in terms of a few ‘coarse’ quantum numbers, while the effective dynamics at the coarse level should agree with the one induced by a description involving many small quantum numbers. Efforts to understand this relationship face the problem of the enormous computational complexity involved in evolving a generic state containing many quanta. In a cosmological context however, certain symmetry assumptions on the quantum states allow one to simplify the problem. In this paper, we will show how quantum states describing a spatially flat homogeneous and isotropic universe can be refined and coarse grained. Invariance of the dynamics of the coarse observables is shown to require a certain scaling property (familiar from loop quantum cosmology) of the quantum states if no running of parameters is taken into account. The involved states are solutions to the Hamiltonian constraint when terms coming from spatial derivatives are neglected, i.e. one works in the approximation of non-interacting FRW patches. The technical means to arrive at this result are a version of loop quantum gravity based on variables inspired by loop quantum cosmology, as well as an exact solution to the quantum dynamics of loop quantum cosmology which extends to the full theory in the chosen approximation.
Universe’s memory and spontaneous coherence in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Pawłowski, Tomasz
2016-07-01
The quantum bounce a priori connects several (semi)classical epochs of universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that regards in the isotropic sector of loop quantum cosmology (LQC). This knowledge is next extended by studies of an isotropic universe admitting positive cosmological constant (featuring an infinite chain of large universe epochs). It is also shown, that such universe always admits a semiclassical epoch thanks to spontaneous coherence, provided it is semiclassical in certain constant of motion playing the role of energy.
Chimera: a hybrid approach to numerical loop quantum cosmology
NASA Astrophysics Data System (ADS)
Diener, Peter; Gupt, Brajesh; Singh, Parampreet
2014-01-01
The existence of a quantum bounce in isotropic spacetimes is a key result in loop quantum cosmology (LQC), which has been demonstrated to arise in all the models studied so far. In most of the models, the bounce has been studied using numerical simulations involving states which are sharply peaked and which bounce at volumes much larger than the Planck volume. An important issue is to confirm the existence of the bounce for states which have a wide spread, or which bounce closer to the Planck volume. Numerical simulations with such states demand large computational domains, making them very expensive and practically infeasible with the techniques which have been implemented so far. To overcome these difficulties, we present an efficient hybrid numerical scheme using the property that at the small spacetime curvature, the quantum Hamiltonian constraint in LQC, which is a difference equation with uniform discretization in volume, can be approximated by a Wheeler-DeWitt differential equation. By carefully choosing a hybrid spatial grid allowing the use of partial differential equations at large volumes, and with a simple change of geometrical coordinate, we obtain a surprising reduction in the computational cost. This scheme enables us to explore regimes which were so far unachievable for the isotropic model in LQC. Our approach also promises to significantly reduce the computational cost for numerical simulations in anisotropic LQC using high performance computing.
Observation of quantum decay of homogeneous, isotropic (grid) turbulence
NASA Astrophysics Data System (ADS)
Ihas, Gary; Munday, Lydia; Yang, Jihee; Thompson, Kyle; Guo, Wei; Chapurin, Roman; Fisher, Shaun; McClintock, Peter; Vinen, W. F.
2014-03-01
In classical grid turbulence fluid is forced through a stationary grid. In the quantum case a grid moves through an initially stationary superfluid driven by a linear motor. We have developed a motor using superconducting drive coils and bearings, moving a grid at constant speed (0 and 15 cm/s). Stalp et al[2] report the decay of vortex-line density L in the grid's wake measured by 2nd sound attenuation. L decayed at large times as t - 3 / 2, interpreted as a quasi-classical Richardson cascade of energy-containing eddies size limited by channel width, associated with a Kolmogorov energy spectrum. It is assumed eddies produced on a scale of the grid mesh grow through the classical fluids mechanism.[3] We can now test a semi-quantitative theory with different mesh grids or channel sizes, relating to the possible existence of inverse turbulent cascades. Our 2nd sound system is conventional, but with a novel phase and amplitude feedback loop making stringent constant temperature unnecessary. Both t - 3 / 2 and non-t - 3 / 2 decays have been observed with 2 mesh sizes. US NSF DMR#0602778 and #1007937 and EPSRC EP/H04762X/1.
Squeezed vacua in loop quantum gravity
NASA Astrophysics Data System (ADS)
Hackl, Lucas; Bianchi, Eugenio; Guglielmon, Jonathan; Yokomizo, Nelson
2017-01-01
Semi-classical states in quantum gravity are expected to exhibit long range correlations. In order to describe such states within the framework of loop quantum gravity, it is important to parametrize states in terms of their correlations. In this talk, I will introduce a new class of states with prescribed correlations, called squeezed vacua. They can be naturally understood in the bosonic Hilbert space representation where they are generated in two steps. First, we squeeze the Ashtekar-Lewandowski vacuum via the action of a quadratic exponential and second, we project the resulting states onto the kinematical Hilbert space of Loop quantum gravity. I will give explicit examples on how to construct states that are peaked on some classical geometry, but whose quantum fluctuations exhibit long range correlations.
Loop-quantum-gravity vertex amplitude.
Engle, Jonathan; Pereira, Roberto; Rovelli, Carlo
2007-10-19
Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one and it yields an SO(4)-covariant vertex amplitude for Euclidean loop gravity.
Radiation from quantum weakly dynamical horizons in loop quantum gravity.
Pranzetti, Daniele
2012-07-06
We provide a statistical mechanical analysis of quantum horizons near equilibrium in the grand canonical ensemble. By matching the description of the nonequilibrium phase in terms of weakly dynamical horizons with a local statistical framework, we implement loop quantum gravity dynamics near the boundary. The resulting radiation process provides a quantum gravity description of the horizon evaporation. For large black holes, the spectrum we derive presents a discrete structure which could be potentially observable.
The JWKB approximation in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David; Singh, Parampreet
2017-01-01
We explore the JWKB approximation in loop quantum cosmology in a flat universe with a scalar matter source. Exact solutions of the quantum constraint are studied at small volume in the JWKB approximation in order to assess the probability of tunneling to small or zero volume. Novel features of the approximation are discussed which appear due to the fact that the model is effectively a two-dimensional dynamical system. Based on collaborative work with Parampreet Singh.
Loop quantum cosmology and the fate of cosmological singularities
NASA Astrophysics Data System (ADS)
Singh, Parampreet
2014-09-01
Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and the breakdown of the geodesic evolution. Recent progress on implementing techniques of loop quantum gravity to cosmological models reveals that such singularities may be generically resolved because of the quantum gravitational effects. Due to the quantum geometry, which replaces the classical differential geometry at the Planck scale, the big bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. In this manuscript, we discuss some of the main features of this approach and the results on the generic resolution of singularities for the isotropic as well as anisotropic models. Using effective spacetime description of the quantum theory, we show the way quantum gravitational effects lead to the universal bounds on the energy density, the Hubble rate and the anisotropic shear. We discuss the geodesic completeness in the effective spacetime and the resolution of all of the strong singularities. It turns out that despite the bounds on energy density and the Hubble rate, there can be divergences in the curvature invariants. However such events are geodesically extendible, with tidal forces not strong enough to cause inevitable destruction of the in-falling objects.
Quantum hyperbolic geometry in loop quantum gravity with cosmological constant
NASA Astrophysics Data System (ADS)
Dupuis, Maïté; Girelli, Florian
2013-06-01
Loop quantum gravity (LQG) is an attempt to describe the quantum gravity regime. Introducing a nonzero cosmological constant Λ in this context has been a standing problem. Other approaches, such as Chern-Simons gravity, suggest that quantum groups can be used to introduce Λ into the game. Not much is known when defining LQG with a quantum group. Tensor operators can be used to construct observables in any type of discrete quantum gauge theory with a classical/quantum gauge group. We illustrate this by constructing explicitly geometric observables for LQG defined with a quantum group and show for the first time that they encode a quantized hyperbolic geometry. This is a novel argument pointing out the usefulness of quantum groups as encoding a nonzero cosmological constant. We conclude by discussing how tensor operators provide the right formalism to unlock the LQG formulation with a nonzero cosmological constant.
Lorentz invariance in loop quantum gravity
NASA Astrophysics Data System (ADS)
Pullin, Jorge; Rastgoo, Saeed; Gambini, Rodolfo
2011-04-01
We reconsider the argument of Collins, Perez, Sudarsky, Urrutia and Vucetich concerning violations of Lorentz invariance in the context of loop quantum gravity. We show that even if one introduces a lattice that violates Lorentz invariance at the Planck scale, this does not translate itself into large violations that would conflict with experiment.
Warm inflationary model in loop quantum cosmology
Herrera, Ramon
2010-06-15
A warm inflationary universe model in loop quantum cosmology is studied. In general we discuss the condition of inflation in this framework. By using a chaotic potential, V({phi}){proportional_to}{phi}{sup 2}, we develop a model where the dissipation coefficient {Gamma}={Gamma}{sub 0}=constant. We use recent astronomical observations for constraining the parameters appearing in our model.
Hybrid models in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.
2016-06-01
In the framework of Loop Quantum Cosmology (LQC), inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid LQC.
Covariant entropy bound and loop quantum cosmology
Ashtekar, Abhay; Wilson-Ewing, Edward
2008-09-15
We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry, which can supply the structure needed to test the bound. We find that the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances.
A new vacuum for loop quantum gravity
NASA Astrophysics Data System (ADS)
Dittrich, Bianca; Geiller, Marc
2015-06-01
We construct a new vacuum and representation for loop quantum gravity. Because the new vacuum is based on BF theory, it is physical for (2+1)-dimensional gravity, and much closer to the spirit of spin foam quantization in general. To construct this new vacuum and the associated representation of quantum observables, we introduce a modified holonomy-flux algebra that is cylindrically consistent with respect to the notion of refinement by time evolution suggested in Dittrich and Steinhaus (2013 arXiv:1311.7565). This supports the proposal for a construction of the physical vacuum made in Dittrich and Steinhaus (2013 arXiv:1311.7565) and Dittrich (2012 New J. Phys. 14 123004), and for (3+1)-dimensional gravity. We expect that the vacuum introduced here will facilitate the extraction of large scale physics and cosmological predictions from loop quantum gravity.
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong; Ma, Yongge
2011-09-01
As modified gravity theories, the four-dimensional metric f(R) theories are cast into connection-dynamical formalism with real su(2) connections as configuration variables. This formalism enables us to extend the nonperturbative loop quantization scheme of general relativity to any metric f(R) theories. The quantum kinematical framework of f(R) gravity is rigorously constructed, where the quantum dynamics can be launched. Both Hamiltonian constraint operator and master constraint operator for f(R) theories are well defined. Our results show that the nonperturbative quantization procedure of loop quantum gravity are valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.
Relating loop quantum cosmology to loop quantum gravity: symmetric sectors and embeddings
NASA Astrophysics Data System (ADS)
Engle, J.
2007-12-01
In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald and Kastrup, of LQC states into loop quantum gravity. Then, using certain holomorphic representations, a new class of embeddings, called b-embeddings, are constructed, following the ideas of Engle (2006 Quantum field theory and its symmetry reduction Class. Quantum Gravity 23 2861 94). We exhibit a class of operators preserving each of these embeddings, and show their consistency with the LQC quantization. In the b-embedding case, the classical analogues of these operators separate points in phase space. Embedding at the gauge and diffeomorphism invariant level is discussed briefly in the conclusions.
Vertex amplitudes in spin foam loop quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David
2016-03-01
We discuss properties of the vertex expansion for homogeneous, isotropic loop quantum cosmological models sourced by a massless, minimally coupled scalar field, which in this model plays the role of an internal matter ``clock''. We show that the vertex expansion, first written down by Ashtekar, Campiglia and Henderson, must be thought of as a short-time expansion in the sense that the amplitude for volume transitions is constrained both by the order of the expansion and by the elapsed scalar field. To calculate the amplitude for significant volume changes or between large differences in the value of the scalar field requires the expansion be evaluated to very high order. This contribution describes work in collaboration with P. Singh.
Quantum Loop Topography for Machine Learning.
Zhang, Yi; Kim, Eun-Ah
2017-05-26
Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems, training neural networks to identify quantum phases is a nontrivial challenge. The key challenge is in efficiently extracting essential information from the many-body Hamiltonian or wave function and turning the information into an image that can be fed into a neural network. When targeting topological phases, this task becomes particularly challenging as topological phases are defined in terms of nonlocal properties. Here, we introduce quantum loop topography (QLT): a procedure of constructing a multidimensional image from the "sample" Hamiltonian or wave function by evaluating two-point operators that form loops at independent Monte Carlo steps. The loop configuration is guided by the characteristic response for defining the phase, which is Hall conductivity for the cases at hand. Feeding QLT to a fully connected neural network with a single hidden layer, we demonstrate that the architecture can be effectively trained to distinguish the Chern insulator and the fractional Chern insulator from trivial insulators with high fidelity. In addition to establishing the first case of obtaining a phase diagram with a topological quantum phase transition with machine learning, the perspective of bridging traditional condensed matter theory with machine learning will be broadly valuable.
Quantum Loop Topography for Machine Learning
NASA Astrophysics Data System (ADS)
Zhang, Yi; Kim, Eun-Ah
2017-05-01
Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems, training neural networks to identify quantum phases is a nontrivial challenge. The key challenge is in efficiently extracting essential information from the many-body Hamiltonian or wave function and turning the information into an image that can be fed into a neural network. When targeting topological phases, this task becomes particularly challenging as topological phases are defined in terms of nonlocal properties. Here, we introduce quantum loop topography (QLT): a procedure of constructing a multidimensional image from the "sample" Hamiltonian or wave function by evaluating two-point operators that form loops at independent Monte Carlo steps. The loop configuration is guided by the characteristic response for defining the phase, which is Hall conductivity for the cases at hand. Feeding QLT to a fully connected neural network with a single hidden layer, we demonstrate that the architecture can be effectively trained to distinguish the Chern insulator and the fractional Chern insulator from trivial insulators with high fidelity. In addition to establishing the first case of obtaining a phase diagram with a topological quantum phase transition with machine learning, the perspective of bridging traditional condensed matter theory with machine learning will be broadly valuable.
Wald entropy formula and loop quantum gravity
NASA Astrophysics Data System (ADS)
Bodendorfer, N.; Neiman, Y.
2014-10-01
We outline how the Wald entropy formula naturally arises in loop quantum gravity based on recently introduced dimension-independent connection variables. The key observation is that in a loop quantization of a generalized gravity theory, the analog of the area operator turns out to measure, morally speaking, the Wald entropy rather than the area. We discuss the explicit example of (higher-dimensional) Lanczos-Lovelock gravity and comment on recent work on finding the correct numerical prefactor of the entropy by comparing it to a semiclassical effective action.
Generalized effective description of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Gupt, Brajesh
2015-10-01
The effective description of loop quantum cosmology (LQC) has proved to be a convenient platform to study phenomenological implications of the quantum bounce that resolves the classical big bang singularity. Originally, this description was derived using Gaussian quantum states with small dispersions. In this paper we present a generalization to incorporate states with large dispersions. Specifically, we derive the generalized effective Friedmann and Raychaudhuri equations and propose a generalized effective Hamiltonian which are being used in an ongoing study of the phenomenological consequences of a broad class of quantum geometries. We also discuss an interesting interplay between the physics of states with larger dispersions in standard LQC, and of sharply peaked states in (hypothetical) LQC theories with larger area gap.
Loop quantum cosmology: a status report
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Singh, Parampreet
2011-11-01
Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction. In cosmological models, while Einstein's equations hold to an excellent degree of approximation at low curvature, they undergo major modifications in the Planck regime: for matter satisfying the usual energy conditions, any time a curvature invariant grows to the Planck scale, quantum geometry effects dilute it, thereby resolving singularities of general relativity. Quantum geometry corrections become more sophisticated as the models become richer. In particular, in anisotropic models, there are significant changes in the dynamics of shear potentials which tame their singular behavior in striking contrast to older results on anisotropies in bouncing models. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues—e.g. the 'horizon problem'—from a new perspective. Such conceptual issues as well as potential observational consequences of the new Planck scale physics are being explored, especially within the inflationary paradigm. These considerations have given rise to a burst of activity in LQC in recent years, with contributions from quantum gravity experts, mathematical physicists and cosmologists. The goal of this review is to provide an overview of the current state of the art in LQC for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general and cosmologists who wish to apply LQC to probe modifications in the standard paradigm of the early universe. In this review, effort has been made to
Black holes in loop quantum gravity.
Perez, Alejandro
2017-07-11
This is a review of the results on black hole physics in the framework of loop quantum gravity. The key feature underlying the results is the discreteness of geometric quantities at the Planck scale predicted by this approach to quantum gravity. Quantum discreteness follows directly from the canonical quantization prescription when applied to the action of general relativity that is suitable for the coupling of gravity with gauge fields and specially with fermions. Planckian discreteness and causal considerations provide the basic structure for the understanding of the thermal properties of black holes close to equilibrium. Discreteness also provides a fresh new look at more (at the moment) speculative issues such as those concerning the fate of information in black hole evaporation. The hypothesis of discreteness leads also to interesting phenomenology with possible observational consequences. The theory of loop quantum gravity is a developing program. This review reports its achievements and open questions in a pedagogical manner with an emphasis on quantum aspects of black hole physics. . © 2017 IOP Publishing Ltd.
Regularization ambiguities in loop quantum gravity
NASA Astrophysics Data System (ADS)
Perez, Alejandro
2006-02-01
One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultraviolet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem—the existence of well-behaved regularization of the constraints—is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities is the one associated to the SU(2) unitary representation used in the diffeomorphism covariant “point-splitting” regularization of the nonlinear functionals of the connection. This ambiguity is labeled by a half-integer m and, here, it is referred to as the m ambiguity. The aim of this paper is to investigate the important implications of this ambiguity. We first study 2+1 gravity (and more generally BF theory) quantized in the canonical formulation of loop quantum gravity. Only when the regularization of the quantum constraints is performed in terms of the fundamental representation of the gauge group does one obtain the usual topological quantum field theory as a result. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear-cut choice in the quantization of the constraints in 2+1 loop quantum gravity. We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher representation quantizations of the Hamiltonian constraint. Although the analysis is not complete in 3+1 dimensions—due to the difficulties associated to the definition of the physical inner product—it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we
Observational constraints on loop quantum cosmology.
Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji
2011-11-18
In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.
Regularization ambiguities in loop quantum gravity
Perez, Alejandro
2006-02-15
One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultraviolet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem--the existence of well-behaved regularization of the constraints--is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities is the one associated to the SU(2) unitary representation used in the diffeomorphism covariant 'point-splitting' regularization of the nonlinear functionals of the connection. This ambiguity is labeled by a half-integer m and, here, it is referred to as the m ambiguity. The aim of this paper is to investigate the important implications of this ambiguity. We first study 2+1 gravity (and more generally BF theory) quantized in the canonical formulation of loop quantum gravity. Only when the regularization of the quantum constraints is performed in terms of the fundamental representation of the gauge group does one obtain the usual topological quantum field theory as a result. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear-cut choice in the quantization of the constraints in 2+1 loop quantum gravity. We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher representation quantizations of the Hamiltonian constraint. Although the analysis is not complete in 3+1 dimensions - due to the difficulties associated to the definition of the physical inner product - it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find
Scholes, Gregory D
2004-11-22
Three-dimensional rotational averages are evaluated for third-order nonlinear spectroscopic measurements of quantum dots. Photon echo, transient grating, and transient absorption are explicitly considered. It is shown that (a) biexciton formation can be suppressed relative to other contributions to nonlinear spectroscopies for isotropic nanocrystal ensembles by choice of polarizations for the excitation pulses; (b) circularly polarized excitation light can differentiate between exciton spin states in nonlinear optical experiments; and (c) electron spin state flip kinetics can be probed directly in an isotropic quantum dot system by using certain sequences of linear cross-polarized pulses. Copyright 2004 American Institute of Physics.
Behavior of nonlinear anisotropies in bouncing Bianchi I models of loop quantum cosmology
Chiou, D.-W.; Vandersloot, Kevin
2007-10-15
In homogeneous and isotropic loop quantum cosmology, gravity can behave repulsively at Planckian energy densities leading to the replacement of the big bang singularity with a big bounce. Yet in any bouncing scenario it is important to include nonlinear effects from anisotropies which typically grow during the collapsing phase. We investigate the dynamics of a Bianchi I anisotropic model within the framework of loop quantum cosmology. Using effective semiclassical equations of motion to study the dynamics, we show that the big bounce is still predicted with only differences in detail arising from the inclusion of anisotropies. We show that the anisotropic shear term grows during the collapsing phase, but remains finite through the bounce. Immediately following the bounce, the anisotropies decay and with the inclusion of matter with equation of state w<+1, the universe isotropizes in the expanding phase.
Phantom field dynamics in loop quantum cosmology
Samart, Daris; Gumjudpai, Burin
2007-08-15
We consider a dynamical system of phantom scalar field under exponential potential in the background of loop quantum cosmology. In our analysis, there is neither stable node nor repeller unstable node but only two saddle points, hence no big rip singularity. Physical solutions always possess potential energy greater than the magnitude of the negative kinetic energy. We found that the universe bounces after accelerating even in the domination of the phantom field. After bouncing, the universe finally enters the oscillatory regime.
Discrete symmetries in covariant loop quantum gravity
NASA Astrophysics Data System (ADS)
Rovelli, Carlo; Wilson-Ewing, Edward
2012-09-01
We study time-reversal and parity—on the physical manifold and in internal space—in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform coherently under such transformations. The classical theory is not affected but the quantum theory is slightly different. In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spin foam to occur only across degenerate regions, thus reducing the sources of potential divergences.
BOOK REVIEW: A First Course in Loop Quantum Gravity A First Course in Loop Quantum Gravity
NASA Astrophysics Data System (ADS)
Dittrich, Bianca
2012-12-01
Students who are interested in quantum gravity usually face the difficulty of working through a large amount of prerequisite material before being able to deal with actual quantum gravity. A First Course in Loop Quantum Gravity by Rodolfo Gambini and Jorge Pullin, aimed at undergraduate students, marvellously succeeds in starting from the basics of special relativity and covering basic topics in Hamiltonian dynamics, Yang Mills theory, general relativity and quantum field theory, ending with a tour on current (loop) quantum gravity research. This is all done in a short 173 pages! As such the authors cannot cover any of the subjects in depth and indeed this book should be seen more as a motivation and orientation guide so that students can go on to follow the hints for further reading. Also, as there are many subjects to cover beforehand, slightly more than half of the book is concerned with more general subjects (special and general relativity, Hamiltonian dynamics, constrained systems, quantization) before the starting point for loop quantum gravity, the Ashtekar variables, are introduced. The approach taken by the authors is heuristic and uses simplifying examples in many places. However they take care in motivating all the main steps and succeed in presenting the material pedagogically. Problem sets are provided throughout and references for further reading are given. Despite the shortness of space, alternative viewpoints are mentioned and the reader is also referred to experimental results and bounds. In the second half of the book the reader gets a ride through loop quantum gravity; the material covers geometric operators and their spectra, the Hamiltonian constraints, loop quantum cosmology and, more broadly, black hole thermodynamics. A glimpse of recent developments and open problems is given, for instance a discussion on experimental predictions, where the authors carefully point out the very preliminary nature of the results. The authors close with an
Embedding loop quantum cosmology without piecewise linearity
NASA Astrophysics Data System (ADS)
Engle, Jonathan
2013-04-01
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. This paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such holonomies, and all elements in its image satisfy an operator equation which classically implies homogeneity and isotropy. The construction is made possible by a recent result proven by Fleischhack. Communicated by P Singh
Asymptotics of loop quantum gravity fusion coefficients
NASA Astrophysics Data System (ADS)
Alesci, Emanuele; Bianchi, Eugenio; Magliaro, Elena; Perini, Claudio
2010-05-01
The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in loop quantum gravity. In this paper we give a simple analytic formula of the Engle-Pereira-Rovelli-Livine fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into SU(2)L × SU(2)R semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.
Effective loop quantum geometry of Schwarzschild interior
NASA Astrophysics Data System (ADS)
Cortez, Jerónimo; Cuervo, William; Morales-Técotl, Hugo A.; Ruelas, Juan C.
2017-03-01
The success of loop quantum cosmology to resolve classical singularities of homogeneous models has led to its application to the classical Schwarszchild black hole interior, which takes the form of a homogeneous Kantowski-Sachs model. The first steps of this were done in pure quantum mechanical terms, hinting at the traversable character of the would-be classical singularity, and then others were performed using effective heuristic models capturing quantum effects that allowed a geometrical description closer to the classical one but avoided its singularity. However, the problem of establishing the link between the quantum and effective descriptions was left open. In this work, we propose to fill in this gap by considering the path-integral approach to the loop quantization of the Kantowski-Sachs model corresponding to the Schwarzschild black hole interior. We show that the transition amplitude can be expressed as a path integration over the imaginary exponential of an effective action which just coincides, under some simplifying assumptions, with the heuristic one. Additionally, we further explore the consequences of the effective dynamics. We prove first that such dynamics imply some rather simple bounds for phase-space variables, and in turn—remarkably, in an analytical way—they imply that various phase-space functions that were singular in the classical model are now well behaved. In particular, the expansion rate, its time derivative, and the shear become bounded, and hence the Raychaudhuri equation is finite term by term, thus resolving the singularities of classical geodesic congruences. Moreover, all effective scalar polynomial invariants turn out to be bounded.
Emergence of space-like correlations in loop quantum gravity
NASA Astrophysics Data System (ADS)
Bianchi, Eugenio
2017-01-01
Vacuum states of a quantum field in a curved space-time have non-trivial correlations at space-like separation. The stretching and squeezing of such correlations plays a crucial role in inflationary cosmology. In this talk I discuss a pre-inflationary scenario where space-like correlations of quantum perturbations arise from an initially unentangled state in loop quantum gravity. This scenario relies on recent results on squeezed vacua and entanglement in loop quantum gravity.
Novel Numerical Approaches to Loop Quantum Cosmology
NASA Astrophysics Data System (ADS)
Diener, Peter
2015-04-01
Loop Quantum Gravity (LQG) is an (as yet incomplete) approach to the quantization of gravity. When applied to symmetry reduced cosmological spacetimes (Loop Quantum Cosmology or LQC) one of the predictions of the theory is that the Big Bang is replaced by a Big Bounce, i.e. a previously existing contracting universe underwent a bounce at finite volume before becoming our expanding universe. The evolution equations of LQC take the form of difference equations (with the discretization given by the theory) that in the large volume limit can be approximated by partial differential equations (PDEs). In this talk I will first discuss some of the unique challenges encountered when trying to numerically solve these difference equations. I will then present some of the novel approaches that have been employed to overcome the challenges. I will here focus primarily on the Chimera scheme that takes advantage of the fact that the LQC difference equations can be approximated by PDEs in the large volume limit. I will finally also briefly discuss some of the results that have been obtained using these numerical techniques by performing simulations in regions of parameter space that were previously unreachable. This work is supported by a grant from the John Templeton Foundation and by NSF grant PHYS1068743.
Lorentz covariance of loop quantum gravity
NASA Astrophysics Data System (ADS)
Rovelli, Carlo; Speziale, Simone
2011-05-01
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the projected spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are precisely in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.
Invariant Connections in Loop Quantum Gravity
NASA Astrophysics Data System (ADS)
Hanusch, Maximilian
2016-04-01
Given a group {G}, and an abelian {C^*}-algebra {A}, the antihomomorphisms {Θ\\colon G→ {Aut}(A)} are in one-to-one with those left actions {Φ\\colon G× {Spec}(A)→ {Spec}(A)} whose translation maps {Φ_g} are continuous; whereby continuities of {Θ} and {Φ} turn out to be equivalent if {A} is unital. In particular, a left action {φ\\colon G × X→ X} can be uniquely extended to the spectrum of a {C^*}-subalgebra {A} of the bounded functions on {X} if {φ_g^*(A)subseteq A} holds for each {gin G}. In the present paper, we apply this to the framework of loop quantum gravity. We show that, on the level of the configuration spaces, quantization and reduction in general do not commute, i.e., that the symmetry-reduced quantum configuration space is (strictly) larger than the quantized configuration space of the reduced classical theory. Here, the quantum-reduced space has the advantage to be completely characterized by a simple algebraic relation, whereby the quantized reduced classical space is usually hard to compute.
Coherent semiclassical states for loop quantum cosmology
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Montoya, Edison
2011-08-01
The spatially flat Friedmann-Robertson-Walker cosmological model with a massless scalar field in loop quantum cosmology admits a description in terms of a completely solvable model. This has been used to prove that: (i) the quantum bounce that replaces the big bang singularity is generic; (ii) there is an upper bound on the energy density for all states, and (iii) semiclassical states at late times had to be semiclassical before the bounce. Here we consider a family of exact solutions to the theory, corresponding to generalized coherent Gaussian and squeezed states. We analyze the behavior of basic physical observables and impose restrictions on the states based on physical considerations. These turn out to be enough to select, from all the generalized coherent states, those that behave semiclassical at late times. We study then the properties of such states near the bounce where the most “quantum behavior” is expected. As it turns out, the states remain sharply peaked and semiclassical at the bounce and the dynamics is very well approximated by the “effective theory” throughout the time evolution. We compare the semiclassicality properties of squeezed states to those of the Gaussian semiclassical states and conclude that the Gaussians are better behaved. In particular, the asymmetry in the relative fluctuations before and after the bounce are negligible, thus ruling out claims of so-called “cosmic forgetfulness.”
Quantum surface and intertwiner dynamics in loop quantum gravity
NASA Astrophysics Data System (ADS)
Feller, Alexandre; Livine, Etera R.
2017-06-01
We introduce simple generic models of surface dynamics in loop quantum gravity (LQG). A quantum surface is defined as a set of elementary patches of area glued together. We provide it with an extra structure of locality (nearest neighbors), thought of as induced by the whole spin network state defining the 3d bulk geometry around the quantum surface. Here, we focus on classical surface dynamics, using a spinorial description of surface degrees of freedom. We introduce two classes of dynamics, to be thought as templates for future investigation of LQG dynamics with the dynamics of quantum black holes in mind. The first defines global dynamics of the closure defect of the surface, with two basic toy models, either a dissipative dynamics relaxing towards the closure constraint or a Hamiltonian dynamics precessing the closure defect. The second class of dynamics describes the isolated regime, when both area and closure defect are conserved throughout the evolution. The surface dynamics is implemented through U (N ) transformations and generalizes to a Bose-Hubbard Hamiltonian with a local quadratic potential interaction. We briefly discuss the implications of modeling the quantum black hole dynamics by a surface Bose-Hubbard model.
On the physical Hilbert space of loop quantum cosmology
Noui, Karim; Perez, Alejandro; Vandersloot, Kevin
2005-02-15
In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable, consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.
Quantum reduced loop gravity: Extension to gauge vector field
NASA Astrophysics Data System (ADS)
Bilski, Jakub; Alesci, Emanuele; Cianfrani, Francesco; Donà, Pietro; Marcianò, Antonino
2017-05-01
Within the framework of quantum reduced loop gravity, we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full loop quantum gravity, while the matrix elements of the resulting operator between basis states are analytic coefficients. This analysis is the first step toward deriving the full quantum gravity corrections to the vector field semiclassical dynamics.
Holographic bound in covariant loop quantum gravity
NASA Astrophysics Data System (ADS)
Tamaki, Takashi
2016-07-01
We investigate puncture statistics based on the covariant area spectrum in loop quantum gravity. First, we consider Maxwell-Boltzmann statistics with a Gibbs factor for punctures. We establish formulas which relate physical quantities such as horizon area to the parameter characterizing holographic degrees of freedom. We also perform numerical calculations and obtain consistency with these formulas. These results tell us that the holographic bound is satisfied in the large area limit and the correction term of the entropy-area law can be proportional to the logarithm of the horizon area. Second, we also consider Bose-Einstein statistics and show that the above formulas are also useful in this case. By applying the formulas, we can understand intrinsic features of Bose-Einstein condensate which corresponds to the case when the horizon area almost consists of punctures in the ground state. When this phenomena occurs, the area is approximately constant against the parameter characterizing the temperature. When this phenomena is broken, the area shows rapid increase which suggests the phase transition from quantum to classical area.
Cosmological perturbations in teleparallel Loop Quantum Cosmology
NASA Astrophysics Data System (ADS)
Haro, Jaime
2013-11-01
Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator. In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce provided by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation. In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.
Phenomenology with fluctuating quantum geometries in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Agullo, Ivan; Ashtekar, Abhay; Gupt, Brajesh
2017-04-01
The goal of this paper is to probe phenomenological implications of large fluctuations of quantum geometry in the Planck era, using cosmology of the early universe. For the background (Friedmann, Lemaître, Robertson, Walker) quantum geometry, we allow ‘widely spread’ states in which the relative dispersions are as large as 168 % in the Planck regime. By introducing suitable methods to overcome the ensuing conceptual and computational issues, we calculate the power spectrum {{P}R}(k) and the spectral index n s (k) of primordial curvature perturbations. These results generalize the previous work in loop quantum cosmology which focused on those states which were known to remain sharply peaked throughout the Planck regime. Surprisingly, even though the fluctuations we now consider are large, their presence does not add new features to the final {{P}R}(k) and n s (k): within observational error bars, their effect is degenerate with a different freedom in the theory, namely the number of pre-inflationary e-folds {{N}\\text{B\\star}} between the bounce and the onset of inflation. Therefore, with regard to observational consequences, one can simulate the freedom in the choice of states with large fluctuations in the Planck era using the simpler, sharply peaked states, simply by allowing for different values of {{N}\\text{B \\star}} .
Absence of a singularity in loop quantum cosmology.
Bojowald, M
2001-06-04
It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstration comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.
Loop quantum cosmology with complex Ashtekar variables
NASA Astrophysics Data System (ADS)
Ben Achour, Jibril; Grain, Julien; Noui, Karim
2015-01-01
We construct and study loop quantum cosmology (LQC) when the Barbero-Immirzi parameter takes the complex value γ =+/- i. We refer to this new approach to quantum cosmology as complex LQC. This formulation is obtained via an analytic continuation of the Hamiltonian constraint (with no inverse volume corrections) from real γ to γ =+/- i, in the simple case of a flat FLRW Universe coupled to a massless scalar field with no cosmological constant. For this, we first compute the non-local curvature operator (defined by the trace of the holonomy of the connection around a fundamental plaquette) evaluated in an arbitrary spin j representation, and find a new close formula for its expression. This allows us to define explicitly a one parameter family of regularizations of the Hamiltonian constraint in LQC, parametrized by the spin j. It is immediate to see that any spin j regularization leads to a bouncing scenario. Then, motivated in particular by previous results on black hole thermodynamics, we perform the analytic continuation of the Hamiltonian constraint to values of the Barbero-Immirzi parameter given by γ =+/- i and to spins j=\\frac{1}{2}(-1+is) where s is real. Even if the area spectrum then becomes continuous, we show that the complex LQC defined in this way does also replace the initial big-bang singularity by a big-bounce. In addition to this, the maximal density and the minimal volume of the Universe are obviously independent of γ . Furthermore, the dynamics before and after the bounce is not symmetrical anymore, which makes a clear distinction between these two phases of the evolution of the Universe.
An introduction to spherically symmetric loop quantum gravity black holes
Gambini, Rodolfo; Pullin, Jorge
2015-03-26
We review recent developments in the treatment of spherically symmetric black holes in loop quantum gravity. In particular, we discuss an exact solution to the quantum constraints that represents a black hole and is free of singularities. We show that new observables that are not present in the classical theory arise in the quantum theory. We also discuss Hawking radiation by considering the quantization of a scalar field on the quantum spacetime.
Ozel, Tuncay; Nizamoglu, Sedat; Sefunc, Mustafa A; Samarskaya, Olga; Ozel, Ilkem O; Mutlugun, Evren; Lesnyak, Vladimir; Gaponik, Nikolai; Eychmuller, Alexander; Gaponenko, Sergey V; Demir, Hilmi Volkan
2011-02-22
We propose and demonstrate a nanocomposite localized surface plasmon resonator embedded into an artificial three-dimensional construction. Colloidal semiconductor quantum dots are assembled between layers of metal nanoparticles to create a highly strong plasmon-exciton interaction in the plasmonic cavity. In such a multilayered plasmonic resonator architecture of isotropic CdTe quantum dots, we observed polarized light emission of 80% in the vertical polarization with an enhancement factor of 4.4, resulting in a steady-state anisotropy value of 0.26 and reaching the highest quantum efficiency level of 30% ever reported for such CdTe quantum dot solids. Our electromagnetic simulation results are in good agreement with the experimental characterization data showing a significant emission enhancement in the vertical polarization, for which their fluorescence decay lifetimes are substantially shortened by consecutive replication of our unit cell architecture design. Such strongly plasmon-exciton coupling nanocomposites hold great promise for future exploitation and development of quantum dot plasmonic biophotonics and quantum dot plasmonic optoelectronics.
Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Singh, Parampreet
2009-08-01
We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.
Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
Corichi, Alejandro; Singh, Parampreet
2009-08-15
We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.
Gravity quantized: Loop quantum gravity with a scalar field
Domagala, Marcin; Kaminski, Wojciech; Giesel, Kristina; Lewandowski, Jerzy
2010-11-15
...''but we do not have quantum gravity.'' This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consists of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except that it involves all the local degrees of freedom of the gravitational field because no symmetry reduction has been performed at the classical level.
Bouncing loop quantum cosmology in Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Haro, J.; Makarenko, A. N.; Myagky, A. N.; Odintsov, S. D.; Oikonomou, V. K.
2015-12-01
We develop an effective Gauss-Bonnet extension of loop quantum cosmology, by introducing holonomy corrections in modified F (G ) theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of loop quantum gravity theories, and we result in having leading order corrections to the classical F (G ) theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes it possible to find the loop quantum cosmology corrected F (G ) theory that can realize various cosmological scenarios. We exemplify our theoretical constructions by using bouncing cosmologies, and we investigate which loop quantum cosmology corrected Gauss-Bonnet modified gravities can successfully realize such cosmologies.
Thermodynamics of spherically symmetric spacetimes in loop quantum gravity
NASA Astrophysics Data System (ADS)
Mäkelä, Jarmo
2015-06-01
The choice of the area operator in loop quantum gravity is by no means unique. In addition to the area operator commonly used in loop quantum gravity there is also an area operator introduced by Krasnov in 1998, which gives uniformly spaced area spectra for the horizons of spacetime. Using Krasnov's area operator we consider the thermodynamics of spherically symmetric spacetimes equipped with horizons in loop quantum gravity. Among other things, our approach implies, in a pretty simple manner, that every horizon of spacetime emits thermal radiation and possesses entropy which, in the natural units, is one-quarter of its area. When applied to the de Sitter spacetime loop quantum gravity provides an explanation both to the presence and the smallness of the cosmological constant.
Geometry of loop quantum gravity on a graph
Rovelli, Carlo; Speziale, Simone
2010-08-15
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the 'twisted geometries' and derive a simple relation between these and Regge geometries.
Tanaka, Tomo; Amemiya, Fumitoshi; Shimano, Masahiro; Harada, Tomohiro; Tamaki, Takashi
2011-05-15
In loop quantum cosmology, the Hamiltonian reduces to a finite difference operator and quantum dynamics are controlled by the difference equation. In this framework, Bojowald [M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001).] showed that the initial singularity is absent in the twofold sense: (i) the spectrum of the inverse scale factor operator is bounded from above; (ii) the wave function of the Universe can be uniquely extended beyond the point which was the initial singularity in classical theory. In this paper, we study the initial singularity in this sense and the large-volume limit against the ambiguities in the discretization and the operator ordering within a homogeneous, isotropic and spatially flat model with the cosmological constant. We find that the absence of the singularity strongly depends on the choice of the operator ordering and the requirement for the absence singles out a very small class of orderings. Moreover we find a general ordering rule required for the absence of the singularity. We also find that the large-volume limit naturally recovers a smooth wave function in the discretization where each step corresponds to a fixed volume increment but not in the one where each step corresponds to a fixed area increment. If loop quantum cosmology is to be a phenomenological realization of full loop quantum gravity, these results are important to fix the theoretical ambiguities.
Universal features of quantum bounce in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Zhu, Tao; Wang, Anzhong; Kirsten, Klaus; Cleaver, Gerald; Sheng, Qin
2017-10-01
In this Letter, we study analytically the evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe and its linear perturbations in the framework of the dressed metric approach in loop quantum cosmology (LQC). Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a Pöschl-Teller (PT) potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch-Davies (BD) vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least 141 e-folds since the bounce.
Inhomogeneous loop quantum cosmology: Hybrid quantization of the Gowdy model
NASA Astrophysics Data System (ADS)
Garay, L. J.; Martín-Benito, M.; Mena Marugán, G. A.
2010-08-01
The Gowdy cosmologies provide a suitable arena to further develop loop quantum cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two different schemes for the quantization of the Bianchi I model within the improved dynamics formalism of loop quantum cosmology. One of these schemes has been recently put forward by Ashtekar and Wilson-Ewing. We address several issues, including the quantum resolution of the cosmological singularity, the structure of the superselection sectors in the quantum system, or the construction of the Hilbert space of physical states.
Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.
Sahlmann, Hanno; Thiemann, Thomas
2012-03-16
We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.
Kinematic projective quantum states for loop quantum gravity coupled to tensor fields
NASA Astrophysics Data System (ADS)
Okołów, Andrzej
2017-04-01
We present a construction of kinematic quantum states for theories of tensor fields of an arbitrary sort. The construction is based on projective techniques by Kijowski. Applying projective quantum states for Loop Quantum Gravity (LQG) obtained by Lanéry and Thiemann we construct quantum states for LQG coupled to tensor fields.
One-loop quantum gravity repulsion in the early Universe.
Broda, Bogusław
2011-03-11
Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lemaître-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.
Conformal loop quantum gravity coupled to the standard model
NASA Astrophysics Data System (ADS)
Campiglia, Miguel; Gambini, Rodolfo; Pullin, Jorge
2017-01-01
We argue that a conformally invariant extension of general relativity coupled to the standard model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge fixing and a modified Higgs mechanism particles acquire mass and one recovers general relativity coupled to the standard model. The theory suggests new views with respect to the definition of the Hamiltonian constraint in loop quantum gravity, the semi-classical limit and the issue of finite renormalization in quantum field theory in quantum space-time. It also gives hints about the elimination of ambiguities that arise in quantum field theory in quantum space-time in the calculation of back-reaction.
Path integrals and the WKB approximation in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam
2010-12-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Loop quantum cosmology of Bianchi type IX models
Wilson-Ewing, Edward
2010-08-15
The loop quantum cosmology 'improved dynamics' of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.
Loop quantum cosmology of Bianchi type IX models
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2010-08-01
The loop quantum cosmology “improved dynamics” of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.
Group Field Theory and Loop Quantum Gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele
The following sections are included: * GFT from LQG Perspective: The Underlying Ideas * GFT Kinematics: Hilbert Space and Observables * The Quantum Dynamics * The Continuum Limit of Quantum Geometry in GFT * Extracting Effective Continuum Physics from GFTs * Conclusions * References
Towards generic resolution of strong singularities in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Singh, Parampreet
2010-10-01
Singularities are the boundaries of classical spacetime in General Relativity. It has been always hoped that quantum gravitational effects may resolve these singularities. In recent years, progress in loop quantum cosmology has provided insights on the resolution of big bang, big crunch and other spacelike singularities. In this talk we will give an update on the recent status of the generic resolution of strong spacelike singularities in loop quantum cosmology. We will show that for flat and curved Roberston-Walker backgrounds and also for Bianchi-I models, loop quantum gravity effects resolve all strong curvature singularities. However, weak curvature singularities, that is those beyond which geodesics can be continued, may not be resolved.
Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Karami, Asieh
2016-06-01
We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic k = 1 model that, classically, is contained within the Bianchi IX model. Somewhat surprisingly, we find the most natural quantization does not reduce to the k = 1 model. We use geometrically defined scalar observables to explore the physical implications of each of these theories. This is the first part in a series of papers analyzing different aspects of the Bianchi IX model, with inverse corrections, within loop quantum cosmology (LQC).
NASA Astrophysics Data System (ADS)
Kirwai, Amey; Chandrakumar, N.
2016-08-01
We report the design and performance evaluation of novel pulse sequences for triple quantum filtered spectroscopy in homonuclear three spin-1/2 systems, employing isotropic mixing (IM) to excite triple quantum coherence (TQC). Our approach involves the generation of combination single quantum coherences (cSQC) from antisymmetric longitudinal or transverse magnetization components employing isotropic mixing (IM). cSQC's are then converted to TQC by a selective 180° pulse on one of the spins. As IM ideally causes magnetization to evolve under the influence of the spin coupling Hamiltonian alone, TQC is generated at a faster rate compared to sequences involving free precession. This is expected to be significant when the spins have large relaxation rates. Our approach is demonstrated experimentally by TQC filtered 1D spectroscopy on a 1H AX2 system (propargyl bromide in the presence of a paramagnetic additive), as well as a 31P linear AMX system (ATP in agar gel). The performance of the IM-based sequences for TQC excitation are compared against the standard three pulse sequence (Ernst et al., 1987) and an AX2 spin pattern recognition sequence (Levitt and Ernst, 1983). The latter reaches the unitary bound on TQC preparation efficiency starting from thermal equilibrium in AX2 systems, not considering relaxation. It is shown that in systems where spins relax rapidly, the new IM-based sequences indeed perform significantly better than the above two known TQC excitation sequences, the sensitivity enhancement being especially pronounced in the case of the proton system investigated. An overview of the differences in relaxation behavior is presented for the different approaches. Applications are envisaged to Overhauser DNP experiments and to in vivo NMR.
Even-odd spatial nonequivalence for atomic quantum gases with isotropic spin-orbit couplings
NASA Astrophysics Data System (ADS)
Singh, G. S.; Gupta, Reena
2014-05-01
A general expression for the density of states (DOS) of power-law trapped d-dimensional ideal quantum gases with isotropic spin-orbit couplings (SOCs) is derived and is found to bifurcate into even- dand odd- d classes. The expressions for the grand potential and hence for several thermodynamic quantities are then shown to be amenable to exact analytical forms provided d is an odd integer. Also, a condition γ < 2 d is obtained in case of odd- d for appearance of the Bose-Einstein condensation with γ as the power-law exponent. It is thus established that isotropic SOCs render even and odd dimensional spaces nonequivalent for uniform as well as trapped gases, and that the DOS of one-dimensional (1D) ideal gases, uniform or trapped, remains unaffected by the SOC. Furthermore, the analytical study of the transition temperature and the condensate fraction in a 3D Bose gas under combined presence of the harmonic trapping and the Weyl coupling shows that the condensation is favored by the former but disfavored by the latter. This countering behavior is discussed to be in conformity with the exchange-symmetry-induced statistical interactions resulting from these two entities as enunciated recently [Phys. Rev. A 88, 053607 (2013)].
Loop quantum cosmology with self-dual variables
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2015-12-01
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann space-time coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular inner product for the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomylike operators of which some are well defined; these operators in turn are used in the definition of the Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum theory is closely related, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived which provide a good approximation to the full quantum dynamics for sharply peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a nonsingular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.
Creation of particles in a cyclic universe driven by loop quantum cosmology
NASA Astrophysics Data System (ADS)
Tavakoli, Yaser; Fabris, Júlio C.
2015-05-01
We consider an isotropic and homogeneous universe in loop quantum cosmology (LQC). We assume that the matter content of the universe is dominated by dust matter in early time and a phantom matter at late time which constitutes the dark energy component. The quantum gravity modifications to the Friedmann equation in this model indicate that the classical big bang singularity and the future big rip singularity are resolved and are replaced by quantum bounce. It turns out that the big bounce and recollapse in the herein model contribute to a cyclic scenario for the universe. We then study the quantum theory of a massive, nonminimally coupled scalar field undergoing cosmological evolution from primordial bounce towards the late time bounce. In particular, we solve the Klein-Gordon equation for the scalar field in the primordial and late time regions, in order to investigate particle production phenomena at late time. By computing the energy density of created particles at late time, we show that this density is negligible in comparison to the quantum background density at Planck era. This indicates that the effects of quantum particle production do not influence the future bounce.
Covariant effective action for loop quantum cosmology a la Palatini
Olmo, Gonzalo J.; Singh, Parampreet E-mail: psingh@perimeterinstitute.ca
2009-01-15
In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a continuum description in terms of an effective Hamiltonian. Here we provide an algorithm to obtain the corresponding effective action, establishing in this way the covariance of the theory for the first time. This result provides new insights on the continuum properties of the discrete structure of quantum geometry and opens new avenues to extract physical predictions such as those related to gauge invariant cosmological perturbations.
NASA Astrophysics Data System (ADS)
Diener, Peter; Gupt, Brajesh; Singh, Parampreet
2014-05-01
A key result of isotropic loop quantum cosmology is the existence of a quantum bounce which occurs when the energy density of the matter field approaches a universal maximum close to the Planck density. Though the bounce has been exhibited in various matter models, due to severe computational challenges, some important questions have so far remained unaddressed. These include the demonstration of the bounce for widely spread states, its detailed properties for the states when matter field probes regions close to the Planck volume and the reliability of the continuum effective spacetime description in general. In this manuscript we rigorously answer these questions using the Chimera numerical scheme for the isotropic spatially flat model sourced with a massless scalar field. We show that, as expected from an exactly solvable model, the quantum bounce is a generic feature of states even with a very wide spread, and for those which bounce much closer to the Planck volume. We perform a detailed analysis of the departures from the effective description and find some expected, and some surprising results. At a coarse level of description, the effective dynamics can be regarded as a good approximation to the underlying quantum dynamics unless the states correspond to small scalar field momenta, in which case they bounce closer to the Planck volume or are very widely spread. Quantifying the amount of discrepancy between the quantum and the effective dynamics, we find that the departure between them depends in a subtle and non-monotonic way on the field momentum and different fluctuations. Interestingly, the departures are generically found to be such that the effective dynamics overestimates the spacetime curvature, and underestimates the volume at the bounce.
On the Convergence in Effective Loop Quantum Cosmology
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2010-07-12
In Loop Quantum Cosmology (LQC) there is a discreteness parameter {lambda}, that has been heuristically associated to a fundamental granularity of quantum geometry. It is also possible to consider {lambda} as a regulator in the same spirit as that used in lattice field theory, where it specifies a regular lattice in the real line. A particular quantization of the k = 0 FLRW loop cosmological model yields a completely solvable model, known as solvable loop quantum cosmology(sLQC). In this contribution, we consider effective classical theories motivated by sLQC and study their {lambda}-dependence, with a special interest on the limit {lambda}{yields}0 and the role of the evolution parameter in the convergence of such limit.
Closed-Loop and Robust Control of Quantum Systems
Wang, Lin-Cheng
2013-01-01
For most practical quantum control systems, it is important and difficult to attain robustness and reliability due to unavoidable uncertainties in the system dynamics or models. Three kinds of typical approaches (e.g., closed-loop learning control, feedback control, and robust control) have been proved to be effective to solve these problems. This work presents a self-contained survey on the closed-loop and robust control of quantum systems, as well as a brief introduction to a selection of basic theories and methods in this research area, to provide interested readers with a general idea for further studies. In the area of closed-loop learning control of quantum systems, we survey and introduce such learning control methods as gradient-based methods, genetic algorithms (GA), and reinforcement learning (RL) methods from a unified point of view of exploring the quantum control landscapes. For the feedback control approach, the paper surveys three control strategies including Lyapunov control, measurement-based control, and coherent-feedback control. Then such topics in the field of quantum robust control as H∞ control, sliding mode control, quantum risk-sensitive control, and quantum ensemble control are reviewed. The paper concludes with a perspective of future research directions that are likely to attract more attention. PMID:23997680
Extension of loop quantum gravity to f(R) theories.
Zhang, Xiangdong; Ma, Yongge
2011-04-29
The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.
Extension of Loop Quantum Gravity to f(R) Theories
NASA Astrophysics Data System (ADS)
Zhang, Xiangdong; Ma, Yongge
2011-04-01
The four-dimensional metric f(R) theories of gravity are cast into connection-dynamical formalism with real su(2) connections as configuration variables. Through this formalism, the classical metric f(R) theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the nonperturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of four-dimensional metric theories of gravity.
Evolution of perturbations in anisotropic loop quantum cosmology
NASA Astrophysics Data System (ADS)
Vijayakumar, Sreenath; Agullo, Ivan; Olmedo, Javier
2017-01-01
In loop quantum cosmology the big bang singularity is replaced by a quantum bounce. The evolution of primordial perturbations through such a bounce in a Friedmann-Lemaître-Robertson-Walker universe has been studied in great detail. However, it is well known that any tiny anisotropy will grow (up to an upper bound) as the universe contracts and undergoes a bounce. Anisotropies will then decrease and eventually dilute in the expanding branch, but quantum perturbations may retain memory of the anisotropic bounce. In this talk, we present our efforts in understanding the effect of anisotropies (of Bianchi-I type) on the evolution of primordial perturbations in loop quantum cosmology, and in exploring its phenomenological implications. This work is supported by the NSF Grant No. PHY-1403943.
Spacetime-noncommutativity regime of loop quantum gravity
NASA Astrophysics Data System (ADS)
Amelino-Camelia, Giovanni; Da Silva, Malú Maira; Ronco, Michele; Cesarini, Lorenzo; Lecian, Orchidea Maria
2017-01-01
A recent study by Bojowald and Paily [M. Bojowald and G. M. Paily, Phys. Rev. D 87, 044044 (2013)., 10.1103/PhysRevD.87.044044] provided a path toward the identification of an effective quantum-spacetime picture of loop quantum gravity, applicable in the "Minkowski regime," the regime where the large-scale (coarse-grained) spacetime metric is flat. A pivotal role in the analysis is played by loop-quantum-gravity-based modifications to the hypersurface deformation algebra, which leave a trace in the Minkowski regime. We here show that the symmetry-algebra results reported by Bojowald and Paily are consistent with a description of spacetime in the Minkowski regime given in terms of the κ -Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem had already been proposed for independent reasons.
Probing loop quantum gravity with evaporating black holes.
Barrau, A; Cailleteau, T; Cao, X; Diaz-Polo, J; Grain, J
2011-12-16
This Letter aims at showing that the observation of evaporating black holes should allow the usual Hawking behavior to be distinguished from loop quantum gravity (LQG) expectations. We present a full Monte Carlo simulation of the evaporation in LQG and statistical tests that discriminate between competing models. We conclude that contrarily to what was commonly thought, the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal quantum gravity footprints.
Black hole state degeneracy in loop quantum gravity
Agullo, Ivan; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique
2008-05-15
The combinatorial problem of counting the black hole quantum states within the isolated horizon framework in loop quantum gravity is analyzed. A qualitative understanding of the origin of the band structure shown by the degeneracy spectrum, which is responsible for the black hole entropy quantization, is reached. Even when motivated by simple considerations, this picture allows to obtain analytical expressions for the most relevant quantities associated to this effect.
New Hamiltonians for loop quantum cosmology with arbitrary spin representations
NASA Astrophysics Data System (ADS)
Ben Achour, Jibril; Brahma, Suddhasattwa; Geiller, Marc
2017-04-01
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the fundamental representation, and very little is known about the physics associated with higher spin labels. This constitutes an ambiguity of which the understanding, we believe, is fundamental for connecting loop quantum cosmology to full theories of quantum gravity like loop quantum gravity, its spin foam formulation, or cosmological group field theory. We take a step in this direction by providing here a new closed formula for the Hamiltonian of flat Friedmann-Lemaître-Robertson-Walker models regularized in a representation of arbitrary spin. This expression is furthermore polynomial in the basic variables which correspond to well-defined operators in the quantum theory, takes into account the so-called inverse-volume corrections, and treats in a unified way two different regularization schemes for the curvature. After studying the effective classical dynamics corresponding to single and multiple-spin Hamiltonians, we study the behavior of the critical density when the number of representations is increased and the stability of the difference equations in the quantum theory.
NASA Astrophysics Data System (ADS)
Saini, Sahil; Singh, Parampreet
2016-12-01
Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events can occur only for very exotic equations of state when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature invariants are proved to remain finite for any evolution in finite proper time. We find the novel result that all strong singularities are resolved for arbitrary matter. Weak singularities pertaining to above potential curvature divergence events can exist. The effective spacetime is found to be geodesically complete for particle and null geodesics in finite time evolution. Our results add to a growing evidence for generic resolution of strong singularities using effective dynamics in loop quantum cosmology by generalizing earlier results on isotropic and Bianchi-I spacetimes.
Linking loop quantum gravity quantization ambiguities with phenomenology
NASA Astrophysics Data System (ADS)
Brahma, Suddhasattwa; Ronco, Michele; Amelino-Camelia, Giovanni; Marcianò, Antonino
2017-02-01
It is well known that extracting viable testable predictions out of fundamental quantum gravity theories is notoriously difficult. In this paper, we aim to incorporate putative quantum corrections coming from loop quantum gravity in deriving modified dispersion relations for particles in a deformed Minkowski spacetime. We show how different choices of the Immirzi parameter can, in some cases, serendipitously lead to different outcomes for such modifications, depending on the quantization scheme chosen. This allows one to differentiate between these quantization choices via testable phenomenological predictions.
Towards new background independent representations for loop quantum gravity
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
2008-05-01
Recently, uniqueness theorems were constructed for the representation used in loop quantum gravity. We explore the existence of alternate representations by weakening the assumptions of the Lewandowski Okolow Sahlmann Thiemann (LOST) uniqueness theorem. The weakened assumptions seem physically reasonable and retain the key requirement of explicit background independence. For simplicity, we restrict attention to the case of gauge group U(1).
Counting black hole microscopic states in loop quantum gravity
Ghosh, A.; Mitra, P.
2006-09-15
Counting of microscopic states of black holes is performed within the framework of loop quantum gravity. This is the first calculation of the pure horizon states using statistical methods, which reveals the possibility of additional states missed in the earlier calculations, leading to an increase of entropy. Also for the first time a microcanonical temperature is introduced within the framework.
Projective loop quantum gravity. I. State space
NASA Astrophysics Data System (ADS)
Lanéry, Suzanne; Thiemann, Thomas
2016-12-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.
On a Continuum Limit for Loop Quantum Cosmology
Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose Antonio
2008-03-06
The use of non-regular representations of the Heisenberg-Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology (LQC), symmetry reduced theory that is related to Loop Quantum Gravity, and that is based on a non-regular, polymeric representation. Recently, a soluble model was used by Ashtekar, Corichi and Singh to study the relation between Loop Quantum Cosmology and the standard Wheeler-DeWitt theory and, in particular, the passage to the limit in which the auxiliary parameter (interpreted as ''quantum geometry discreetness'') is sent to zero in hope to get rid of this 'regulator' that dictates the LQC dynamics at each 'scale'. In this note we outline the first steps toward reformulating this question within the program developed by the authors for studying the continuum limit of polymeric theories, which was successfully applied to simple systems such as a Simple Harmonic Oscillator.
Dirac fields in loop quantum gravity and big bang nucleosynthesis
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Das, Rupam; Scherrer, Robert J.
2008-04-01
Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansion-dependent multiplicative factor in the total density. We use these results, along with the predictions of big bang nucleosynthesis, to place bounds on these corrections and especially the patch size of discrete quantum gravity states.
Dirac fields in loop quantum gravity and big bang nucleosynthesis
Bojowald, Martin; Das, Rupam; Scherrer, Robert J.
2008-04-15
Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansion-dependent multiplicative factor in the total density. We use these results, along with the predictions of big bang nucleosynthesis, to place bounds on these corrections and especially the patch size of discrete quantum gravity states.
Measure problem in slow roll inflation and loop quantum cosmology
Corichi, Alejandro; Karami, Asieh
2011-05-15
We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to 1 in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity-free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.
Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Diener, Peter; Gupt, Brajesh; Megevand, Miguel; Singh, Parampreet
2014-08-01
In recent years, numerical simulations with Gaussian initial states have demonstrated the existence of a quantum bounce in loop quantum cosmology in various models. A key issue pertaining to the robustness of the bounce and the associated physics is to understand the quantum evolution for more general initial states, which may depart significantly from Gaussianity and may have no well defined peakedness properties. The analysis of such states, including squeezed and highly non-Gaussian states, has been computationally challenging until now. In this paper, we overcome these challenges by using the Chimera scheme for the spatially flat, homogeneous and isotropic model sourced with a massless scalar field. We demonstrate that the quantum bounce in this model occurs even for states that are highly squeezed or are non-Gaussian with multiple peaks and with little resemblance to semi-classical states. The existence of the bounce is found to be robust, being independent of the properties of the states. The evolution of squeezed and non-Gaussian states turns out to be qualitatively similar to that of Gaussian states, and satisfies strong constraints on the growth of the relative fluctuations across the bounce. We also compare the results from the effective dynamics and find that, although it captures the qualitative aspects of the evolution for squeezed and highly non-Gaussian states, it always underestimates the bounce volume. We show that various properties of the evolution, such as the energy density at the bounce, are in excellent agreement with the predictions from an exactly solvable loop quantum cosmological model for arbitrary states.
Loop quantum cosmology of diagonal Bianchi type I model: Simplifications and scaling problems
Szulc, Lukasz
2008-09-15
A simplified theory of the diagonal Bianchi type I model coupled with a massless scalar field in loop quantum cosmology is constructed according to the {mu} scheme. Kinematical and physical sectors of the theory are under good analytical control as well as the scalar constraint operator. Although it is possible to compute numerically the nonsingular evolution of the three gravitational degrees of freedom, the naive implementation of the {mu} scheme to the diagonal Bianchi type I model is problematic. The lack of the full invariance of the theory with respect to the fiducial cell and fiducial metric scaling causes serious problems in the semiclassical limit of the theory. Because of this behavior it is very difficult to extract reasonable physics from the model. The weaknesses of the implementation of the {mu} scheme to the Bianchi I model do not imply limitations of the {mu} scheme in the isotropic case.
The diffeomorphism constraint operator in loop quantum gravity
NASA Astrophysics Data System (ADS)
Laddha, Alok; Varadarajan, Madhavan
2011-10-01
We construct the smeared diffeomorphism constraint operator at finite triangulation from the basic holonomy-flux operators of loop quantum gravity (LQG), evaluate its continuum limit on the Lewandowski-Marolf habitat and show that the action of the continuum operator provides an anomaly-free representation of the Lie algebra of diffeomorphisms of the 3-manifold. Key features of our analysis include (i) finite triangulation approximants to the curvature, Fiab, of the Ashtekar-Barbero connection which involve not only small loop holonomies but also small surface fluxes as well as an explicit dependence on the edge labels of the spin network being acted on (ii) the dependence of the small loop underlying the holonomy on both the direction and magnitude of the shift vector field, (iii) continuum constraint operators which do not have finite action on the kinematic Hilbert space, thus implementing a key lesson from recent studies of parameterized field theory by the authors. Features (i) and (ii) provide the first hints in LQG of a conceptual similarity with the so-called mu-bar scheme of loop quantum cosmology. We expect our work to be of use in the construction of an anomaly-free quantum dynamics for LQG.
Loop-corrected Virasoro symmetry of 4D quantum gravity
NASA Astrophysics Data System (ADS)
He, T.; Kapec, D.; Raclariu, A.; Strominger, A.
2017-08-01
Recently a boundary energy-momentum tensor T zz has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an "anomaly" which is one-loop exact, T zz generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts T zz .
Phenomenological loop quantum geometry of the Schwarzschild black hole
Chiou, D.-W.
2008-09-15
The interior of a Schwarzschild black hole is investigated at the level of phenomenological dynamics with the discreteness corrections of loop quantum geometry implemented in two different improved quantization schemes. In one scheme, the classical black hole singularity is resolved by the quantum bounce, which bridges the black hole interior with a white hole interior. In the other scheme, the classical singularity is resolved and the event horizon is also diffused by the quantum bounce. Jumping over the quantum bounce, the black hole gives birth to a baby black hole with a much smaller mass. This lineage continues as each classical black hole brings forth its own descendant in the consecutive classical cycle, giving the whole extended spacetime fractal structure, until the solution eventually descends into the deep Planck regime, signaling a breakdown of the semiclassical description. The issues of scaling symmetry and no-hair theorem are also discussed.
Phenomenological loop quantum geometry of the Schwarzschild black hole
NASA Astrophysics Data System (ADS)
Chiou, Dah-Wei
2008-09-01
The interior of a Schwarzschild black hole is investigated at the level of phenomenological dynamics with the discreteness corrections of loop quantum geometry implemented in two different improved quantization schemes. In one scheme, the classical black hole singularity is resolved by the quantum bounce, which bridges the black hole interior with a white hole interior. In the other scheme, the classical singularity is resolved and the event horizon is also diffused by the quantum bounce. Jumping over the quantum bounce, the black hole gives birth to a baby black hole with a much smaller mass. This lineage continues as each classical black hole brings forth its own descendant in the consecutive classical cycle, giving the whole extended spacetime fractal structure, until the solution eventually descends into the deep Planck regime, signaling a breakdown of the semiclassical description. The issues of scaling symmetry and no-hair theorem are also discussed.
PREFACE: Loops 11: Non-Perturbative / Background Independent Quantum Gravity
NASA Astrophysics Data System (ADS)
Mena Marugán, Guillermo A.; Barbero G, J. Fernando; Garay, Luis J.; Villaseñor, Eduardo J. S.; Olmedo, Javier
2012-05-01
Loops 11 The international conference LOOPS'11 took place in Madrid from the 23-28 May 2011. It was hosted by the Instituto de Estructura de la Materia (IEM), which belongs to the Consejo Superior de Investigaciones Cientĺficas (CSIC). Like previous editions of the LOOPS meetings, it dealt with a wealth of state-of-the-art topics on Quantum Gravity, with special emphasis on non-perturbative background-independent approaches to spacetime quantization. The main topics addressed at the conference ranged from the foundations of Quantum Gravity to its phenomenological aspects. They encompassed different approaches to Loop Quantum Gravity and Cosmology, Polymer Quantization, Quantum Field Theory, Black Holes, and discrete approaches such as Dynamical Triangulations, amongst others. In addition, this edition celebrated the 25th anniversary of the introduction of the now well-known Ashtekar variables and the Wednesday morning session was devoted to this silver jubilee. The structure of the conference was designed to reflect the current state and future prospects of research on the different topics mentioned above. Plenary lectures that provided general background and the 'big picture' took place during the mornings, and the more specialised talks were distributed in parallel sessions during the evenings. To be more specific, Monday evening was devoted to Shape Dynamics and Phenomenology Derived from Quantum Gravity in Parallel Session A, and to Covariant Loop Quantum Gravity and Spin foams in Parallel Session B. Tuesday's three Parallel Sessions dealt with Black Hole Physics and Dynamical Triangulations (Session A), the continuation of Monday's session on Covariant Loop Quantum Gravity and Spin foams (Session B) and Foundations of Quantum Gravity (Session C). Finally, Thursday and Friday evenings were devoted to Loop Quantum Cosmology (Session A) and to Hamiltonian Loop Quantum Gravity (Session B). The result of the conference was very satisfactory and enlightening. Not
Loop quantum cosmology, non-Gaussianity, and CMB power asymmetry
NASA Astrophysics Data System (ADS)
Agullo, Ivan
2015-09-01
We argue that the anomalous power asymmetry observed in the cosmic microwave background (CMB) may have originated in a cosmic bounce preceding inflation. In loop quantum cosmology (LQC), the big bang singularity is generically replaced by a bounce due to quantum gravitational effects. We compute the spectrum of inflationary non-Gaussianity and show that strong correlation between observable scales and modes with longer (superhorizon) wavelength arise as a consequence of the evolution of perturbations across the LQC bounce. These correlations are strongly scale dependent and induce a dipole-dominated modulation on large angular scales in the CMB, in agreement with observations.
Unified model of loop quantum gravity and matter
NASA Astrophysics Data System (ADS)
Gambini, Rodolfo; Olson, S. Jay; Pullin, Jorge
2006-04-01
We reconsider the unified model of gravitation and Yang Mills interactions proposed by Chakraborty and Peldán, in the light of recent formal developments in loop quantum gravity. In particular, we show that one can promote the Hamiltonian constraint of the unified model to a well defined anomaly-free quantum operator using the techniques introduced by Thiemann, at least for the Euclidean theory. The Lorentzian version of the model can be consistently constructed, but at the moment appears to yield a correct weak field theory only under restrictive assumptions, and its quantization appears problematic.
Spin-foams for all loop quantum gravity
NASA Astrophysics Data System (ADS)
Kamiński, Wojciech; Kisielowski, Marcin; Lewandowski, Jerzy
2010-05-01
The simplicial framework of Engle-Pereira-Rovelli-Livine spin-foam models is generalized to match the diffeomorphism invariant framework of loop quantum gravity. The simplicial spin-foams are generalized to arbitrary linear 2-cell spin-foams. The resulting framework admits all the spin-network states of loop quantum gravity, not only those defined by triangulations (or cubulations). In particular, the notion of embedded spin-foam we use allows us to consider knotting or linking spin-foam histories. Also the main tools, the vertex structure and the vertex amplitude, are naturally generalized to an arbitrary valency case. The correspondence between all the SU(2) intertwiners and the SU(2)×SU(2) EPRL intertwiners is proved to be 1-1 in the case of the Barbero-Immirzi parameter |γ| >= 1.
Toward explaining black hole entropy quantization in loop quantum gravity
NASA Astrophysics Data System (ADS)
Sahlmann, Hanno
2007-11-01
In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this steplike behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking.
Directed-Loop Quantum Monte Carlo Method for Retarded Interactions
NASA Astrophysics Data System (ADS)
Weber, Manuel; Assaad, Fakher F.; Hohenadler, Martin
2017-09-01
The directed-loop quantum Monte Carlo method is generalized to the case of retarded interactions. Using the path integral, fermion-boson or spin-boson models are mapped to actions with retarded interactions by analytically integrating out the bosons. This yields an exact algorithm that combines the highly efficient loop updates available in the stochastic series expansion representation with the advantages of avoiding a direct sampling of the bosons. The application to electron-phonon models reveals that the method overcomes the previously detrimental issues of long autocorrelation times and exponentially decreasing acceptance rates. For example, the resulting dramatic speedup allows us to investigate the Peierls quantum phase transition on chains of up to 1282 sites.
Towards loop quantum gravity without the time gauge.
Cianfrani, Francesco; Montani, Giovanni
2009-03-06
The Hamiltonian formulation of the Holst action is reviewed and it provides a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the loop quantum gravity quantization procedure can be applied when the time-gauge condition does not stand.
Towards Loop Quantum Gravity without the Time Gauge
NASA Astrophysics Data System (ADS)
Cianfrani, Francesco; Montani, Giovanni
2009-03-01
The Hamiltonian formulation of the Holst action is reviewed and it provides a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the loop quantum gravity quantization procedure can be applied when the time-gauge condition does not stand.
Statistics, holography, and black hole entropy in loop quantum gravity
NASA Astrophysics Data System (ADS)
Ghosh, Amit; Noui, Karim; Perez, Alejandro
2014-04-01
In loop quantum gravity the quantum states of a black hole horizon consist of pointlike discrete quantum geometry excitations (or punctures) labeled by spin j. The excitations possibly carry other internal degrees of freedom, and the associated quantum states are eigenstates of the area A operator. The appropriately scaled area operator A/(8πℓ) can also be interpreted as the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance ℓ from the horizon. Thus, the local energy is entirely accounted for by the geometric operator A. Assuming that: Close to the horizon the quantum state has a regular energy momentum tensor and hence the local temperature measured by stationary observers is the Unruh temperature. Degeneracy of matter states is exponential with the area exp(λA/ℓp2), which is supported by the well-established results of QFT in curved spacetimes, which do not determine λ but assert an exponential behavior. The geometric excitations of the horizon (punctures) are indistinguishable. And finally that the semiclassical limit the area of the black hole horizon is large in Planck units. It follows that: Up to quantum corrections, matter degrees of freedom saturate the holographic bound, viz., λ must be equal to 1/4. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-Hawking entropy S =A/(4ℓp2). The number of horizon punctures goes like N∝√A/ℓp2 ; i.e., the number of punctures N remains large in the semiclassical limit. Fluctuations of the horizon area are small ΔA/A ∝(ℓp2/A)1/4, while fluctuations of the area of an individual puncture are large (large spins dominate). A precise notion of local conformal invariance of the thermal state is recovered in the A→∞ limit where the near horizon geometry becomes Rindler. We also show how the present model (constructed from loop quantum gravity) provides a regularization of (and gives a concrete meaning to) the formal
The matter bounce scenario in loop quantum cosmology
Wilson-Ewing, Edward
2013-03-01
In the matter bounce scenario, a dust-dominated contracting space-time generates scale-invariant perturbations that, assuming a nonsingular bouncing cosmology, propagate to the expanding branch and set appropriate initial conditions for the radiation-dominated era. Since this scenario depends on the presence of a bounce, it seems appropriate to consider it in the context of loop quantum cosmology where a bouncing universe naturally arises. For a pressureless collapsing universe in loop quantum cosmology, the predicted power spectrum of the scalar perturbations after the bounce is scale-invariant and the tensor to scalar ratio is negligibly small. A slight red tilt can be given to the scale-invariance of the scalar perturbations by a scalar field whose equation of state is P = −ερ, where ε is a small positive number. Then, the power spectrum for tensor perturbations is also almost scale-invariant with the same red tilt as the scalar perturbations, and the tensor to scalar ratio is expected to be r ≈ 9 × 10{sup −4}. Finally, for the predicted amplitude of the scalar perturbations to agree with observations, the critical density in loop quantum cosmology must be of the order ρ{sub c} ∼ 10{sup −9}ρ{sub Pl}.
Single-loop multiple-pulse nonadiabatic holonomic quantum gates
NASA Astrophysics Data System (ADS)
Herterich, Emmi; Sjöqvist, Erik
2016-11-01
Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [E. Sjöqvist et al., New J. Phys. 14, 103035 (2012), 10.1088/1367-2630/14/10/103035] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a Λ -type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level Λ -coupling structure by utilizing carefully chosen laser pulses.
Averaged null energy condition in loop quantum cosmology
Li Lifang; Zhu Jianyang
2009-02-15
Wormholes and time machines are objects of great interest in general relativity. However, to support them it needs exotic matters which are impossible at the classical level. Semiclassical gravity introduces the quantum effects into the stress-energy tensor and constructs many self-consistent wormholes. But they are not traversable due to the averaged null energy condition. Loop quantum gravity (LQG) significantly modifies the Einstein equation in the deep quantum region. If we write the modified Einstein equation in the form of the standard one but with an effective stress-energy tensor, it is convenient to analyze the geometry in LQG through the energy condition. Loop quantum cosmology (LQC), an application of LQG, has an effective stress-energy tensor which violates some kinds of local energy conditions. So it is natural that the inflation emerges in LQC. In this paper, we investigate the averaged null energy condition in LQC in the framework of the effective Hamiltonian, and we find that the effective stress-energy tensor in LQC violates the averaged null energy condition in the massless scalar field coupled model.
A new look at Lorentz-covariant loop quantum gravity
NASA Astrophysics Data System (ADS)
Geiller, Marc; Lachièze-Rey, Marc; Noui, Karim
2011-08-01
In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the second-class constraints inherited from the canonical analysis of the Holst action without the time gauge. We show that it has the property of lying in the conjugacy class of a pure su(2) connection, a result which enables one to construct the kinematical Hilbert space of the Lorentz-covariant theory in terms of the usual SU(2) spin-network states. Furthermore, we show that there is a unique Lorentz-covariant electric field, up to trivial and natural equivalence relations. The Lorentz-covariant electric field transforms under the adjoint action of the Lorentz group, and the associated Casimir operators are shown to be proportional to the area density. This gives a very interesting algebraic interpretation of the area. Finally, we show that the action of the surface operator on the Lorentz-covariant holonomies reproduces exactly the usual discrete SU(2) spectrum of time-gauge loop quantum gravity. In other words, the use of the time gauge does not introduce anomalies in the quantum theory.
Loop quantum cosmology: from pre-inflationary dynamics to observations
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Barrau, Aurélien
2015-12-01
The Planck collaboration has provided us rich information about the early Universe, and a host of new observational missions will soon shed further light on the ‘anomalies’ that appear to exist on the largest angular scales. From a quantum gravity perspective, it is natural to inquire if one can trace back the origin of such puzzling features to Planck scale physics. Loop quantum cosmology provides a promising avenue to explore this issue because of its natural resolution of the big bang singularity. Thanks to advances over the last decade, the theory has matured sufficiently to allow concrete calculations of the phenomenological consequences of its pre-inflationary dynamics. In this article we summarize the current status of the ensuing two-way dialog between quantum gravity and observations.
Avoidance of future singularities in loop quantum cosmology
Sami, M.; Singh, Parampreet; Tsujikawa, Shinji
2006-08-15
We consider the fate of future singularities in the effective dynamics of loop quantum cosmology. Nonperturbative quantum geometric effects which lead to {rho}{sup 2} modification of the Friedmann equation at high energies result in generic resolution of singularities whenever energy density {rho} diverges at future singularities of Friedmann dynamics. Such quantum effects lead to the avoidance of a big rip, which is followed by a recollapsing universe stable against perturbations. Resolution of sudden singularity, the case when pressure diverges but energy density approaches a finite value depends on the ratio of the latter to a critical energy density of the order of the Planck value. If the value of this ratio is greater than unity, the universe escapes the sudden future singularity and becomes oscillatory.
Stottmeister, Alexander Thiemann, Thomas
2016-08-15
In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity.
NASA Astrophysics Data System (ADS)
Dupuy, John L.; Singh, Parampreet
2017-01-01
The spatially closed Friedmann-Lemaître-Robertson-Walker model in loop quantum cosmology admits two inequivalent consistent quantizations: one based on expressing the field strength in terms of the holonomies over closed loops and another using a connection operator and open holonomies. Using the effective dynamics, we investigate the phenomenological differences between the two quantizations for the single-fluid and the two-fluid scenarios with various equations of state, including the phantom matter. We show that a striking difference between the two quantizations is the existence of two distinct quantum turnarounds, either bounces or recollapses, in the connection quantization, in contrast to a single distinct quantum bounce or a recollapse in the holonomy quantization. These results generalize an earlier result on the existence of two distinct quantum bounces for stiff matter by Corichi and Karami. However, we find that in certain situations two distinct quantum turnarounds can become virtually indistinguishable. And depending on the initial conditions, a pure quantum cyclic universe can also exist undergoing a quantum bounce and a quantum recollapse. We show that for various equations of states, connection-based quantization leads to super-Planckian values of the energy density and the expansion scalar at quantum turnarounds. Interestingly, we find that very extreme energy densities can also occur for the holonomy quantization, breaching the maximum allowed density in the spatially flat loop quantized model. However, the expansion scalar in all these cases is bounded by a universal value.
Superconducting quantum criticality of topological surface states at three loops
NASA Astrophysics Data System (ADS)
Zerf, Nikolai; Lin, Chien-Hung; Maciejko, Joseph
2016-11-01
The semimetal-superconductor quantum phase transition on the two-dimensional (2D) surface of a 3D topological insulator is conjectured to exhibit an emergent N =2 supersymmetry, based on a one-loop renormalization group (RG) analysis in the ɛ expansion. We provide additional support for this conjecture by performing a three-loop RG analysis and showing that the supersymmetric fixed point found at this order survives the extrapolation to 2D. We compute critical exponents to order ɛ3, obtaining the more accurate value ν ≈0.985 for the correlation length exponent and confirming that the fermion and boson anomalous dimensions remain unchanged beyond one loop, as expected from non-renormalization theorems in supersymmetric theories. We further couple the system to a dynamical U(1) gauge field, and argue that the transition becomes fluctuation-induced first order in an appropriate type-I regime. We discuss implications of this result for quantum phase transitions between certain symmetry-preserving correlated surface states of 3D topological insulators.
Loop quantum cosmology of Bianchi IX: effective dynamics
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Montoya, Edison
2017-03-01
We study solutions to the effective equations for the Bianchi IX class of spacetimes within loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a massless scalar field, by numerically solving the loop quantum cosmology effective equations, with and without inverse triad corrections. The solutions are classified using certain geometrically motivated classical observables. We show that both effective theories—with lapse N = V and N = 1—resolve the big bang singularity and reproduce the classical dynamics far from the bounce. Moreover, due to the positive spatial curvature, there is an infinite number of bounces and recollapses. We study the limit of large field momentum and show that both effective theories reproduce the same dynamics, thus recovering general relativity. We implement a procedure to identify amongst the Bianchi IX solutions, those that behave like k = 0,1 FLRW as well as Bianchi I, II, and VII0 models. The effective solutions exhibit Bianchi I phases with Bianchi II transitions and also Bianchi VII0 phases, which had not been studied before. We comment on the possible implications of these results for a quantum modification to the classical BKL behaviour.
Secular effects on inflation from one-loop quantum gravity
NASA Astrophysics Data System (ADS)
Cabrer, J. A.; Espriu, D.
2008-06-01
In this Letter we revisit and extend a previous analysis where the possible relevance of quantum gravity effects in a cosmological setup was studied. The object of interest are non-local (logarithmic) terms generated in the effective action of gravity due to the exchange in loops of massless modes (such as photons or the gravitons themselves). We correct one mistake existing in the previous work and discuss the issue in a more general setting in different cosmological scenarios. We obtain the one-loop quantum-corrected evolution equations for the cosmological scale factor up to a given order in a derivative expansion in two particular cases: a matter dominated universe with vanishing cosmological constant, and in a de Sitter universe. We show that the quantum corrections, albeit tiny, may have a secular effect that eventually modifies the expansion rate. For a de Sitter universe they tend to slow down the rate of the expansion, while the effect may be the opposite in a matter dominated universe.
2-loop quantum Yang Mills condensate as dark energy
NASA Astrophysics Data System (ADS)
Xia, T. Y.; Zhang, Y.
2007-11-01
In seeking a model solving the coincidence problem, the effective Yang Mills condensate (YMC) is an alternative candidate for dark energy. A study is made for the model up to the 2-loop order of quantum corrections. It is found that, like in the 1-loop model, for generic initial conditions during the radiation era, there is always a desired tracking solution, yielding the current status Ω≃0.73 and Ω≃0.27. As the time t→∞ the dynamics is a stable attractor. Thus the model naturally solves the coincidence problem of dark energy. Moreover, if YMC decays into matter, its equation of state (EoS) crosses -1 and takes w˜-1.1, as indicated by the recent observations.
Loop equations and KDV hierarchy in 2-D quantum gravity
Fucito, F. ); Martellini, M. )
1992-04-20
In this paper a derivation of the loop equation for two-dimensional quantum gravity from the KdV equations and the string equation of the one-matrix model is given. The loop equation was found to be equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the virasoro algebra. Starting form the equations expressing these constraints. The authors are able to rederive the equations of the KdV hierarchy using the vertex operator construction of the A{sup (I)}{sub I} infinite dimensional twisted Kac-Moody algebra. From these considerations it follows that the solutions of the string equation of the one-matrix model are given by a subset of the solutions of the KdV hierarchy.
Separate universes in loop quantum cosmology: Framework and applications
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2016-06-01
I present a streamlined review of how the separate universe approach to cosmological perturbation theory can be used to study the dynamics of long-wavelength scalar perturbations in loop quantum cosmology (LQC), and then use it to calculate how long-wavelength curvature perturbations evolve across the LQC bounce assuming a constant equation of state. A similar calculation is possible for tensor modes using results from a complementary approach to cosmological perturbation theory in LQC based on an effective Hamiltonian constraint. An interesting result is that the tensor-to-scalar ratio can be suppressed or amplified by quantum gravity effects during the bounce, depending on the equation of state of the matter field dominating the dynamics. In particular, if the equation of state lies between - 1/3 and 1, the value of the tensor-to-scalar ratio will be suppressed during the bounce, in some cases significantly.
Phenomenology of loop quantum cosmology and observational consequences
NASA Astrophysics Data System (ADS)
Gupt, Brajesh
2016-03-01
An important feature of singularity resolution in loop quantum cosmology (LQC) is the occurrence of the quantum bounce when the spacetime curvature becomes Planckian leading the pre-inflationary evolution of the universe to be greatly modified. Due to the modified dynamics in the pre-inflationary era the initial conditions for both the background and cosmological perturbations are different from those in the standard inflationary scenario. We find that such modifications can lead to observational signatures on the cosmic microwave background (CMB) anisotropy spectrum, and provide a new window to explore the CMB anomalies. In this talk we describe these initial conditions, discuss their consequences on the inflationary power spectrum, and compare our results with data from recent CMB experiments. NSF.
Slow-roll approximation in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Luc, Joanna; Mielczarek, Jakub
2017-01-01
The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term. The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.
NASA Astrophysics Data System (ADS)
Amaral, Marcelo M.; Aschheim, Raymond; Bubuianu, Laurenţiu; Irwin, Klee; Vacaru, Sergiu I.; Woolridge, Daniel
2017-09-01
The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/(super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi–Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.
Loop quantum cosmology of k=1 FRW models
Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet; Vandersloot, Kevin
2007-01-15
The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semiclassical at some late time, the big bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the 'difficulties' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists.
Closed-loop quantum control utilizing time domain maps
NASA Astrophysics Data System (ADS)
Biteen, Julie S.; Geremia, J. M.; Rabitz, Herschel
2003-05-01
Closed-loop laser control of quantum dynamics phenomena may be accomplished through frequency domain manipulations in the laboratory guided by a learning algorithm. This paper presents an alternative method based on the use of nonlinear input→output maps generated in the time domain, although the actual experiments and control optimization are carried out in the frequency domain. The procedure first involves the construction of input→output maps relating the field structure to the observed control performance. These maps are utilized as a substitute for actual experiments in the subsequent optimization stage in order to find the field that drives the system to a specified target. This closed-loop learning process is repeated with a sufficient number of maps until a control field is found that yields the target observable as best as possible. The overall algorithm is simulated with two model quantum systems. It is shown that excellent quality control can be achieved through this sequential learning procedure, even with individual maps that have only modest global accuracy.
Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets.
Owerre, S A
2017-07-31
In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling J and interlayer coupling J L , which is realizable in the honeycomb chromium compounds CrX3 (X ≡ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for J L ≠ 0 and form 1D closed lines of Dirac magnon nodes in 2D momentum space. The 2D Dirac magnon nodal-line loops are topologically protected by inversion and time-reversal symmetry. Furthermore, we show that they are robust against weak Dzyaloshinskii-Moriya interaction Δ DM < J L and possess chiral magnon edge modes.
Hung, Ivan; Wong, Alan; Howes, Andy P; Anupõld, Tiit; Samoson, Ago; Smith, Mark E; Holland, Diane; Brown, Steven P; Dupree, Ray
2009-04-01
Using a two-dimensional multiple-quantum (MQ) double rotation (DOR) experiment the contributions of the chemical shift and quadrupolar interaction to isotropic resonance shifts can be completely separated. Spectra were acquired using a three-pulse triple-quantum z-filtered pulse sequence and subsequently sheared along both the nu(1) and nu(2) dimensions. The application of this method is demonstrated for both crystalline (RbNO(3)) and amorphous samples (vitreous B(2)O(3)). The existence of the two rubidium isotopes ((85)Rb and (87)Rb) allows comparison of results for two nuclei with different spins (I=3/2 and 5/2), as well as different dipole and quadrupole moments in a single chemical compound. Being only limited by homogeneous line broadening and sample crystallinity, linewidths of approximately 0.1 and 0.2 ppm can be measured for (87)Rb in the quadrupolar and chemical shift dimensions, enabling highly accurate determination of the isotropic chemical shift and the quadrupolar product, P(Q). For vitreous B(2)O(3), the use of MQDOR allows the chemical shift and electric field gradient distributions to be directly determined-information that is difficult to obtain otherwise due to the presence of second-order quadrupolar broadening.
Tosner, Zdenek; Glaser, Steffen J; Khaneja, Navin; Nielsen, Niels Chr
2006-11-14
We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.
3D Lorentzian loop quantum gravity and the spinor approach
NASA Astrophysics Data System (ADS)
Girelli, Florian; Sellaroli, Giuseppe
2015-12-01
We consider the generalization of the "spinor approach" to the Lorentzian case, in the context of three-dimensional loop quantum gravity with cosmological constant Λ =0 . The key technical tool that allows this generalization is the recoupling theory between unitary infinite-dimensional representations and nonunitary finite-dimensional ones, obtained in the process of generalizing the Wigner-Eckart theorem to SU(1,1). We use SU(1,1) tensor operators to build observables and a solvable quantum Hamiltonian constraint, analogous to the one introduced by V. Bonzom and his collaborators in the Euclidean case (with both Λ =0 and Λ ≠0 ). We show that the Lorentzian Ponzano-Regge amplitude is the solution of the quantum Hamiltonian constraint by recovering the Biedenharn-Elliott relation [generalized to the case where unitary and nonunitary SU(1,1) representations are coupled to each other]. Our formalism is sufficiently general that both the Lorentzian and the Euclidean case can be recovered (with Λ =0 ).
Covariance in models of loop quantum gravity: Spherical symmetry
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Brahma, Suddhasattwa; Reyes, Juan D.
2015-08-01
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).
Tachyon field in loop quantum cosmology: Inflation and evolution picture
Xiong Huaui; Zhu Jianyang
2007-04-15
Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universne through a bounce in the high energy region. We show that this is always true in tachyon matter LQC. Differing from the classical Friedman-Robertson-Walker (FRW) cosmology, the super inflation can appear in the tachyon matter LQC; furthermore, the inflation can be extended to the region where classical inflation stops. Using the numerical method, we give an evolution picture of the tachyon field with an exponential potential in the context of LQC. It indicates that the quantum dynamical solutions have the same attractive behavior as the classical solutions do. The whole evolution of the tachyon field is that in the distant past, the tachyon field--being in the contracting cosmology--accelerates to climb up the potential hill with a negative velocity; then at the boundary the tachyon field is bounced into an expanding universe with positive velocity rolling down to the bottom of the potential. In the slow roll limit, we compare the quantum inflation with the classical case in both an analytic and a numerical way.
Semiclassical Analysis of Fundamental Amplitudes in Loop Quantum Gravity
NASA Astrophysics Data System (ADS)
Hedeman, Austin J.
Spin networks arise in many areas of physics and are a key component in both the canonical formulation (loop quantum gravity) and the path-integral formulation (spin-foam gravity) of quantum gravity. In loop quantum gravity the spin networks are used to construct a countable basis for the physical Hilbert space of gravity. The basis states may be interpreted as gauge-invariant wavefunctionals of the connection. Evaluating the wavefunctional on a specific classical connection involves embedding the spin network into a spacelike hypersurface and finding the holonomy around the network. This is equivalent to evaluating a ''g-inserted'' spin network (a spin network with a group action acting on all of the edges of the network). The spin-foam approach to quantum gravity is a path-integral formulation of loop quantum gravity in which the paths are world-histories of embedded spin networks. Depending on the spin-foam model under consideration the vertex amplitude (the contribution a spin-foam vertex makes to the transition amplitude) may be represented by a specific simple closed spin network. The most important examples use the 6j-symbol, the 15j-symbol, and the Riemannian 10j-symbol. The semiclassical treatment of spin networks is the main theme of this dissertation. To show that classical solutions of general relativity emerge in the appropriate limits of loop quantum gravity or spin-foam gravity requires knowledge of the semiclassical limits of spin networks. This involves interpreting the spin networks as inner products and then treating the inner products semiclassically using the WKB method and the stationary phase approximation. For any given spin network there are many possible inner product models which correspond to how the spin network is ''split up'' into pieces. For example the 6 j-symbol has been studied in both a model involving four angular momenta (Aquilanti et al 2012) and a model involving twelve angular momenta (Roberts 1999). Each of these models
The Continuum Limit of Loop Quantum Gravity: A Framework for Solving the Theory
NASA Astrophysics Data System (ADS)
Dittrich, Bianca
The following sections are included: * Solving the Dynamics of Loop Quantum Gravity * Continuum Limit in Canonical Loop Quantum Gravity * Continuum Limit for the Dynamics of the Theory * Renormalization Flow and Scale in Background Independent Theories * (Decorated) Tensor Network Renormalization for Spin Nets and Spin Foams * Diffeomorphism Symmetry in the Discrete, Constraints and Divergences * Summary and Outlook * Acknowledgements * References
Quintessence and (anti-)Chaplygin gas in loop quantum cosmology
Lamon, Raphael; Woehr, Andreas J.
2010-01-15
The concordance model of cosmology contains several unknown components such as dark matter and dark energy. Many proposals have been made to describe them by choosing an appropriate potential for a scalar field. We study four models in the realm of loop quantum cosmology: the Chaplygin gas, an inflationary and radiationlike potential, quintessence and an anti-Chaplygin gas. For the latter we show that all trajectories start and end with a type II singularity and, depending on the initial value, may go through a bounce. On the other hand the evolution under the influence of the first three scalar fields behaves classically at times far away from the big bang singularity and bounces as the energy density approaches the critical density.
Superbounce and loop quantum cosmology ekpyrosis from modified gravity
NASA Astrophysics Data System (ADS)
Oikonomou, V. K.
2015-09-01
As is known, in modified cosmological theories of gravity many of the cosmologies which could not be generated by standard Einstein gravity, can be consistently described by theories. Using known reconstruction techniques, we investigate which theories can lead to a Hubble parameter describing two types of cosmological bounces, the superbounce model, related to supergravity and non-supersymmetric models of contracting ekpyrosis and also the Loop Quantum Cosmology modified ekpyrotic model. Since our method is an approximate method, we investigate the problem at large and small curvatures. As we evince, both models yield power law reconstructed gravities, with the most interesting new feature being that both lead to accelerating cosmologies, in the large curvature approximation. The mathematical properties of the some Friedmann-Robertson-Walker spacetimes , that describe superbounce-like cosmologies are also pointed out, with regards to the group of curvature collineations.
Anisotropic loop quantum cosmology with self-dual variables
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2016-04-01
A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies of the Ashtekar connection, and the reality conditions are implemented via the choice of the inner product on the kinematical Hilbert space. The action of the Hamiltonian constraint operator is given explicitly for the case when the matter content is a massless scalar field (in which case the scalar field can be used as a relational clock), and it is shown that the big bang and big crunch singularities are resolved in the sense that singular and nonsingular states decouple under the action of the Hamiltonian constraint operator.
One-loop renormalization of quantum electrodynamics in curved spacetime
NASA Astrophysics Data System (ADS)
Panangaden, Prakash
1981-04-01
In this paper we discuss the renormalizability of quantum electrodynamics (QED) in a general curved spacetime. A generating functional is introduced and position-space Feynman rules are obtained. Functional techniques are used to show that a form of Ward's identity can be derived in curved spacetime. A local momentum representation for the scalar and vector propagators is introduced. The one-loop diagrams for the electron and photon self-energy are computed and it is shown that there are no divergences that are not present in flat space. It is shown that this latter result depends crucially on the gauge invariance of the theory and is not merely a trivial consequence of renormalizability of QED in flat spacetime.
NASA Astrophysics Data System (ADS)
Bunao, J.
2017-02-01
This study considers the operator \\hat{T} corresponding to the classical spacetime four-volume \\tilde{T} (on-shell) of a finite patch of spacetime in the context of unimodular loop quantum cosmology for the homogeneous and isotropic model with flat spatial sections and without matter sources. Since the spacetime four-volume is canonically conjugate to the cosmological ‘constant’, the operator \\hat{T} is constructed by solving its canonical commutation relation with {\\hat Λ } —the operator corresponding to the classical cosmological constant on-shell {\\tilde Λ } . This conjugacy, along with the action of \\hat{T} on definite volume states reducing to \\tilde{T} , allows us to interpret that \\hat{T} is indeed a quantum spacetime four-volume operator. The discrete spectrum of \\hat{T} is calculated by considering the set of all τ’s where the eigenvalue equation has a solution {{ Φ }τ} in the domain of \\hat{T} . It turns out that, upon assigning the maximal domain D≤ft(\\hat{T}\\right) to \\hat{T} , we have {{ Φ }τ}\\in D≤ft(\\hat{T}\\right) for all τ \\in {C} so that the spectrum of \\hat{T} is purely discrete and is the entire complex plane. A family of operators {{\\hat{T}}≤ft({{b0},{φ0}\\right)}} was also considered as possible self-adjoint versions of \\hat{T} . They represent the restrictions of \\hat{T} on their respective domains D≤ft({{\\hat{T}}≤ft({{b0},{φ0}\\right)}}\\right) which are just the maximal domain with additional quasi-periodic conditions. Their possible self-adjointness is motivated by their discrete spectra only containing real and discrete numbers {τm} for m=0,+/- 1,+/- 2,... .
Fusion basis for lattice gauge theory and loop quantum gravity
NASA Astrophysics Data System (ADS)
Delcamp, Clement; Dittrich, Bianca; Riello, Aldo
2017-02-01
We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2 + 1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.
An embedding of loop quantum cosmology in (b,v) variables into a full theory context
NASA Astrophysics Data System (ADS)
Bodendorfer, N.
2016-06-01
Loop quantum cosmology in (b, v) variables, which is governed by a unit step size difference equation, is embedded into a full theory context based on similar variables. A full theory context here means a theory of quantum gravity arrived at using the quantisation techniques used in loop quantum gravity, however based on a different choice of elementary variables and classical gauge fixing suggested by loop quantum cosmology. From the full theory perspective, the symmetry reduction is characterised by the vanishing of certain phase space functions which are implemented as operator equations in the quantum theory. The loop quantum cosmology dynamics arise as the action of the full theory Hamiltonian on maximally coarse states in the kernel of the reduction constraints. An application of this reduction procedure to spherical symmetry is also sketched, with similar results, but only one canonical pair in (b, v) form.
Symmetry reduced loop quantum gravity: A bird’s eye view
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay
2016-06-01
This is a brief overview of the current status of symmetry reduced models in Loop Quantum Gravity. The goal is to provide an introduction to other more specialized and detailed reviews that follow. Since most of this work is motivated by the physics of the very early universe, I will focus primarily on Loop Quantum Cosmology and discuss quantum aspects of black holes only briefly.
Observational test of inflation in loop quantum cosmology
Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji E-mail: calcagni@aei.mpg.de
2011-11-01
We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings, we show that they can generate large running spectral indices, which generally lead to an enhancement of power at large scales. We provide explicit formulæ for the scalar/tensor power spectra under the slow-roll approximation, by taking into account corrections of order higher than the runnings. Via a standard analysis, we place observational bounds on the inverse-volume quantum correction δ∝a{sup −σ} (σ > 0, a is the scale factor) and the slow-roll parameter ε{sub V} for power-law potentials as well as exponential potentials by using the data of WMAP 7yr combined with other observations. We derive the constraints on δ for two pivot wavenumbers k{sub 0} for several values of δ. The quadratic potential can be compatible with the data even in the presence of the LQC corrections, but the quartic potential is in tension with observations. We also find that the upper bounds on δ(k{sub 0}) for given σ and k{sub 0} are insensitive to the choice of the inflaton potentials.
Loop quantum gravity, exact holographic mapping, and holographic entanglement entropy
NASA Astrophysics Data System (ADS)
Han, Muxin; Hung, Ling-Yan
2017-01-01
The relation between loop quantum gravity (LQG) and tensor networks is explored from the perspectives of the bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space Σ with boundary ∂Σ is an exact holographic mapping similar to the proposal in [X.-L. Qi, Exact holographic mapping and emergent space-time geometry, arXiv:1309.6282]. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse-graining procedure of spin networks. Furthermore, when a region A and its complement A ¯ are specified on the boundary ∂Σ , we show that the boundary entanglement entropy S (A ) of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e., S (A ) is proportional to the minimal area of the bulk surface attached to the boundary of A in ∂Σ .
Time evolution in deparametrized models of loop quantum gravity
NASA Astrophysics Data System (ADS)
Assanioussi, Mehdi; Lewandowski, Jerzy; Mäkinen, Ilkka
2017-07-01
An important aspect in understanding the dynamics in the context of deparametrized models of loop quantum gravity (LQG) is to obtain a sufficient control on the quantum evolution generated by a given Hamiltonian operator. More specifically, we need to be able to compute the evolution of relevant physical states and observables with a relatively good precision. In this article, we introduce an approximation method to deal with the physical Hamiltonian operators in deparametrized LQG models, and we apply it to models in which a free Klein-Gordon scalar field or a nonrotational dust field is taken as the physical time variable. This method is based on using standard time-independent perturbation theory of quantum mechanics to define a perturbative expansion of the Hamiltonian operator, the small perturbation parameter being determined by the Barbero-Immirzi parameter β . This method allows us to define an approximate spectral decomposition of the Hamiltonian operators and hence to compute the evolution over a certain time interval. As a specific example, we analyze the evolution of expectation values of the volume and curvature operators starting with certain physical initial states, using both the perturbative method and a straightforward expansion of the expectation value in powers of the time variable. This work represents a first step toward achieving the goal of understanding and controlling the new dynamics developed in Alesci et al. [Phys. Rev. D 91, 124067 (2015), 10.1103/PhysRevD.91.124067] and Assanioussi et al. [Phys. Rev. D 92, 044042 (2015), 10.1103/PhysRevD.92.044042].
Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
NASA Astrophysics Data System (ADS)
Nahum, Adam; Chalker, J. T.; Serna, P.; Ortuño, M.; Somoza, A. M.
2015-10-01
Numerical studies of the transition between Néel and valence bond solid phases in two-dimensional quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to realize the universal physics of the Néel-valence-bond-solid (VBS) transition in a three-dimensional classical loop model (this model includes the subtle interference effect that suppresses hedgehog defects in the Néel order parameter). We use the loop model for simulations of unprecedentedly large systems (up to linear size L =512 ). Our results are compatible with a continuous transition at which both Néel and VBS order parameters are critical, and we do not see conventional signs of first-order behavior. However, we show that the scaling violations are stronger than previously realized and are incompatible with conventional finite-size scaling, even if allowance is made for a weakly or marginally irrelevant scaling variable. In particular, different approaches to determining the anomalous dimensions ηVBS and ηN é el yield very different results. The assumption of conventional finite-size scaling leads to estimates that drift to negative values at large sizes, in violation of the unitarity bounds. In contrast, the decay with distance of critical correlators on scales much smaller than system size is consistent with large positive anomalous dimensions. Barring an unexpected reversal in behavior at still larger sizes, this implies that the transition, if continuous, must show unconventional finite-size scaling, for example, from an additional dangerously irrelevant scaling variable. Another possibility is an anomalously weak first-order transition. By analyzing the renormalization group flows for the noncompact CP n -1 field theory (the n -component Abelian Higgs model) between two and four dimensions, we give the simplest scenario by which an anomalously weak first
Oriented matroids—combinatorial structures underlying loop quantum gravity
NASA Astrophysics Data System (ADS)
Brunnemann, Johannes; Rideout, David
2010-10-01
We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator (Ashtekar A and Lewandowski J 1998 Adv. Theor. Math. Phys. 1 388) in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence vertices of a graph in three-dimensional Riemannian space and can be represented by sign strings containing relative orientations of embedded edges. We demonstrate that these signature factors are a special representation of the general mathematical concept of an oriented matroid (Ziegler G M 1998 Electron. J. Comb.; Björner A et al 1999 Oriented Matroids (Cambridge: Cambridge University Press)). Moreover, we show that oriented matroids can also be used to describe the topology (connectedness) of directed graphs. Hence, the mathematical methods developed for oriented matroids can be applied to the difficult combinatorics of embedded graphs underlying the construction of LQG. As a first application we revisit the analysis of Brunnemann and Rideout (2008 Class. Quantum Grav. 25 065001 and 065002), and find that enumeration of all possible sign configurations used there is equivalent to enumerating all realizable oriented matroids of rank 3 (Ziegler G M 1998 Electron. J. Comb.; Björner A et al 1999 Oriented Matroids (Cambridge: Cambridge University Press)), and thus can be greatly simplified. We find that for 7-valent vertices having no coplanar triples of edge tangents, the smallest non-zero eigenvalue of the volume spectrum does not grow as one increases the maximum spin jmax at the vertex, for any orientation of the edge tangents. This indicates that, in contrast to the area operator, considering large jmax does not necessarily imply large volume eigenvalues. In addition we give an outlook to possible starting points for rewriting the combinatorics of LQG in terms of oriented matroids.
Flux formulation of loop quantum gravity: classical framework
NASA Astrophysics Data System (ADS)
Dittrich, Bianca; Geiller, Marc
2015-07-01
We recently introduced a new representation for loop quantum gravity (LQG), which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying this new formulation. The central objects in our construction are the so-called integrated fluxes, which are defined as the integral of the electric field variable over surfaces of codimension one, and related in turn to Wilson surface operators. These integrated flux observables will play an important role in the coarse graining of states in LQG, and can be used to encode in this context the notion of curvature-induced torsion. We furthermore define a continuum phase space as the modified projective limit of a family of discrete phase spaces based on triangulations. This continuum phase space yields a continuum (holonomy-flux) algebra of observables. We show that the corresponding Poisson algebra is closed by computing the Poisson brackets between the integrated fluxes, which have the novel property of being allowed to intersect each other.
One-loop quantum gravity in the Einstein universe
NASA Astrophysics Data System (ADS)
Avramidi, Ivan G.; Collopy, Samuel J.
2015-11-01
We study quantum gravity with the Einstein-Hilbert action including the cosmological constant on the Euclidean Einstein universe S 1 × S 3. We compute exactly the spectra and the heat kernels of the relevant operators on S 3 and use these results to compute the heat trace of the graviton and ghost operators and the exact one-loop effective action on S 1 × S 3. We show that the system is unstable in the infrared limit due to the presence of the negative modes of the graviton and the ghost operators. We study the thermal properties of the model with the temperature T = (2 πa 1)-1 determined by the radius a 1 of the circle S 1. We show that the heat capacity C v is well defined and behaves like ˜ T 3 in the high temperature limit and has a singularity of the type ˜ ( T - T c )-1, indicating a second-order phase transition, with the critical temperature T c determined by the cosmological constant Λ and the radius a of the sphere S 3. We also discuss some peculiar properties of the model such as the negative heat capacity as well as possible physical applications.
The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology
NASA Astrophysics Data System (ADS)
Haro, Jaume; Amorós, Jaume; Aresté Saló, Llibert
2017-09-01
We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar field, at very late times, in the contracting phase, all orbits depict a matter dominated Universe, which evolves to an ekpyrotic phase. After the bounce the Universe enters in the expanding phase, where the orbits leave the ekpyrotic regime going to a kination (also named deflationary) regime. Moreover, this scenario supports the production of heavy massive particles conformally coupled with gravity, which reheats the universe at temperatures compatible with the nucleosynthesis bounds and also the production of massless particles non-conformally coupled with gravity leading to very high reheating temperatures but ensuring the nucleosynthesis success. Dealing with cosmological perturbations, these background dynamics produce a nearly scale invariant power spectrum for the modes that leave the Hubble radius, in the contracting phase, when the Universe is quasi-matter dominated, whose spectral index and corresponding running is compatible with the recent experimental data obtained by PLANCK's team.
Future singularities and teleparallelism in loop quantum cosmology
Bamba, Kazuharu; Haro, Jaume de; Odintsov, Sergei D. E-mail: jaime.haro@upc.edu
2013-02-01
We demonstrate how holonomy corrections in loop quantum cosmology (LQC) prevent the Big Rip singularity by introducing a quadratic modification in terms of the energy density ρ in the Friedmann equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) space-time in a consistent and useful way. In addition, we investigate whether other kind of singularities like Type II,III and IV singularities survive or are avoided in LQC when the universe is filled by a barotropic fluid with the state equation P = −ρ−f(ρ), where P is the pressure and f(ρ) a function of ρ. It is shown that the Little Rip cosmology does not happen in LQC. Nevertheless, the occurrence of the Pseudo-Rip cosmology, in which the phantom universe approaches the de Sitter one asymptotically, is established, and the corresponding example is presented. It is interesting that the disintegration of bound structures in the Pseudo-Rip cosmology in LQC always takes more time than that in Einstein cosmology. Our investigation on future singularities is generalized to that in modified teleparallel gravity, where LQC and Brane Cosmology in the Randall-Sundrum scenario are the best examples. It is remarkable that F(T) gravity may lead to all the kinds of future singularities including Little Rip.
Cosmological study in loop quantum cosmology through dark energy model
NASA Astrophysics Data System (ADS)
Jawad, Abdul; Rani, Shamaila; Salako, Ines G.; Gulshan, Faiza
The interacting generalized ghost version of pilgrim dark energy (GGPDE) is discussed in the framework of loop quantum cosmology (LQC). We analyze the behavior of cosmological parameters (Hubble, equation of state (EoS), deceleration) and cosmological planes (ωD ‑ ωD‧ and r-s) in the present scenario (ωD represents the EoS parameter and ωD‧ indicates the evolution of the EoS parameter, r,s are statefinder parameters). It is observed that the deceleration parameter corresponds to the accelerated expansion of the universe. The EoS parameter lies in vacuum and phantom regions for all cases of u (pilgrim dark energy (PDE) parameter). The ωD ‑ ωD‧ plane lies in thawing region for all cases of u. The r ‑ s plane corresponds to Λ cold dark matter (CDM) and Chaplygin gas model. We have also mentioned the constraints on calculated cosmological parameters and found that all the trajectories of cosmological parameters and planes show the consistence behavior with the observational schemes.
Fischer, Stefan; Goldschmidt, Jan Christoph; Johnson, Noah J. J.; Pichaandi, Jothirmayanantham; Veggel, Frank C. J. M. van
2015-11-21
Colloidal upconverter nanocrystals (UCNCs) that convert near-infrared photons to higher energies are promising for applications ranging from life sciences to solar energy harvesting. However, practical applications of UCNCs are hindered by their low upconversion quantum yield (UCQY) and the high irradiances necessary to produce relevant upconversion luminescence. Achieving high UCQY under practically relevant irradiance remains a major challenge. The UCQY is severely limited due to non-radiative surface quenching processes. We present a rate equation model for migration of the excitation energy to show that surface quenching does not only affect the lanthanide ions directly at the surface but also many other lanthanide ions quite far away from the surface. The average migration path length is on the order of several nanometers and depends on the doping as well as the irradiance of the excitation. Using Er{sup 3+}-doped β-NaYF{sub 4} UCNCs, we show that very isotropic and thick (∼10 nm) β-NaLuF{sub 4} inert shells dramatically reduce the surface-related quenching processes, resulting in much brighter upconversion luminescence at simultaneously considerably lower irradiances. For these UCNCs embedded in poly(methyl methacrylate), we determined an internal UCQY of 2.0% ± 0.2% using an irradiance of only 0.43 ± 0.03 W/cm{sup 2} at 1523 nm. Normalized to the irradiance, this UCQY is 120× higher than the highest values of comparable nanomaterials in the literature. Our findings demonstrate the important role of isotropic and thick shells in achieving high UCQY at low irradiances from UCNCs. Additionally, we measured the additional short-circuit current due to upconversion in silicon solar cell devices as a proof of concept and to support our findings determined using optical measurements.
Uran, Can; Erdem, Talha; Guzelturk, Burak; Perkgöz, Nihan Kosku; Jun, Shinae; Jang, Eunjoo; Demir, Hilmi Volkan
2014-10-06
In this work, we demonstrate a proof-of-concept system for generating highly polarized light from colloidal quantum dots (QDs) coupled with magnetically aligned segmented Au/Ni/Au nanowires (NWs). Optical characterizations reveal that the optimized QD-NW coupled structures emit highly polarized light with an s-to p-polarization (s/p) contrast as high as 15:1 corresponding to a degree of polarization of 0.88. These experimental results are supported by the finite-difference time-domain simulations, which demonstrate the interplay between the inter-NW distance and the degree of polarization.
Quantum Phase Transition and Thermal Entanglement in the Isotropic XXX Model
NASA Astrophysics Data System (ADS)
Ma, Fu-Wu; Kong, Xiang-Mu
2012-06-01
We investigate the quantum phase transition (QPT) and the pairwise thermal entanglement in the three-qubit Heisenberg XXX chain with Dzyaloshinskii—Moriya (DM) interaction under a magnetic field. The ground states of the system exist crossing points, which shows that the system exhibits a QPT. At a given temperature, the entanglement undergoes two sudden changes (platform-like behavior) as the DM interaction or external magnetic field increases. This special property can be used as the entanglement switch, which is also influenced by the temperature. We can modulate the DM interaction or external magnetic field to control the entanglement switch.
Entropic corrected Newton's law of gravitation and the loop quantum black hole gravitational atom
NASA Astrophysics Data System (ADS)
Aragão, R. G. L.; Silva, C. A. S.
2016-07-01
One proposal by Verlinde is that gravity is not a fundamental, but an entropic force (Verlinde in JHEP 1104:029, 2011. arXiv:hep-th/1001.0785). Based on this new interpretation of the gravity, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that such corrections could be inherited by Newton's law. In this sense, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravity in an observationally accessible regimes. On the other hand, loop quantum gravity is a theory that provide a scheme to approach the quantum properties of spacetime. From this theory, emerges a quantum corrected semiclassical black hole solution called loop quantum black hole or self-dual black hole. Among the interesting features of loop quantum black holes, is the fact that they give rise to a modified entropy-area relation where quantum gravity corrections are present. In this work, we obtain a quantum corrected Newton's law from the entropy-area relation given by loop quantum black holes by using the nonrelativistic Verlinde's approach. Moreover, in order to relate our results with the recent experimental activity, we consider the quantum mechanical properties of a huge gravitational atom consisting in a light neutral elementary particle in the presence of a loop quantum black hole.
Large isotropic negative thermal expansion above a structural quantum phase transition
Handunkanda, Sahan Uddika; Curry, Erin B.; Voronov, Vladimir; Said, Ayman H.; Guzman-Verri, Gian G.; Brierley, Richard; Littlewood, Peter B.; Hancock, Jason N.
2015-10-01
Perovskite structured materials contain myriad tunable ordered phases of electronic and magnetic origin with proven technological importance and strong promise for a variety of energy solutions. An always-contributing influence beneath these cooperative and competing interactions is the lattice, whose physics may be obscured in complex perovskites by the many coupled degrees of freedom which makes these systems interesting. Here we report signatures of an approach to a quantum phase transition very near the ground state of the nonmagnetic, ionic insulating, simple cubic perovskite material ScF3 and show that its physical properties are strongly effected as much as 100 K above the putative transition. Spatial and temporal correlations in the high-symmetry cubic phase determined using energy- and momentum-resolved inelastic X-ray scattering as well as X-ray diffraction reveal that soft mode, central peak and thermal expansion phenomena are all strongly influenced by the transition.
Teleparallel loop quantum cosmology in a system of intersecting branes
NASA Astrophysics Data System (ADS)
Sepehri, Alireza; Pradhan, Anirudh; Beesham, Aroonkumar; de Haro, Jaume
2016-09-01
Recently, some authors have removed the big bang singularity in teleparallel Loop Quantum Cosmology (LQC) and have shown that the universe may undergo a number of oscillations. We investigate the origin of this type of teleparallel theory in a system of intersecting branes in M-theory in which the angle between them changes with time. This system is constructed by two intersecting anti-D8-branes, one compacted D4-brane and a D3-brane. These branes are built by joining M0-branes which develop in decaying fundamental strings. The compacted D4-brane is located between two intersecting anti-D8 branes and glues to one of them. Our universe is located on the D3 brane which wraps around the D4 brane from one end and sticks to one of the anti-D8 branes from the other one. In this system, there are three types of fields, corresponding to compacted D4 branes, intersecting branes and D3-branes. These fields interact with each other and make the angle between branes oscillate. By decreasing this angle, the intersecting anti-D8 branes approach each other, the D4 brane rolls, the D3 brane wraps around the D4 brane, and the universe contracts. By separating the intersecting branes and increasing the angle, the D4 brane rolls in the opposite direction, the D3 brane separates from it and the expansion branch begins. Also, the interaction between branes in this system gives us the exact form of the relevant Lagrangian for teleparallel LQC.
Open-loop quantum control as a resource for secure communications
NASA Astrophysics Data System (ADS)
Pastorello, Davide
2016-05-01
Properties of unitary time evolution of quantum systems can be applied to define quantum cryptographic protocols. Dynamics of a qubit can be exploited as a data encryption/decryption procedure by means of timed measurements, implementation of an open-loop control scheme over a qubit increases robustness of a protocol employing this principle.
Diffeomorphism invariant cosmological symmetry in full quantum gravity
NASA Astrophysics Data System (ADS)
Beetle, Christopher; Engle, Jonathan S.; Hogan, Matthew E.; Mendonça, Phillip
2016-06-01
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase-space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.
Chiou, D.-W.; Li Lifang
2009-03-15
A well-motivated extension of higher order holonomy corrections in loop quantum cosmology (LQC) for the k=0 Friedmann-Robertson-Walker model is investigated at the level of heuristic effective dynamics. It reveals that the quantum bounce is generic, regardless of the order of corrections, and the matter density remains finite, bounded from above by an upper bound in the regime of the Planckian density, even if all orders of corrections are included. This observation provides further evidence that the quantum bounce is essentially a consequence of the loopy nature (i.e. intrinsic discreteness) of LQC and LQC is fundamentally different from the Wheeler-DeWitt theory; it also encourages one to construct the quantum theory of LQC with the higher order holonomy corrections, which might be understood as related to the higher j representations in the Hamiltonian operator of loop quantum gravity.
Three-dimensional loop quantum gravity: Particles and the quantum double
Noui, Karim
2006-10-15
It is well known that the quantum double structure plays an important role in three-dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three-dimensional Riemannian loop quantum gravity (LQG) coupled to a finite number of massive spinless point particles. In LQG, physical states are usually constructed from the notion of SU(2) cylindrical functions on a Riemann surfaced {sigma} and the Hilbert structure is defined by the Ashtekar-Lewandowski measure. In the case where {sigma} is the sphere S{sup 2}, we show that the physical Hilbert space is in fact isomorphic to a tensor product of simple unitary representations of the Drinfeld double DSU(2): the masses of the particles label the simple representations, the physical states are tensor products of vectors of simple representations, and the physical scalar product is given by intertwining coefficients between simple representations. This result is generalized to the case of any Riemann surface {sigma}.
Three-dimensional loop quantum gravity: Particles and the quantum double
NASA Astrophysics Data System (ADS)
Noui, Karim
2006-10-01
It is well known that the quantum double structure plays an important role in three-dimensional quantum gravity coupled to matter field. In this paper, we show how this algebraic structure emerges in the context of three-dimensional Riemannian loop quantum gravity (LQG) coupled to a finite number of massive spinless point particles. In LQG, physical states are usually constructed from the notion of SU(2) cylindrical functions on a Riemann surfaced Σ and the Hilbert structure is defined by the Ashtekar-Lewandowski measure. In the case where Σ is the sphere S2, we show that the physical Hilbert space is in fact isomorphic to a tensor product of simple unitary representations of the Drinfeld double DSU(2): the masses of the particles label the simple representations, the physical states are tensor products of vectors of simple representations, and the physical scalar product is given by intertwining coefficients between simple representations. This result is generalized to the case of any Riemann surface Σ.
Invariant measure of the one-loop quantum gravitational backreaction on inflation
NASA Astrophysics Data System (ADS)
Miao, S. P.; Tsamis, N. C.; Woodard, R. P.
2017-06-01
We use dimensional regularization in pure quantum gravity on a de Sitter background to evaluate the one-loop expectation value of an invariant operator which gives the local expansion rate. We show that the renormalization of this nonlocal composite operator can be accomplished using the counterterms of a simple local theory of gravity plus matter, at least at one-loop order. This renormalization completely absorbs the one-loop correction, which accords with the prediction that the lowest secular backreaction should be a two-loop effect.
Quantum Gowdy model within the new loop quantum cosmology improved dynamics
NASA Astrophysics Data System (ADS)
Martín-Benito, M.; Garay, L. J.; Mena Marugán, G. A.
2011-09-01
The linearly polarized Gowdy T3 model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltonian constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe, with a well posed initial value problem. This fact allows us to construct the Hilbert space of physical states and to show that we recover the standard quantum field theory for the inhomogeneities.
Contact effects and quantum interference in engineered dangling bond loops on silicon surfaces
NASA Astrophysics Data System (ADS)
Kleshchonok, Andrii; Gutierrez, Rafael; Cuniberti, Gianaurelio
2015-08-01
Dangling bond structures created on H-passivated silicon surfaces offer a novel platform for engineering planar nanoscale circuits, compatible with conventional semiconductor technologies. In this investigation we focus on the electronic structure and quantum transport signatures of dangling bond loops built on H-passivated Si(100) surfaces contacted by carbon nanoribbons, thus leading to a two-terminal planar, nanoscale setup. The computational studies were carried out to rationalize the influence of the local atomic-scale contacts of the dangling bond system to the mesoscopic electrodes as well as the possibility of revealing quantum interference effects in the dangling bond loops. Our results reveal a strong sensitivity of the low-energy quantum transmission to the loop topology and to the atomistic details of the electrode-loop contact. Varying the length of the loop or the spatial position of at least one of the electrodes has a drastic impact on the quantum interference pattern; depending on whether constructive or destructive interference within the loop takes place, the conductance of the system can be tuned over several orders of magnitude, thus suggesting the possibility of exploiting such quantum mechanical effects in the design of two-dimensional, atomic-scale electronic devices such as logic gates.Dangling bond structures created on H-passivated silicon surfaces offer a novel platform for engineering planar nanoscale circuits, compatible with conventional semiconductor technologies. In this investigation we focus on the electronic structure and quantum transport signatures of dangling bond loops built on H-passivated Si(100) surfaces contacted by carbon nanoribbons, thus leading to a two-terminal planar, nanoscale setup. The computational studies were carried out to rationalize the influence of the local atomic-scale contacts of the dangling bond system to the mesoscopic electrodes as well as the possibility of revealing quantum interference effects in
Loop quantum cosmology: The horizon problem and the probability of inflation
NASA Astrophysics Data System (ADS)
Chen, Long; Zhu, Jian-Yang
2015-10-01
Anomaly-free perturbations of loop quantum cosmology reveal a deformed space-time structure, in which the signature changes when the energy density is ρ =ρc/2 . Furthermore, in loop quantum cosmology, one can obtain an effective causal structure only for a low density region (ρ ≤ρc/2 ), which gives a natural initial condition to consider the horizon problem. Choosing the initial value at ρ (0 )=ρc/2 in this paper, we investigate the horizon problem and the probability of inflation in the framework of loop quantum cosmology. Two models are considered: the quadratic inflation and the natural inflation. We use the Liouville measure to calculate the probability of inflation which solves the horizon problem, and find that, for the quadratic inflation model, the probability is very close to unity, while for the natural inflation model, the probability is about 35%.
Charge-driven feedback loop in the resonance fluorescence of a single quantum dot
NASA Astrophysics Data System (ADS)
Merkel, B.; Kurzmann, A.; Schulze, J.-H.; Strittmatter, A.; Geller, M.; Lorke, A.
2017-03-01
We demonstrate a feedback loop that manifests itself in a strong hysteresis and bistability of the exciton resonance fluorescence signal. Field ionization of photogenerated quantum dot excitons leads to the formation of a charged interface layer that drags the emission line along over a frequency range of more than 30 GHz . These measurements are well described by a rate equation model. With a time-resolved resonance fluorescence measurement we determined the buildup times for the hole gas in the orders of milliseconds. This internal charge-driven feedback loop could be used to reduce the spectral wandering in the emission spectra of single self-assembled quantum dots.
Detailed analysis of the predictions of loop quantum cosmology for the primordial power spectra
NASA Astrophysics Data System (ADS)
Agullo, Ivan; Morris, Noah A.
2015-12-01
We provide an exhaustive numerical exploration of the predictions of loop quantum cosmology with a postbounce phase of inflation for the primordial power spectrum of scalar and tensor perturbations. We extend previous analysis by characterizing the phenomenologically relevant parameter space and by constraining it using observations. Furthermore, we characterize the shape of loop quantum cosmology corrections to observable quantities across this parameter space. Our analysis provides a framework to contrast more accurately the theory with forthcoming polarization data, and it also paves the road for the computation of other observables beyond the power spectra, such as non-Gaussianity.
Black hole entropy in loop quantum gravity: The role of internal symmetries
NASA Astrophysics Data System (ADS)
Barbero G, J. Fernando
2009-06-01
I will discuss here the role of the internal symmetry group in the computations of black hole entropy in loop quantum gravity according to the standard prescription given by Domagala and Lewandowski [1]. In particular I will show how it is possible to take into account the possible choice of either SO(3) or SU(2) as the internal symmetry groups of general relativity in Loop Quantum Gravity and how this choice changes the combinatorial problem of counting the black hole degrees of freedom.
Some implications of signature-change in cosmological models of loop quantum gravity
Bojowald, Martin; Mielczarek, Jakub E-mail: jakub.mielczarek@uj.edu.pl
2015-08-01
Signature change at high density has been obtained as a possible consequence of deformed space-time structures in models of loop quantum gravity. This article provides a conceptual discussion of implications for cosmological scenarios, based on an application of mathematical results for mixed-type partial differential equations (the Tricomi problem). While the effective equations from which signature change has been derived are shown to be locally regular and therefore reliable, the underlying theory of loop quantum gravity may face several global problems in its semiclassical solutions.
Reverse quantum state engineering using electronic feedback loops
NASA Astrophysics Data System (ADS)
Kießlich, Gerold; Emary, Clive; Schaller, Gernot; Brandes, Tobias
2012-12-01
We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and, in particular, a single-electron transistor. We provide a general scheme for stabilizing pure states in the quantum system and use an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the solution of an inverse eigenvalue problem. Two applications of the feedback scheme are presented in detail: (i) stabilization of delocalized pure states in a single charge qubit and (ii) entanglement stabilization in two coupled charge qubits. In the latter example, we demonstrate the stabilization of a maximally entangled Bell state for certain detector positions and local feedback operations.
Koshnick, Nicholas C.; Bert, Julie A.; Hicks, Clifford W.; Huber, Martin E.; Moler, Kathryn A.; Large, Jeff; Edwards, Hal
2008-12-15
Superconducting quantum interference devices (SQUIDs) can have excellent spin sensitivity depending on their magnetic flux noise, pickup loop diameter, and distance from the sample. We report a family of scanning SQUID susceptometers with terraced tips that position the pickup loops 300 nm from the sample. The 600 nm-2 {mu}m pickup loops, defined by focused ion beam, are integrated into a 12-layer optical lithography process allowing flux-locked feedback, in situ background subtraction and optimized flux noise. These features enable a sensitivity of {approx}70 electron spins per root hertz at 4 K.
Quantum Faraday effect in a double-dot Aharonov-Bohm loop
NASA Astrophysics Data System (ADS)
Kang, Kicheon
2012-07-01
We investigate the role of Faraday's law of induction manifested in the quantum state of Aharonov-Bohm (AB) loops. In particular, a flux-switching experiment is proposed for a double-dot AB loop to verify the phase shift induced by Faraday's law. The induced Faraday phase is shown to be geometric and nontopological. This study demonstrates that the relation between the local phases of a ring at different fluxes is not arbitrary but is instead determined by Faraday's inductive law, which is in contrast to the arbitrary local phase of an AB loop for a given flux.
NASA Astrophysics Data System (ADS)
Balagović, Martina
2015-03-01
We show that, under Drinfeld's degeneration (Proceedings of the International Congress of Mathematicians. American Mathematical Society, Providence, pp 798-820, 1987) of quantum loop algebras to Yangians, the trigonometric dynamical difference equations [Etingof and Varchenko (Adv Math 167:74-127, 2002)] for the quantum affine algebra degenerate to the trigonometric Casimir differential equations [Toledano Laredo (J Algebra 329:286-327, 2011)] for Yangians.
Generating loop graphs via Hopf algebra in quantum field theory
Mestre, Angela; Oeckl, Robert
2006-12-15
We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number.
Two-loop renormalization of quantum gravity simplified
Bern, Zvi; Chi, Huan -Hang; Dixon, Lance; ...
2017-02-22
The coefficient of the dimensionally regularized two-loop R 3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple.more » As a result, we explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.« less
Two-loop renormalization of quantum gravity simplified
NASA Astrophysics Data System (ADS)
Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex
2017-02-01
The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.
Group field theory as the second quantization of loop quantum gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele
2016-04-01
We construct a second quantized reformulation of canonical loop quantum gravity (LQG) at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the group field theory (GFT) formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
Reconstructing the evolution of the Universe from loop quantum cosmology scalar fields
NASA Astrophysics Data System (ADS)
Oikonomou, V. K.
2016-08-01
We extend the scalar-tensor reconstruction techniques for classical cosmology frameworks, in the context of loop quantum cosmology. After presenting in some detail how the equations are generalized in the loop quantum cosmology case, we discuss which new features and limitations the quantum framework introduces, and we use various illustrative examples in order to demonstrate how the method works. As we show, the energy density has two different classes of solutions, and one of these yields the correct classical limit, while the second captures the quantum phenomena. We study in detail the scalar tensor reconstruction method for both of these solutions. We also discuss some scenarios for which the Hubble rate becomes unbounded at finite time, which corresponds for example to the case in which the big rip occurs. As we show, this issue is nontrivial and we discuss how this case should be treated in a consistent way. Finally, we investigate how the classical stability conditions for the scalar-tensor solutions are generalized in the loop quantum framework.
Surface state decoherence in loop quantum gravity, a first toy model
NASA Astrophysics Data System (ADS)
Feller, Alexandre; Livine, Etera R.
2017-02-01
The quantum-to-classical transition through decoherence is a major facet of the semi-classical analysis of quantum models that are supposed to admit a classical regime, as quantum gravity should be. A particular problem of interest is the decoherence of black hole horizons and holographic screens induced by the bulk-boundary coupling with interior degrees of freedom. Here in this paper we present a first toy-model, in the context of loop quantum gravity, for the dynamics of a surface geometry as an open quantum system. We discuss the resulting decoherence and recoherence and compare the exact density matrix evolution to the commonly used master equation approximation à la Lindblad underlining its merits and limitations. The prospect of this study is to have a clearer understanding of the boundary decoherence of black hole horizons seen by outside observers.
NASA Astrophysics Data System (ADS)
Alesci, Emanuele; Thiemann, Thomas; Zipfel, Antonia
2012-07-01
It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical loop quantum gravity. As a first test, we analyze the one-vertex expansion of a simple Euclidean spin foam. We find that for fixed Barbero-Immirzi parameter γ=1, the one-vertex amplitude in the Kaminski, Kisielowski, and Lewandowski prescription annihilates the Euclidean Hamiltonian constraint of loop quantum gravity [T. Thiemann, Classical Quantum Gravity 15, 839 (1998).]. Since, for γ=1, the Lorentzian part of the Hamiltonian constraint does not contribute, this gives rise to new solutions of the Euclidean theory. Furthermore, we find that the new states only depend on the diagonal matrix elements of the volume. This seems to be a generic property when applying the spin-foam projector.
Minimal subtraction and momentum subtraction in quantum chromodynamics at two-loop order
Braaten, E.; Leveille, J.P.
1981-09-01
The momentum-subtraction coupling constant ..cap alpha../sub MOM/ yields consistently smaller one-loop corrections to many quantum-chromodynamics (QCD) processes than the minimal-subtraction couplings ..cap alpha../sub MS/ and ..cap alpha../sub M/S. By shifting the renormalization scale ..mu.. of ..cap alpha../sub MS/(..mu..), we obtain a minimal-subtraction coupling with the same small one-loop corrections. It is shown, by studying the effective charges of QCD, that at two-loop order this coupling constant will continue to yield corrections to physical quantities that are comparable to those obtained by momentum subtraction. We also introduce a momentum-subtraction scheme which treats the triple-gluon, quark, and ghost vertices equally at one-loop order and is more convenient for higher-order calculations than the MOM scheme.
NASA Astrophysics Data System (ADS)
Krokhmalskii, Taras; Baliha, Vasyl; Derzhko, Oleg; Schulenburg, Jörg; Richter, Johannes
2017-03-01
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop-like transition in the considered isotropic spin model.
Stability of Quantum Loops and Exchange Operations in the Construction of Quantum Computation Gates
NASA Astrophysics Data System (ADS)
Bermúdez, D.; Delgado, F.
2017-05-01
Quantum information and quantum computation is a rapidly emergent field where quantum systems and their applications play a central role. In the gate version of quantum computation, the construction of universal quantum gates to manipulate quantum information is currently an intensive arena for quantum engineering. Specific properties of systems should be able to reproduce such idealized gates imitating the classically inspired computational gates. Recently, for magnetic systems driven by the bipartite Heisenberg-Ising model a universal set of gates has been realized, an alternative easy design for the Boykin set but using the Bell states as grammar. Exact control can be then used to construct specific prescriptions to achieve those gates. Physical parameters impose a challenge in the gate control. This work analyzes, based on the worst case quantum fidelity, the associated instability for the proposed set of gates. An strong performance is found in those gates for the most of quantum states involved.
Tachyon field in loop quantum cosmology: An example of traversable singularity
Li Lifang; Zhu Jianyang
2009-06-15
Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. But LQC has an ambiguity about the quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)] proposed a new quantization scheme. Similar to others, this new quantization scheme also replaces the big bang singularity with the quantum bounce. More interestingly, it introduces a quantum singularity, which is traversable. We investigate this novel dynamics quantitatively with a tachyon scalar field, which gives us a concrete example. Our result shows that our universe can evolve through the quantum singularity regularly, which is different from the classical big bang singularity. So this singularity is only a weak singularity.
SO*(2N) coherent states for loop quantum gravity
NASA Astrophysics Data System (ADS)
Girelli, Florian; Sellaroli, Giuseppe
2017-07-01
A SU(2) intertwiner with N legs can be interpreted as the quantum state of a convex polyhedron with N faces (when working in 3D). We show that the intertwiner Hilbert space carries a representation of the non-compact group SO*(2 N ) . This group can be viewed as the subgroup of the symplectic group Sp(4 N ,R ) which preserves the SU(2) invariance. We construct the associated Perelomov coherent states and discuss the notion of semi-classical limit, which is more subtle than we could expect. Our work completes the work by Freidel and Livine [J. Math. Phys. 51, 082502 (2010) and J. Math. Phys. 52, 052502 (2011)], which focused on the U (N ) subgroup of SO*(2 N ) .
Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?
Haro, Jaume de
2012-11-01
It is stated that holonomy corrections in loop quantum cosmology introduce a modification in Friedmann's equation which prevent the big rip singularity. Recently in [1] it has been proved that this modified Friedmann equation is obtained in an inconsistent way, what means that the results deduced from it, in particular the big rip singularity avoidance, are not justified. The problem is that holonomy corrections modify the gravitational part of the Hamiltonian of the system leading, after Legendre's transformation, to a non covariant Lagrangian which is in contradiction with one of the main principles of General Relativity. A more consistent way to deal with the big rip singularity avoidance is to disregard modification in the gravitational part of the Hamiltonian, and only consider inverse volume effects [2]. In this case we will see that, not like the big bang singularity, the big rip singularity survives in loop quantum cosmology. Another way to deal with the big rip avoidance is to take into account geometric quantum effects given by the the Wheeler-De Witt equation. In that case, even though the wave packets spread, the expectation values satisfy the same equations as their classical analogues. Then, following the viewpoint adopted in loop quantum cosmology, one can conclude that the big rip singularity survives when one takes into account these quantum effects. However, the spreading of the wave packets prevents the recover of the semiclassical time, and thus, one might conclude that the classical evolution of the universe come to and end before the big rip is reached. This is not conclusive because. as we will see, it always exists other external times that allows us to define the classical and quantum evolution of the universe up to the big rip singularity.
Testing the master constraint programme for loop quantum gravity: V. Interacting field theories
NASA Astrophysics Data System (ADS)
Dittrich, B.; Thiemann, T.
2006-02-01
This is the fifth and final paper in our series of five in which we test the master constraint programme for solving the Hamiltonian constraint in loop quantum gravity. Here we consider interacting quantum field theories, specifically we consider the non-Abelian Gauss constraints of Einstein Yang Mills theory and 2 + 1 gravity. Interestingly, while Yang Mills theory in 4D is not yet rigorously defined as an ordinary (Wightman) quantum field theory on Minkowski space, in background-independent quantum field theories such as loop quantum gravity (LQG) this might become possible by working in a new, background-independent representation. While for the Gauss constraint the master constraint can be solved explicitly, for the 2 + 1 theory we are only able to rigorously define the master constraint operator. We show that the, by other methods known, physical Hilbert is contained in the kernel of the master constraint, however, to systematically derive it by only using spectral methods is as complicated as for 3 + 1 gravity and we therefore leave the complete analysis for 3 + 1 gravity.
Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects
NASA Astrophysics Data System (ADS)
Craig, David A.; Singh, Parampreet
2017-04-01
We explore the structure of the spin foam-like vertex expansion in loop quantum cosmology and discuss properties of the corresponding amplitudes, with the aim of elucidating some of the expansion’s useful properties and features. We find that the expansion is best suited for consideration of conceptual questions and for investigating short-time, highly quantum behavior. In order to study dynamics at cosmological scales, the expansion must be carried to very high order, limiting its direct utility as a calculational tool for such questions. Conversely, it is unclear that the expansion can be truncated at finite order in a controlled manner.
A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity
NASA Astrophysics Data System (ADS)
Cattaneo, Alberto S.; Perez, Alejandro
2017-05-01
We show that the non-Abelian nature of geometric fluxes—the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG)—follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.
NASA Astrophysics Data System (ADS)
Takeda, Shuntaro; Furusawa, Akira
2017-09-01
We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically processed in a nested loop by an electrically programmable gate sequence. This architecture can process any input state and an arbitrary number of modes with almost minimum resources, and offers a universal gate set for both qubits and continuous variables. Furthermore, quantum computing can be performed fault tolerantly by a known scheme for encoding a qubit in an infinite-dimensional Hilbert space of a single light mode.
Analysing Hessence Intermediate and Logamediate Universe in Loop Quantum Cosmological Background
NASA Astrophysics Data System (ADS)
Mandal, Jyotirmay Das; Debnath, Ujjal
2017-06-01
We have discussed here Hessence inflation in Loop Quantum Cosmological background. In this work, we have emphasized on late times, taking into account various slow-roll conditions. This model has been constructed taking intermediate and logamediate scale factors. In both cases the forms of hessence field, potential, number of e-folds, slow-roll parameters are manipulated by taking the dissipative co-efficient Γ =Γ0, where Γ0 > 0 is a constant, in accordance with second law of thermodynamics.
Black holes in loop quantum gravity: the complete space-time.
Gambini, Rodolfo; Pullin, Jorge
2008-10-17
We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.
Black hole state counting in loop quantum gravity: a number-theoretical approach.
Agulló, Iván; Barbero G, J Fernando; Díaz-Polo, Jacobo; Fernández-Borja, Enrique; Villaseñor, Eduardo J S
2008-05-30
We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.
Denseness of Ashtekar Lewandowski states and a generalized cut-off in loop quantum gravity
NASA Astrophysics Data System (ADS)
Velhinho, J. M.
2005-07-01
We show that the set of states of the Ashtekar Isham Lewandowski holonomy algebra defined by elements of the Ashtekar Lewandowski Hilbert space is dense in the space of all states. We consider weak convergence properties of a modified version of the cut-off procedure currently in use in loop quantum gravity. This version is adapted to vector states rather than to general distributions.
One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
Ellis, R. Keith; Kunszt, Zoltan; Melnikov, Kirill; Zanderighi, Giulia
2012-09-01
The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of one-loop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques become inefficient. Recently new approaches based on unitarity have been developed for calculating one-loop scattering amplitudes in quantum field theory. These methods are especially suitable for the description of multi-particle processes in QCD and are amenable to numerical implementations. We present a systematic pedagogical description of both conceptual and technical aspects of the new methods.
Self-dual black holes in loop quantum gravity: Theory and phenomenology
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Prémont-Schwarz, Isabeau
2009-09-01
In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner-Nordström-like metric is self-dual in the sense of T-duality: the form of the metric obtained in loop quantum gravity is invariant under the exchange r→a0/r where a0 is proportional to the minimum area in loop quantum gravity and r is the standard Schwarzschild radial coordinate at asymptotic infinity. Of particular interest, the symmetry imposes that if an observer in r→+∞ sees a black hole of mass m an observer in the other asymptotic infinity beyond the horizon (at r≈0) sees a dual mass mP/m. We then show that small LQBH are stable and could be a component of dark matter. Ultralight LQBHs created shortly after the big bang would now have a mass of approximately 10-5mP and emit radiation with a typical energy of about 1013-1014eV but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way’s Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultralight black holes would be compatible with the observed rate of the Auger detector.
The perturbed universe in the deformed algebra approach of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Grain, Julien
2016-06-01
Loop Quantum Cosmology (LQC) is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical spacetime is inspired by Loop Quantum Gravity (LQG) ideas. In addition, LQC could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modelings in the light of observations. To do so however, modeling both the background evolution and its perturbations is needed. The latter described cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, assuming initial conditions are set in the contracting phase preceding the quantum bounce and the well-known expanding phase of the cosmic history. These spectra are subsequently propagated to angular power spectra of the anisotropies of the cosmic microwave background. It is then shown that regardless of the choice for the initial conditions inside the effective approach for the background evolution (except that they are set in the contracting phase), the predicted angular power spectra of the polarized B-modes exceed the upper bound currently set by observations. The exclusion of this specific version of LQC establishes the falsifiability of the approach, though one shall not conclude here that either LQC or LQG excluded.
Non-singular bounce scenarios in loop quantum cosmology and the effective field description
Cai, Yi-Fu; Wilson-Ewing, Edward E-mail: wilson-ewing@phys.lsu.edu
2014-03-01
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmology and in a non-singular bouncing effective field model with a non-standard kinetic term at both the background and perturbative levels. We find that these two settings share many important properties, including the result that they both generate scale-invariant scalar perturbations. This shows that some quantum gravity effects of the very early universe may be mimicked by effective field models.
Properties of the volume operator in loop quantum gravity: I. Results
NASA Astrophysics Data System (ADS)
Brunnemann, Johannes; Rideout, David
2008-03-01
We analyze the spectral properties of the volume operator of Ashtekar and Lewandowski in loop quantum gravity, which is the quantum analog of the classical volume expression for regions in three-dimensional Riemannian space. Our analysis considers for the first time generic graph vertices of valence greater than four. Here we find that the geometry of the underlying vertex characterizes the spectral properties of the volume operator; in particular the presence of a 'volume gap' (a smallest non-zero eigenvalue in the spectrum) is found to depend on the vertex embedding. We compute the set of all non-spatially diffeomorphic non-coplanar vertex embeddings for vertices of valence 5 7, and argue that these sets can be used to label spatial diffeomorphism invariant states. We observe how gauge invariance connects vertex geometry and representation properties of the underlying gauge group in a natural way. Analytical results on the spectrum of 4-valent vertices are included, for which the presence of a volume gap is shown. This paper presents our main results; details are provided by a companion paper (Brunnemann and Rideout 2007 Properties of the volume operator in loop quantum gravity: II. Detailed presentation Class. Quantum Grav. 25 065002).
Correlation effects and quantum oscillations in topological nodal-loop semimetals
NASA Astrophysics Data System (ADS)
Liu, Jianpeng; Balents, Leon
2017-02-01
We study the unique physical properties of topological nodal-loop semimetals protected by the coexistence of time-reversal and inversion symmetries with negligible spin-orbit coupling. We argue that strong correlation effects occur at the surface of such systems for relatively small Hubbard interaction U , due to the narrow bandwidth of the "drumhead" surface states. In the Hartree-Fock approximation, at small U we obtain a surface ferromagnetic phase through a continuous quantum phase transition characterized by the surface-mode divergence of the spin susceptibility, while the bulk states remain very robust against local interactions and remain nonordered. At slightly increased interaction strength, the system quickly changes from a surface ferromagnetic phase to a surface charge-ordered phase through a first-order transition. When Rashba-type spin-orbit coupling is applied to the surface states, a canted ferromagnetic phase occurs at the surface for intermediate values of U . The quantum critical behavior of the surface ferromagnetic transition is nontrivial in the sense that the surface spin order parameter couples to Fermi-surface excitations from both surface and bulk states. This leads to unconventional Landau damping and consequently a naïve dynamical critical exponent z ≈1 when the Fermi level is close to the bulk nodal energy. We also show that, already without interactions, quantum oscillations arise due to bulk states, despite the absence of a Fermi surface when the chemical potential is tuned to the energy of the nodal loop. The bulk magnetic susceptibility diverges logarithmically whenever the nodal loop exactly overlaps with a quantized magnetic orbit in the bulk Brillouin zone. These correlation and transport phenomena are unique signatures of nodal-loop states.
Kinematical uniqueness of homogeneous isotropic LQC
NASA Astrophysics Data System (ADS)
Engle, Jonathan; Hanusch, Maximilian
2017-01-01
In a paper by Ashtekar and Campiglia, invariance under volume preserving residual diffeomorphisms has been used to single out the standard representation of the reduced holonomy-flux algebra in homogeneous loop quantum cosmology (LQC). In this paper, we use invariance under all residual diffeomorphisms to single out the standard kinematical Hilbert space of homogeneous isotropic LQC for both the standard configuration space {{{R}}\\text{Bohr}} , as well as for the Fleischhack one {R}\\sqcup {{{R}}\\text{Bohr}} . We first determine the scale invariant Radon measures on these spaces, and then show that the Haar measure on {{{R}}\\text{Bohr}} is the only such measure for which the momentum operator is hermitian w.r.t. the corresponding inner product. In particular, the measure is forced to be identically zero on {R} in the Fleischhack case, so that for both approaches, the standard kinematical LQC-Hilbert space is singled out.
NASA Astrophysics Data System (ADS)
Lewandowski, Jerzy; Lin, Chun-Yen
2017-03-01
We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity, in a large subspace of the model's kinematic Hilbert space, which is the space of the charge network states. In doing so, we first identified the subspace on which each of the constraints acts convergingly, and then by explicitly evaluating such actions we found the complete set of the solutions in the identified subspace. We showed that the space of solutions consists of two classes of states, with the first class having a property that involves the condition known from the Minkowski theorem on polyhedra, and the second class satisfying a weaker form of the spatial diffeomorphism invariance.
Simple way to calculate a UV-finite one-loop quantum energy in the Randall-Sundrum model
NASA Astrophysics Data System (ADS)
Altshuler, Boris L.
2017-04-01
The surprising simplicity of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants permits us to obtain compact expressions for a UV-finite difference of one-loop quantum energies for two arbitrary values of the parameter of the double-trace asymptotic boundary conditions. This result generalizes the Gubser and Mitra calculation for the particular case of difference of "regular" and "irregular" one-loop energies in the one-brane Randall-Sundrum model. The approach developed in the paper also allows us to get "in one line" the one-loop quantum energies in the two-brane Randall-Sundrum model. The relationship between "one-loop" expressions corresponding to the mixed Robin and to double-trace asymptotic boundary conditions is traced.
A general transfer-function approach to noise filtering in open-loop quantum control
NASA Astrophysics Data System (ADS)
Viola, Lorenza
2015-03-01
Hamiltonian engineering via unitary open-loop quantum control provides a versatile and experimentally validated framework for manipulating a broad class of non-Markovian open quantum systems of interest, with applications ranging from dynamical decoupling and dynamically corrected quantum gates, to noise spectroscopy and quantum simulation. In this context, transfer-function techniques directly motivated by control engineering have proved invaluable for obtaining a transparent picture of the controlled dynamics in the frequency domain and for quantitatively analyzing performance. In this talk, I will show how to identify a computationally tractable set of ``fundamental filter functions,'' out of which arbitrary filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. I will show, in particular, how the resulting notion of ``filtering order'' reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the ``cancellation order,'' traditionally defined in the Magnus sense. Implications for current quantum control experiments will be discussed. Work supported by the U.S. Army Research Office under Contract No. W911NF-14-1-0682.
Callan-Giddings-Harvey-Strominger vacuum in loop quantum gravity and singularity resolution
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Olmedo, Javier; Rastgoo, Saeed
2016-10-01
We study here a complete quantization of a Callan-Giddings-Harvey-Strominger vacuum model following loop quantum gravity techniques. Concretely, we adopt a formulation of the model in terms of a set of new variables that resemble the ones commonly employed in spherically symmetric loop quantum gravity. The classical theory consists of two pairs of canonical variables plus a scalar and diffeomorphism (first class) constraints. We consider a suitable redefinition of the Hamiltonian constraint such that the new constraint algebra (with structure constants) is well adapted to the Dirac quantization approach. For it, we adopt a polymeric representation for both the geometry and the dilaton field. On the one hand, we find a suitable invariant domain of the scalar constraint operator, and we construct explicitly its solution space. There, the eigenvalues of the dilaton and the metric operators cannot vanish locally, allowing us to conclude that singular geometries are ruled out in the quantum theory. On the other hand, the physical Hilbert space is constructed out of them, after group averaging the previous states with the diffeomorphism constraint. In turn, we identify the standard observable corresponding to the mass of the black hole at the boundary, in agreement with the classical theory. We also construct an additional observable on the bulk associated with the square of the dilaton field, with no direct classical analog.
Properties of the volume operator in loop quantum gravity: II. Detailed presentation
NASA Astrophysics Data System (ADS)
Brunnemann, Johannes; Rideout, David
2008-03-01
The properties of the volume operator in loop quantum gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater than four. We find that the occurrence of a smallest non-zero eigenvalue is dependent upon the geometry of the underlying graph and is not a property of the volume operator itself. The present analysis benefits from the general simplified formula for matrix elements of the volume operator derived in Brunnemann and Thiemann (2006 Class. Quantum Grav. 23 1289), making it feasible to implement it on a computer as a matrix which is then diagonalized numerically. The resulting eigenvalues serve as a database to investigate the spectral properties of the volume operator. Analytical results on the spectrum at 4-valent vertices are included. This is a companion paper to Brunnemann and Rideout (2007 Properties of the volume operator in loop quantum gravity: I. Results Preprint 0706.0469), providing details of the analysis presented there.
Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity
NASA Astrophysics Data System (ADS)
Yang, Jinsong; Ma, Yongge
2017-04-01
To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature.
Quantum Chemical Studies on Stability and Chemical Activities in Calcium Ion Bound Calmodulin Loops.
Sikdar, Samapan; Ghosh, Mahua; De Raychaudhury, Molly; Chakrabarti, J
2015-11-19
Quantum chemical (QC) calculations for macromolecules require truncation of the molecule, highlighting the portion of interest due to heavy computation cost. As a result, an estimation of the effects of truncation is important to interpret the energy spectrum of such calculations. We perform density functional theory based QC calculations on calcium ion bound EF-hand loops of Calmodulin isolated from the crystal structure in an implicit solvent. We find that the terminal contributions of neutral capping are negligible across the entire ground-state energy spectrum. The coordination energy range and the nature of hybridization of the coordination state molecular orbitals remain qualitatively similar across these loops. While the HOMO and LUMO of loops in the N-terminal domain are dominated by the acidic aspartates, and the polar/hydrophobic residues, respectively, these levels of the C-terminal domain loops show strong localized electron density on the phenyl rings of the tyrosines. The Fukui index calculation identifies the hydroxyl oxygen in the phenyl ring of Y99 as a potent nucleophile. Our analysis indicates a general way of interpreting the electronic energy spectra to understand stability and functions of large biomolecules where the truncation of the molecule and, hence, the terminal capping effects are inevitable.
Uniqueness of the Representation in Homogeneous Isotropic LQC
NASA Astrophysics Data System (ADS)
Engle, Jonathan; Hanusch, Maximilian; Thiemann, Thomas
2017-08-01
We show that the standard representation of homogeneous isotropic loop quantum cosmology (LQC) is the GNS-representation that corresponds to the unique state on the reduced quantum holonomy-flux *-algebra that is invariant under residual diffeomorphisms— both when the standard algebra is used as well as when one uses the extended algebra proposed by Fleischhack. More precisely, we find that in both situations the GNS-Hilbert spaces coincide, and that in the Fleischhack case the additional algebra elements are just mapped to zero operators. In order for the residual diffeomorphisms to have a well-defined action on the quantum algebra, we have let them act on the fiducial cell as well as on the dynamical variables, thereby recovering covariance. Consistency with Ashtekar and Campilgia in the Bianchi case is also shown.
Inflation in loop quantum cosmology: Dynamics and spectrum of gravitational waves
Mielczarek, Jakub; Cailleteau, Thomas; Grain, Julien; Barrau, Aurelien
2010-05-15
Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Because of holonomy corrections, the singularity is replaced by a 'bounce'. The dynamics of the background is investigated into the details, as a function of the parameters of the model. In particular, the conditions required for inflation to occur are carefully considered and are shown to be generically met. The propagation of gravitational waves is then investigated in this framework. By both numerical and analytical approaches, the primordial tensor power spectrum is computed for a wide range of parameters. Several interesting features could be observationally probed.
Fine-grained state counting for black holes in loop quantum gravity.
Ghosh, A; Mitra, P
2009-04-10
A state of a black hole in loop quantum gravity is given by a distribution of spins on punctures on the horizon. The distribution is of the Boltzmann type, with the area playing the role of the energy. In investigations where the total area was kept approximately constant, there was a kind of thermal equilibrium between the spins which have the same analogue temperature and the entropy was proportional to the area. If the area is precisely fixed, however, multiple constraints appear, different spins have different analogue temperatures and the entropy is not strictly linear in the area, but is bounded by a linear rise.
NASA Astrophysics Data System (ADS)
Das Mandal, Jyotirmay; Debnath, Ujjal
2016-08-01
We have studied the tachyon intermediate and logamediate warm inflation in loop quantum cosmological background by taking the dissipative co-efficient Γ = Γ0 (where Γ0 is a constant) in “intermediate” inflation and Γ = V(ϕ), (where V(ϕ) is the potential of tachyonic field) in “logamediate” inflation. We have assumed slow-roll condition to construct scalar field ϕ, potential V, N-folds, etc. Various slow-roll parameters have also been obtained. We have analyzed the stability of this model through graphical representations.
Signature change in loop quantum gravity: Two-dimensional midisuperspace models and dilaton gravity
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Brahma, Suddhasattwa
2017-06-01
Models of loop quantum gravity based on real connections have a deformed notion of general covariance, which leads to the phenomenon of signature change. This result is confirmed here in a general analysis of all midisuperspace models without local degrees of freedom. As a subclass of models, two-dimensional theories of dilaton gravity appear, but a larger set of examples is possible based only on the condition of anomaly freedom. While the classical dilaton gravity models are the only such systems without deformed covariance, they do give rise to signature change when holonomy modifications are included.
Thibault, Franck; Boulet, Christian; Ma, Qiancheng
2014-01-28
We present quantum calculations of the relaxation matrix for the Q branch of N{sub 2} at room temperature using a recently proposed N{sub 2}-N{sub 2} rigid rotor potential. Close coupling calculations were complemented by coupled states studies at high energies and provide about 10 200 two-body state-to state cross sections from which the needed one-body cross-sections may be obtained. For such temperatures, convergence has to be thoroughly analyzed since such conditions are close to the limit of current computational feasibility. This has been done using complementary calculations based on the energy corrected sudden formalism. Agreement of these quantum predictions with experimental data is good, but the main goal of this work is to provide a benchmark relaxation matrix for testing more approximate methods which remain of a great utility for complex molecular systems at room (and higher) temperatures.
NASA Technical Reports Server (NTRS)
Thibault, Franck; Boulet, Christian; Ma, Qiancheng
2014-01-01
We present quantum calculations of the relaxation matrix for the Q branch of N2 at room temperature using a recently proposed N2-N2 rigid rotor potential. Close coupling calculations were complemented by coupled states studies at high energies and provide about 10200 two-body state-to state cross sections from which the needed one-body cross-sections may be obtained. For such temperatures, convergence has to be thoroughly analyzed since such conditions are close to the limit of current computational feasibility. This has been done using complementary calculations based on the energy corrected sudden formalism. Agreement of these quantum predictions with experimental data is good, but the main goal of this work is to provide a benchmark relaxation matrix for testing more approximate methods which remain of a great utility for complex molecular systems at room (and higher) temperatures.
Oscillatory universes in loop quantum cosmology and initial conditions for inflation
Lidsey, James E.; Mulryne, David J.; Nunes, N. J.; Tavakol, Reza
2004-09-15
Positively curved oscillatory universes are studied within the context of loop quantum cosmology subject to a consistent semiclassical treatment. The semiclassical effects are reformulated in terms of an effective phantom fluid with a variable equation of state. In cosmologies sourced by a massless scalar field, these effects lead to a universe that undergoes ever-repeating cycles of expansion and contraction. The presence of a self-interaction potential for the field breaks the symmetry of the cycles and can enable the oscillations to establish the initial conditions for successful slow-roll inflation, even when the field is initially at the minimum of its potential with a small kinetic energy. The displacement of the field from its minimum is enhanced for lower and more natural values of the parameter that sets the effective quantum gravity scale. For sufficiently small values of this parameter, the universe can enter a stage of eternal self-reproduction.
Loop quantum cosmology of the k=1 FRW: A tale of two bounces
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Karami, Asieh
2011-08-01
We consider the k=1 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process. In spatially nonflat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible. Instead, one has to implement the quantum constraints by approximating the connection via open holonomies. In the case of flat k=0 FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed k=1 FRW model they might yield different quantum theories. In this manuscript we explore these two quantizations and the different effective descriptions they provide of the bouncing cyclic universe. In particular, as we show in detail, the most dramatic difference is that in the theory defined by the new quantization method, there is not one, but two different bounces through which the cyclic universe alternates. We show that for a “large” universe, these two bounces are very similar and, therefore, practically indistinguishable, approaching the dynamics of the “curvature-based” quantum theory.
Gravitational lensing by self-dual black holes in loop quantum gravity
NASA Astrophysics Data System (ADS)
Sahu, Satyabrata; Lochan, Kinjalk; Narasimha, D.
2015-03-01
We study gravitational lensing by a recently proposed black hole solution in loop quantum gravity. We highlight the fact that the quantum gravity corrections to the Schwarzschild metric in this model evade the "mass suppression" effects (that the usual quantum gravity corrections are susceptible to) by virtue of one of the parameters in the model being dimensionless, which is unlike any other quantum gravity motivated parameter. Gravitational lensing in the strong and weak deflection regimes is studied, and a sample consistency relation is presented which could serve as a test of this model. We discuss that, though the consistency relation for this model is qualitatively similar to what would have been in Brans-Dicke, in general it can be a good discriminator between many alternative theories. Although the observational prospects do not seem to be very optimistic even for a galactic supermassive black hole case, time delay between relativistic images for a billion solar mass black holes in other galaxies might be within reach of future relativistic lensing observations.
Scalar and tensor perturbations in loop quantum cosmology: high-order corrections
Zhu, Tao; Wang, Anzhong; Wu, Qiang; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin E-mail: anzhong_wang@baylor.edu E-mail: klaus_kirsten@baylor.edu E-mail: wuq@zjut.edu.cn
2015-10-01
Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using the third-order uniform asymptotic approximations, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are ∼< 0.15%, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.
Scalar and tensor perturbations in loop quantum cosmology: high-order corrections
NASA Astrophysics Data System (ADS)
Zhu, Tao; Wang, Anzhong; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin; Wu, Qiang
2015-10-01
Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using the third-order uniform asymptotic approximations, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are lesssim 0.15%, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.
NASA Astrophysics Data System (ADS)
Heidmann, P.; Liu, H.; Noui, K.
2017-02-01
We introduce the notion of fluid approximation of a quantum spherical black hole in the context of loop quantum gravity. In this limit, the microstates of the black hole are intertwiners between "large" representations si that typically scale as si˜√{aH } where aH denotes the area of the horizon in Planck units. The punctures with large colors are, for the black hole horizon, similar to what the fluid parcels are for a classical fluid. We dub them puncels. Hence, in the fluid limit, the horizon is composed by puncels that are themselves interpreted as composed (in the sense of the tensor product) by a large number of more fundamental intertwiners. We study the spectrum of the Euclidean volume acting on puncels and we compute its quantum fluctuations. Then, we propose an interpretation of black hole radiation based on the properties of the quantum fluctuations of the Euclidean volume operator. We estimate a typical temperature of the black hole and we show that it scales as the Hawking temperature.
2007-11-30
require only sequences of simple control pulses such as square wave pulses with finite rise and decay times or Gaussian wavepackets . To illustrate the...21. Quantum Optimal Control of Wave Packet Dynamics under the Influence of Dissipation. Optimal control within the density matrix formalism is...directly in terms of the physically relevant control field and the density matrix at the target time, including an elaboration of the topology around
NASA Astrophysics Data System (ADS)
Aldaya, V.; Navarro-Salas, J.
1991-04-01
We introduce a highest weight type representation of the Rovelli-Smolin algebra of loop observables for quantum gravity. In terms of this representation, new solutions of the hamiltonian and diffeomorphism constraints are given. Assuming the locality of the quantum hamiltonian constraint we show that any functional depending on the generalized link class of the disjoint union of arbitrary simple loops is a solution. Finally we argue that this is the general solution in the irreducible representation space. On leave of absence from the Departamento de Fisica Teorica, Universidad de Valencia, and IFIC, Centro Mixto Universidad de Valencia - CSIC, Burjassot, Spain.
Quantum gravity slows inflation
Tsamis, N.C. |; Woodard, R.P.
1996-02-01
We consider the quantum gravitational back-reaction on an initially inflating, homogeneous and isotropic universe whose topology is T{sup 3} {times} {Re}. Although there is no secular effect at one loop, an explicit calculation shows that two-loop processes act to slow the rate of expansion by an amount which becomes non-pertubatively large at late times. By exploiting Feynman`s tree theorem we show that all higher loops act in the same sense. 18 refs., 1 fig.
NASA Astrophysics Data System (ADS)
Chien, Chihchun; Metcalf, Mekena; Lai, Chenyen
2016-05-01
Memory effects are observable in magnetization, rechargeable batteries, and many systems exhibiting history-dependent states. Quantum memory effects are observable, for instance, in atomic superfluids. A counter-intuitive question is whether quantum memory effects can exist in noninteracting systems. Here we present two examples of cold-atom systems demonstrating memory effects in noninteracting systems. The first example is a ring-shaped potential loaded with noninteracting fermions. An artificial vector potential drives a current and with a tunable dissipative background, the current lags behind the driving and exhibits hysteresis loops. The dissipative energy can be controlled by the coupling between the fermions and the background. In the second example, cold atoms loaded in a tunable optical lattice transformed from the triangular to the kagome geometry. The kagome lattice supports a flat-band consisting of degenerate localized states. Quantum memory effects are observable after a lattice transformation as the steady-state density depends on the rate of the transformation. The versatility of memory effects in cold-atom systems promises novel applications in atomtronics.
NASA Astrophysics Data System (ADS)
Grillo, Nicola
2001-02-01
Quantum gravity coupled to scalar massive matter fields is investigated in the framework of causal perturbation theory using the Epstein-Glaser regularization/renormalization scheme. Detailed one-loop calculations include the matter loop graviton self-energy and the matter self-energy. The condition of perturbative operator gauge invariance to second order implies the usual Slavnov-Ward identities for the graviton two-point connected Green function in the loop graph sector and generates the correct quartic graviton-matter interaction in the tree graph sector. The mass zero case is also discussed.
NASA Astrophysics Data System (ADS)
Wu, Chiu-Hsien; Yang, Hong-Chang; Chen, Ji-Cheng; Chen, Kuen-Lin; Chen, M. J.; Jeng, J. T.; Horng, Herng-Er
2006-09-01
In this work, we studied the engineering of high-transition-temperature superconductor Josephson junctions and superconducting quantum interference device (SQUID) by using step-edge or the bicrystal grain-boundary technologies. Serial Josephson junctions and bare SQUID array reveal high quality device characteristics. A high-Tc SQUID magnetometer exhibiting magnetic field sensitivity of 33fT/Hz1/2 in the white regime and 80fT/Hz1/2 at 1Hz was demonstrated by incorporating the flux dams and serial SQUID into the pickup loop of magnetometer. Furthermore, we demonstrate the opening of the flux dams by applying an external magnetic field to induce a current higher than the critical current of the serial flux dams. We show that the serial flux dams effectively suppress the low frequency 1/f-like noises.
General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control
NASA Astrophysics Data System (ADS)
Paz-Silva, Gerardo A.; Viola, Lorenza
2014-12-01
We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-function set suffices to characterize the error suppression capabilities of the control protocol in both the time and the frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.
Slow-roll inflation in loop quantum cosmology of scalar-tensor theories of gravity
NASA Astrophysics Data System (ADS)
Han, Yu
2015-07-01
The slow-roll inflation of scalar-tensor theories (STTs) of gravity in the context of loop quantum cosmology (LQC) is investigated in this paper. After deriving the effective Hamiltonian, we obtain the semiclassical equations of motion for the background variables in both Jordan frame and Einstein frame of STTs. Then we apply these equations in the slow-roll limit and derive the LQC corrections to the scalar spectral index ns and the tensor-to-scalar ratio r in the two frames of STTs. Finally, we take two special sectors of STTs as specific examples, namely the Starobinsky model and the non-minimally coupled scalar field model (with the coupling function ξϕ2R and the potential λ 4 ϕ4). We derive the detailed expressions of the LQC corrections to ns and r in terms of the e-folding number for these two models in both frames.
Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
Chiou, D.-W.
2008-08-15
The fundamental theory and the semiclassical description of loop quantum cosmology (LQC) have been studied in the Friedmann-Robertson-Walker and Bianchi I models. As an extension to include both anisotropy and intrinsic curvature, this paper investigates the cosmological model of Kantowski-Sachs spacetime with a free massless scalar field at the level of phenomenological dynamics with the LQC discreteness corrections. The LQC corrections are implemented in two different improved quantization schemes. In both schemes, the big bang and big crunch singularities of the classical solution are resolved and replaced by the big bounces when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. Symmetries of scaling are also noted and suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale. The bouncing scenarios are in an analogous fashion of the Bianchi I model, naturally extending the observations obtained previously.
Quantum interference based Boolean gates in dangling bond loops on Si(100):H surfaces.
Kleshchonok, Andrii; Gutierrez, Rafael; Joachim, Christian; Cuniberti, Gianaurelio
2015-09-15
Implementing atomic and molecular scale electronic functionalities represents one of the major challenges in current nano-electronic developments. Engineered dangling bond nanostructures on Silicon or Germanium surfaces posses the potential to provide novel routes towards the development of non-conventional electronic circuits. These structures are built by selectively removing hydrogen atoms from an otherwise fully passivated Si(100) or Ge(100) substrate. In this theoretical study, we demonstrate how dangling bond loops can be used to implement different Boolean logic gates. Our approach exploits quantum interference effects in such ring-like structures combined with an appropriate design of the interfacing of the dangling bond system with mesoscopic electrodes. We show how OR, AND, and NOR gates can be realized by tuning either the global symmetry of the system in a multi-terminal setup—by arranging the position of the input and output electrodes—or, alternatively, by selectively applying electrostatic gates in a two-terminal configuration.
Quantum interference based Boolean gates in dangling bond loops on Si(100):H surfaces
NASA Astrophysics Data System (ADS)
Kleshchonok, Andrii; Gutierrez, Rafael; Joachim, Christian; Cuniberti, Gianaurelio
2015-09-01
Implementing atomic and molecular scale electronic functionalities represents one of the major challenges in current nano-electronic developments. Engineered dangling bond nanostructures on Silicon or Germanium surfaces posses the potential to provide novel routes towards the development of non-conventional electronic circuits. These structures are built by selectively removing hydrogen atoms from an otherwise fully passivated Si(100) or Ge(100) substrate. In this theoretical study, we demonstrate how dangling bond loops can be used to implement different Boolean logic gates. Our approach exploits quantum interference effects in such ring-like structures combined with an appropriate design of the interfacing of the dangling bond system with mesoscopic electrodes. We show how OR, AND, and NOR gates can be realized by tuning either the global symmetry of the system in a multi-terminal setup—by arranging the position of the input and output electrodes—or, alternatively, by selectively applying electrostatic gates in a two-terminal configuration.
A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce
NASA Astrophysics Data System (ADS)
Chinaglia, Stefano; Colléaux, Aimeric; Zerbini, Sergio
2017-09-01
Recently the so-called mimetic gravity approach has been used to obtain corrections to Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists in adding geometric non-polynomial higher derivative terms to Hilbert-Einstein action, which are nonetheless polynomials and lead to second order differential equation in Friedmann-Lema\\^itre-Robertson-Walker spacetimes. Our explicit action turns out to be a realization of the Helling proposal of effective action with infinite number of terms. The model is investigated also in presence of non vanishing cosmological constant and a new exact bounce solution is found and studied.
Einstein equation from covariant loop quantum gravity in semiclassical continuum limit
NASA Astrophysics Data System (ADS)
Han, Muxin
2017-07-01
In this paper we explain how four-dimensional general relativity and, in particular, the Einstein equation, emerge from the spin-foam amplitude in loop quantum gravity. We propose a new limit that couples both the semiclassical limit and continuum limit of spin-foam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of the Einstein equation can be approached by dominant configurations in spin-foam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important ingredient in the derivation is a regularization for the sum over spins, which is necessary for the semiclassical continuum limit. We also explain in this paper the role played by the so-called flatness in spin-foam formulation, and how to take advantage of it.
Coherent 3 j -symbol representation for the loop quantum gravity intertwiner space
NASA Astrophysics Data System (ADS)
Alesci, E.; Lewandowski, J.; Mäkinen, I.
2016-10-01
We introduce a new technique for dealing with the matrix elements of the Hamiltonian operator in loop quantum gravity, based on the use of intertwiners projected on coherent states of angular momentum. We give explicit expressions for the projections of intertwiners on the spin coherent states in terms of complex numbers describing the unit vectors which label the coherent states. Operators such as the Hamiltonian can then be reformulated as differential operators acting on polynomials of these complex numbers. This makes it possible to describe the action of the Hamiltonian geometrically, in terms of the unit vectors originating from the angular momentum coherent states, and opens up a way towards investigating the semiclassical limit of the dynamics via asymptotic approximation methods.
Seeking the loop quantum gravity Barbero-Immirzi parameter and field in 4D, N=1 supergravity
Gates, S. James Jr.; Ketov, Sergei V.; Yunes, Nicolas
2009-09-15
We embed the loop quantum gravity Barbero-Immirzi parameter and field within an action describing 4D, N=1 supergravity and thus within a low-energy effective action of superstring/M theory. We use the fully gauge-covariant description of supergravity in (curved) superspace. The gravitational constant is replaced with the vacuum expectation value of a scalar field, which in local supersymmetry is promoted to a complex, covariantly chiral scalar superfield. The imaginary part of this superfield couples to a supersymmetric Holst term. The Holst term also serves as a starting point in the loop quantum gravity action. This suggest the possibility of a relation between loop quantum gravity and supersymmetric string theory, where the Barbero-Immirzi parameter and field of the former play the role of the supersymmetric axion in the latter. Adding matter fermions in loop quantum gravity may require the extension of the Holst action through the Nieh-Yan topological invariant, while in pure, matter-free supergravity their supersymmetric extensions are the same. We show that, when the Barbero-Immirzi parameter is promoted to a field in the context of 4D supergravity, it is equivalent to adding a dynamical complex chiral (dilaton-axion) superfield with a nontrivial kinetic term (or Kaehler potential), coupled to supergravity.
Seeking the loop quantum gravity Barbero-Immirzi parameter and field in 4D, N=1 supergravity
NASA Astrophysics Data System (ADS)
Gates, S. James, Jr.; Ketov, Sergei V.; Yunes, Nicolás
2009-09-01
We embed the loop quantum gravity Barbero-Immirzi parameter and field within an action describing 4D, N=1 supergravity and thus within a low-energy effective action of superstring/M theory. We use the fully gauge-covariant description of supergravity in (curved) superspace. The gravitational constant is replaced with the vacuum expectation value of a scalar field, which in local supersymmetry is promoted to a complex, covariantly chiral scalar superfield. The imaginary part of this superfield couples to a supersymmetric Holst term. The Holst term also serves as a starting point in the loop quantum gravity action. This suggest the possibility of a relation between loop quantum gravity and supersymmetric string theory, where the Barbero-Immirzi parameter and field of the former play the role of the supersymmetric axion in the latter. Adding matter fermions in loop quantum gravity may require the extension of the Holst action through the Nieh-Yan topological invariant, while in pure, matter-free supergravity their supersymmetric extensions are the same. We show that, when the Barbero-Immirzi parameter is promoted to a field in the context of 4D supergravity, it is equivalent to adding a dynamical complex chiral (dilaton-axion) superfield with a nontrivial kinetic term (or Kähler potential), coupled to supergravity.
Effective dynamics, big bounces, and scaling symmetry in Bianchi type I loop quantum cosmology
Chiou, D.-W.
2007-12-15
The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to 3 times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.
Projective loop quantum gravity. II. Searching for semi-classical states
NASA Astrophysics Data System (ADS)
Lanéry, Suzanne; Thiemann, Thomas
2017-05-01
In the first paper of this series, an extension of the Ashtekar-Lewandowski state space of loop quantum gravity was set up with the help of a projective formalism introduced by Kijowski. The motivation for this work was to achieve a more balanced treatment of the position and momentum variables (also known as holonomies and fluxes). While this is the first step toward the construction of states semi-classical with respect to a full set of observables, one uncovers a deeper issue, which we analyse in the present article in the case of real-valued holonomies. Specifically, we show that, in this case, there does not exist any state on the holonomy-flux algebra in which the variances of the holonomy and flux observables would all be finite, let alone small. It is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space, for it arises from the structure of the algebra itself. A way out would be to suitably restrict the algebra of observables: we take the first step in this direction in a companion paper.
Imaginary action, spinfoam asymptotics and the ‘transplanckian’ regime of loop quantum gravity
NASA Astrophysics Data System (ADS)
Bodendorfer, N.; Neiman, Y.
2013-10-01
It was recently noted that the on-shell Einstein-Hilbert action with York-Gibbons-Hawking boundary term has an imaginary part, proportional to the area of the codimension-2 surfaces on which the boundary normal becomes null. We discuss the extension of this result to first-order formulations of gravity. As a side effect, we settle the issue of the Holst modification versus the Nieh-Yan density by demanding a variational principle with suitable boundary conditions. We then set out to find the imaginary action in the large-spin 4-simplex limit of the Lorentzian EPRL/FK spinfoam. It turns out that the spinfoam’s effective action indeed has the correct imaginary part, but only if the Barbero-Immirzi parameter γ is set to ±i after the quantum calculation. We point out an agreement between this effective action and a recent black hole state-counting calculation in the same limit. Finally, we propose that the large-spin limit of loop quantum gravity can be viewed as a high-energy ‘transplanckian’ regime.
Effective dynamics, big bounces, and scaling symmetry in Bianchi type I loop quantum cosmology
NASA Astrophysics Data System (ADS)
Chiou, Dah-Wei
2007-12-01
The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to 3 times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.
Quantum nature of the big bang: Improved dynamics
Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet
2006-10-15
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as ''emergent time'', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness.
NASA Astrophysics Data System (ADS)
Chaicherdsakul, Kanokkuan
2006-08-01
Quantum theory of cosmological fluctuations with other matters is studied to higher order to understand the origin of the universe during the time of inflation. This study also links gravitational and all matter fluctuations with the observed cosmic microwave background (CMB) anisotropy. It is important to keep in mind that what is tested observationally is the paradigm that the primordial spectrum of inhomogeneities was nearly scale invariant and predominantly adiabatic. Therefore, if other matters such as fermion and gauge fields which do not drive inflation predict the scale invariant spectrums, their existence during inflation cannot be ruled out. We therefore extend the calculation of quantum corrections to the cosmological correlation
NASA Astrophysics Data System (ADS)
Bilal, Adel; Leduc, Laetitia
2015-07-01
We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kähler formalism where the basic quantum field is the (Laplacian of the) Kähler potential. We do a careful first-principles computation of the fixed-area partition function Z [ A ] up to and including all two-loop contributions. This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices. Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur. We consistently determine the relevant counterterms from a one-loop computation of the full two-point Green's function of the Kähler field. Throughout this paper we use the general spectral cutoff regularization developed recently and which is well-suited for multi-loop computations on curved manifolds. At two loops, while all "unwanted" contributions to ln (Z [ A ] / Z [A0 ]) correctly cancel, it appears that the finite coefficient of ln (A /A0) does depend on the finite part of a certain counterterm coefficient, i.e. on the finite renormalization conditions one has to impose. There exists a choice that reproduces the famous KPZ-scaling, but it seems to be only one consistent choice among others. Maybe, this hints at the possibility that other renormalization conditions could eventually provide a way to circumvent the famous c = 1 barrier.
"Loops and Legs in Quantum Field Theory", 12th DESY Workshop on Elementary Particle Physics
NASA Astrophysics Data System (ADS)
The bi-annual international conference "Loops and Legs in Quantum Field Theory" has been held at Weimar, Germany, from April 27 to May 02, 2014. It has been the 12th conference of this series, started in 1992. The main focus of the conference are precision calculations of multi- loop and multi-leg processes in elementary particle physics for processes at present and future high-energy facilities within and beyond the Standard Model. At present many physics questions studied deal with processes at the LHC and future facilities like the ILC. A growing number of contributions deals with important developments in the field of computational technologies and algorithmic methods, including large-scale computer algebra, efficient methods to compute large numbers of Feynman diagrams, analytic summation and integration methods of various kinds, new related function spaces, precise numerical methods and Monte Carlo simulations. The present conference has been attended by more than 110 participants from all over the world, presenting more than 75 contributions, most of which have been written up for these pro- ceedings. The present volume demonstrates in an impressive way the enormous development of the field during the last few years, reaching the level of 5-loop calculations in QCD and a like- wise impressive development in massive next-to-leading order and next-to-next-to-leading order processes. Computer algebraic and numerical calculations require terabyte storage and many CPU years, even after intense parallelization, to obtain state-of-the-art theoretical predictions. The city of Weimar gave a suitable frame to the conference, with its rich history, especially in literature, music, arts, and architecture. Goethe, Schiller, Wieland, Herder, Bach and Liszt lived there and created many of their masterpieces. The many young participants signal that our field is prosperous and faces an exciting future. The conference hotel "Kaiserin Augusta" offered a warm hospitality and
Quantum interference based Boolean gates in dangling bond loops on Si(100):H surfaces
Kleshchonok, Andrii; Gutierrez, Rafael; Joachim, Christian; Cuniberti, Gianaurelio
2015-01-01
Implementing atomic and molecular scale electronic functionalities represents one of the major challenges in current nano-electronic developments. Engineered dangling bond nanostructures on Silicon or Germanium surfaces posses the potential to provide novel routes towards the development of non-conventional electronic circuits. These structures are built by selectively removing hydrogen atoms from an otherwise fully passivated Si(100) or Ge(100) substrate. In this theoretical study, we demonstrate how dangling bond loops can be used to implement different Boolean logic gates. Our approach exploits quantum interference effects in such ring-like structures combined with an appropriate design of the interfacing of the dangling bond system with mesoscopic electrodes. We show how OR, AND, and NOR gates can be realized by tuning either the global symmetry of the system in a multi-terminal setup—by arranging the position of the input and output electrodes—or, alternatively, by selectively applying electrostatic gates in a two-terminal configuration. PMID:26370919
A note on the secondary simplicity constraints in loop quantum gravity
NASA Astrophysics Data System (ADS)
Anzà, Fabio; Speziale, Simone
2015-10-01
A debate has appeared in the literature on loop quantum gravity and spin foams over whether the secondary simplicity constraints, reducing the connection to be Levi-Civita, should imply shape-matching conditions, reducing twisted geometries to Regge geometries. We address the question using a simple model with flat dynamics in which secondary simplicity constraints arise from a dynamical preservation of the primary ones. We find that shape-matching conditions arise, thus providing support to an affirmative answer to the question. In our model, these extra conditions come from the different graph localizations of the Hamiltonian (faces) and primary simplicity constraints (links). Our results are consistent with previous claims by Dittrich and Ryan and extend their validity to Lorentzian signature and arbitrary cellular decompositions. We show in particular how the (gauge-invariant version of the) twist angle ξ featuring in twisted geometries equals on-shell the Regge dihedral angle multiplied by the Immirzi parameter, thus recovering the discrete extrinsic geometry from the Ashtekar-Barbero holonomy. Finally, we confirm that flatness implies both Levi-Civita and shape-matching conditions using twisted geometries and a four-dimensional version of the vertex condition appearing in ’t Hooft’s polygon model.
NASA Astrophysics Data System (ADS)
Lucky Chang, Wen-Hsuan; Proty Wu, Jiun-Huei
2016-06-01
We aim to use the observations of B-mode polarization in the Cosmic Microwave Background (CMB) to probe the ‘parent universe’ under the context of Loop Quantum Cosmology (LQC). In particular, we investigate the possibility for the gravitational waves (GW) such as those from the stellar binary systems in the parent universe to survive the big bounce and thus to be still observable today. Our study is based on the background dynamics with the zeroth-order holonomy correction using the Arnowitt-Deser-Misner (ADM) formalism. We propose a new framework in which transfer functions are invoked to bring the GWs in the parent universe through the big bounce, inflation, and big bang to reach today. This transparent and intuitive formalism allows us to accurately discuss the influence of the GWs from the parent universe on the B-mode polarization in the CMB today under backgrounds of different LQC parameters. These features can soon be tested by the forth-coming CMB observations and we note that the LQC backgrounds with symmetric bouncing scenarios are ruled out by the latest observational results from Planck and BICEP2/Keck experiments.
Barbero-Immirzi parameter as a scalar field: K-inflation from loop quantum gravity?
NASA Astrophysics Data System (ADS)
Taveras, Victor; Yunes, Nicolás
2008-09-01
We consider a loop-quantum gravity inspired modification of general relativity, where the Holst action is generalized by making the Barbero-Immirzi (BI) parameter a scalar field, whose value could be dynamically determined. The modified theory leads to a nonzero torsion tensor that corrects the field equations through quadratic first derivatives of the BI field. Such a correction is equivalent to general relativity in the presence of a scalar field with nontrivial kinetic energy. This stress energy of this field is automatically covariantly conserved by its own dynamical equations of motion, thus satisfying the strong equivalence principle. Every general relativistic solution remains a solution to the modified theory for any constant value of the BI field. For arbitrary time-varying BI fields, a study of cosmological solutions reduces the scalar-field stress energy to that of a pressureless perfect fluid in a comoving reference frame, forcing the scale-factor dynamics to be equivalent to those of a stiff equation of state. Upon ultraviolet completion, this model could provide a natural mechanism for k inflation, where the role of the inflaton is played by the BI field and inflation is driven by its nontrivial kinetic energy instead of a potential.
Beyond-one-loop quantum gravity action yielding both inflation and late-time acceleration
NASA Astrophysics Data System (ADS)
Elizalde, E.; Odintsov, S. D.; Sebastiani, L.; Myrzakulov, R.
2017-08-01
A unified description of early-time inflation with the current cosmic acceleration is achieved by means of a new theory that uses a quadratic model of gravity, with the inclusion of an exponential F (R)-gravity contribution for dark energy. High-curvature corrections of the theory come from higher-derivative quantum gravity and yield an effective action that goes beyond the one-loop approximation. It is shown that, in this theory, viable inflation emerges in a natural way, leading to a spectral index and tensor-to-scalar ratio that are in perfect agreement with the most reliable Planck results. At low energy, late-time accelerated expansion takes place. As exponential gravity, for dark energy, must be stabilized during the matter and radiation eras, we introduce a curing term in order to avoid nonphysical singularities in the effective equation of state parameter. The results of our analysis are confirmed by accurate numerical simulations, which show that our model does fit the most recent cosmological data for dark energy very precisely.
Inflation and bounce from classical and loop quantum cosmology imperfect fluids
NASA Astrophysics Data System (ADS)
Oikonomou, V. K.
We investigate how various inflationary and bouncing cosmologies can be realized by imperfect fluids with a generalized equation of state, in the context of both classical and loop quantum cosmologies. With regards to the inflationary cosmologies, we study the intermediate inflation scenario, the R2 inflation scenario and two constant-roll inflation scenarios, and with regards to the bouncing cosmologies, we study the matter bounce scenario, the singular bounce and the super bounce scenario. Within the context of the classical cosmology, we calculate the spectral index of the power spectrum of primordial curvature perturbations, the scalar-to-tensor ratio and the running of the spectral index and we compare the resulting picture with the Planck data. As we demonstrate, partial compatibility with the observational data is achieved in the imperfect fluid description, however none of the above scenarios is in full agreement with data. This result shows that although it is possible to realize various cosmological scenarios using different theoretical frameworks, it is not guaranteed that all the theoretical descriptions are viable.
Viability of the matter bounce scenario in Loop Quantum Cosmology from BICEP2 last data
De Haro, Jaume; Amorós, Jaume E-mail: jaume.amoros@upc.edu
2014-08-01
The CMB map provided by the Planck project constrains the value of the ratio of tensor-to-scalar perturbations, namely r, to be smaller than 0.11 (95 % CL). This bound rules out the simplest models of inflation. However, recent data from BICEP2 is in strong tension with this constrain, as it finds a value r=0.20{sup +0.07}{sub -0.05} with 0r= disfavored at 7.0 σ, which allows these simplest inflationary models to survive. The remarkable fact is that, even though the BICEP2 experiment was conceived to search for evidence of inflation, its experimental data matches correctly theoretical results coming from the matter bounce scenario (the alternative model to the inflationary paradigm). More precisely, most bouncing cosmologies do not pass Planck's constrains due to the smallness of the value of the tensor/scalar ratio r≤ 0.11, but with new BICEP2 data some of them fit well with experimental data. This is the case with the matter bounce scenario in the teleparallel version of Loop Quantum Cosmology.
NASA Astrophysics Data System (ADS)
Bolliet, Boris; Grain, Julien; Stahl, Clément; Linsefors, Linda; Barrau, Aurélien
2015-04-01
Loop quantum cosmology tries to capture the main ideas of loop quantum gravity and to apply them to the Universe as a whole. Two main approaches within this framework have been considered to date for the study of cosmological perturbations: the dressed metric approach and the deformed algebra approach. They both have advantages and drawbacks. In this article, we accurately compare their predictions. In particular, we compute the associated primordial tensor power spectra. We show—numerically and analytically—that the large scale behavior is similar for both approaches and compatible with the usual prediction of general relativity. The small scale behavior is, the other way round, drastically different. Most importantly, we show that in a range of wave numbers explicitly calculated, both approaches do agree on predictions that, in addition, differ from standard general relativity and do not depend on unknown parameters. These features of the power spectrum at intermediate scales might constitute a universal loop quantum cosmology prediction that can hopefully lead to observational tests and constraints. We also present a complete analytical study of the background evolution for the bouncing universe that can be used for other purposes.
NASA Astrophysics Data System (ADS)
El-Kader, M. S. A.; Maroulis, G.
2017-02-01
The rototranslational collision-induced absorption (CIA) of carbon dioxide CO2 and of carbon dioxide with inert gas mixtures CO2-He, CO2-Ar and CO2-Xe at different temperature are analyzed in terms of new isotropic intermolecular potentials and multipole-induced dipole function models, using quantum spectral lineshape computations. The irreducible spherical form for the induced operator of light absorption mechanisms was determined. The quality of the present potentials have been checked by comparing between calculated and experimental thermo-physical and transport properties over a wide temperature range. Quite a good agreement is observed for all carbon dioxide noble gas mixtures.
Quantum Einstein-Maxwell fields: A unified viewpoint from the loop representation
NASA Astrophysics Data System (ADS)
Gambini, Rodolfo; Pullin, Jorge
1993-06-01
We propose a naive unification of electromagnetism and general relativity based on enlarging the gauge group of Ashtekar's variables. We construct the connection and loop representations and analyze the space of states. In the loop representation, the wave functions depend on two loops, each of them carrying information about both gravitation and electromagnetism. We find that the Chern-Simons form and the Jones polynomial play a role in the model.
Schwartz, M.W.
1981-04-30
A probabilistic safety criterion for isotropic flywheel rotors is established based on the tolerated noncontainment failure rates of commercial aircraft turbojet engine rotors. A technique is developed combining reliability with fracture mechanics, and a sample calculation provided, to show the energy-storage levels that isotropic flywheel rotors could achieve within the constraints of this safety criterion.
NASA Astrophysics Data System (ADS)
Wu, Yue-Liang
2014-04-01
To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff Mc and infrared cutoff μs to avoid infinities. As Mc can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales Mc and μs in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet
NASA Astrophysics Data System (ADS)
Wu, Yue-Liang
2014-02-01
To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff Mc and infrared cutoff μs to avoid infinities. As Mc can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales Mc and μs in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet
Fukugita, M.; Ukawa, A.
1986-08-04
Finite-temperature behavior of quantum chromodynamics is investigated with the Langevin technique including the dynamical quark loops. The deconfining and chiral transitions occur at the same temperature. The strength of transition weakens initially as the quark mass decreases from infinity, but at small quark masses it strengthens again and shows the characteristic of a first-order transition. We estimate the inverse coupling constant at zero quark mass to be beta/sub c/ = 6/g/sub c//sup 2/approx. =4.9--5.0 for four flavors on an 8/sup 3/ x 4 lattice.
Zhu, Tao; Wang, Anzhong; Wu, Qiang; Kirsten, Klaus; Sheng, Qin; Cleaver, Gerald E-mail: anzhong_wang@baylor.edu E-mail: gerald_cleaver@baylor.edu E-mail: wuq@zjut.edu.cn
2016-03-01
We first derive the primordial power spectra, spectral indices and runnings of both scalar and tensor perturbations of a flat inflationary universe to the second-order approximations of the slow-roll parameters, in the framework of loop quantum cosmology with the inverse-volume quantum corrections. This represents an extension of our previous work in which the parameter σ was assumed to be an integer, where σ characterizes the quantum corrections and in general can take any of values from the range σ element of (0, 6]. Restricting to the first-order approximations of the slow-roll parameters, we find corrections to the results obtained previously in the literature, and point out the causes for such errors. To our best knowledge, these represent the most accurate calculations of scalar and tensor perturbations given so far in the literature. Then, fitting the perturbations to the recently released data by Planck (2015), we obtain the most severe constraints for various values of σ. Using these constraints as our referring point, we discuss whether these quantum gravitational corrections can lead to measurable signatures in the future cosmological observations. We show that, depending on the value of σ, the scale-dependent contributions to the relativistic inflationary spectra due to the inverse-volume corrections could be well within the range of the detectability of the forthcoming generations of experiments, such as the Stage IV experiments.
Evidence for maximal acceleration and singularity resolution in covariant loop quantum gravity.
Rovelli, Carlo; Vidotto, Francesca
2013-08-30
A simple argument indicates that covariant loop gravity (spin foam theory) predicts a maximal acceleration and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
Nonequilibrium phase transitions in isotropic Ashkin-Teller model
NASA Astrophysics Data System (ADS)
Akıncı, Ümit
2017-03-01
Dynamic behavior of an isotropic Ashkin-Teller model in the presence of a periodically oscillating magnetic field has been analyzed by means of the mean field approximation. The dynamic equation of motion has been constructed with the help of a Glauber type stochastic process and solved for a square lattice. After defining the possible dynamical phases of the system, phase diagrams have been given and the behavior of the hysteresis loops has been investigated in detail. The hysteresis loop for specific order parameter of isotropic Ashkin-Teller model has been defined and characteristics of this loop in different dynamical phases have been given.
Schrödinger-like quantum dynamics in loop quantized black holes
NASA Astrophysics Data System (ADS)
Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge
2016-06-01
We show, following a previous quantization of a vacuum spherically symmetric spacetime carried out in [R. Gambini, J. Olmedo and J. Pullin, Class. Quantum Grav. 31 (2014) 095009.] that this setting admits a Schrödinger-like picture. More precisely, the technique adopted there for the definition of parametrized Dirac observables (that codify local information of the quantum theory) can be extended in order to accommodate different pictures. In this new picture, the quantum states are parametrized in terms of suitable gauge parameters and the observables constructed out of the kinematical ones on this space of parametrized states.
DMRG Study of the S >= 1 quantum Heisenberg Antiferromagnet on a Kagome-like lattice without loops
NASA Astrophysics Data System (ADS)
Lamberty, R. Zach; Changlani, Hitesh J.; Henley, Christopher L.
2013-03-01
The Kagome quantum Heisenberg antiferromagnet, for spin up to S = 1 and perhaps S = 3 / 2 , is a prime candidate to realize a quantum spin liquid or valence bond crystal state, but theoretical or computational studies for S > 1 / 2 are difficult and few. We consider instead the same interactions and S >= 1 on the Husimi Cactus, a graph of corner sharing triangles whose centers are vertices of a Bethe lattice, using a DMRG procedure tailored for tree graphs. Since both lattices are locally identical, properties of the Kagome antiferromagnet dominated by nearest-neighbor spin correlations should also be exhibited on the Cactus, whereas loop-dependent effects will be absent on the loopless Cactus. Our study focuses on the possible transition(s) that must occur with increasing S for the Cactus antiferromagnet. (It has a disordered valence bond state at S = 1 / 2 but a 3-sublattice coplanar ordered state in the large S limit). We also investigate the phase diagram of the S = 1 quantum XXZ model with on-site anisotropy, which we expect to have three-sublattice and valence-bond-crystal phases similar to the kagome case. This work is supported by the National Science Foundation through a Graduate Research Fellowship to R. Zach Lamberty, as well as grant DMR-
One-loop omega-potential of quantum fields with ellipsoid constant-energy surface dispersion law
Kazinski, P.O.; Shipulya, M.A.
2011-10-15
Rapidly convergent expansions of a one-loop contribution to the partition function of quantum fields with ellipsoid constant-energy surface dispersion law are derived. The omega-potential is naturally decomposed into three parts: the quasiclassical contribution, the contribution from the branch cut of the dispersion law, and the oscillating part. The low- and high-temperature expansions of the quasiclassical part are obtained. An explicit expression and a relation of the contribution from the cut with the Casimir term and vacuum energy are established. The oscillating part is represented in the form of the Chowla-Selberg expansion of the Epstein zeta function. Various resummations of this expansion are considered. The general procedure developed is then applied to two models: massless particles in a box both at zero and nonzero chemical potential, and electrons in a thin metal film. Rapidly convergent expansions of the partition function and average particle number are obtained for these models. In particular, the oscillations of the chemical potential of conduction electrons in graphene and a thin metal film due to a variation of size of the crystal are described. - Highlights: > We study quantum fields with ellipsoid constant-energy surface dispersion law. > Rapidly convergent expansions of the omega-potential are derived. > Various resummations of the Chowla-Selberg expansion are obtained. > We establish a relation of the Casimir term with the vacuum energy. > Oscillations of the chemical potential of electrons in graphene are described.
Rainbow metric from quantum gravity: Anisotropic cosmology
NASA Astrophysics Data System (ADS)
Assanioussi, Mehdi; Dapor, Andrea
2017-03-01
In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter β in the modified dispersion relation of the modes, hence, inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [M. Assanioussi, A. Dapor, and J. Lewandowski, Phys. Lett. B 751, 302 (2015), 10.1016/j.physletb.2015.10.043], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.
The isotropic Hamiltonian formalism
Vaisman, Izu
2011-02-10
A Hamiltonian formalism is a procedure that allows to associate a dynamical system to a function and that includes classical Hamiltonian mechanics as a particular case. The present, expository paper gives a survey of the Hamiltonian formalism defined by an isotropic subbundle of TM+T*M, in particular, by a Dirac structure. We discuss reduction and geometric quantization of the Hamiltonian dynamical systems provided by this formalism.
Linearly Forced Isotropic Turbulence
NASA Technical Reports Server (NTRS)
Lundgren, T. S.
2003-01-01
Stationary isotropic turbulence is often studied numerically by adding a forcing term to the Navier-Stokes equation. This is usually done for the purpose of achieving higher Reynolds number and longer statistics than is possible for isotropic decaying turbulence. It is generally accepted that forcing the Navier-Stokes equation at low wave number does not influence the small scale statistics of the flow provided that there is wide separation between the largest and smallest scales. It will be shown, however, that the spectral width of the forcing has a noticeable effect on inertial range statistics. A case will be made here for using a broader form of forcing in order to compare computed isotropic stationary turbulence with (decaying) grid turbulence. It is shown that using a forcing function which is directly proportional to the velocity has physical meaning and gives results which are closer to both homogeneous and non-homogeneous turbulence. Section 1 presents a four part series of motivations for linear forcing. Section 2 puts linear forcing to a numerical test with a pseudospectral computation.
Loop quantum gravity simplicity constraint as surface defect in complex Chern-Simons theory
NASA Astrophysics Data System (ADS)
Han, Muxin; Huang, Zichang
2017-05-01
The simplicity constraint is studied in the context of four-dimensional spinfoam models with a cosmological constant. We find that the quantum simplicity constraint is realized as the two-dimensional surface defect in SL (2 ,C ) Chern-Simons theory in the construction of spinfoam amplitudes. By this realization of the simplicity constraint in Chern-Simons theory, we are able to construct the new spinfoam amplitude with a cosmological constant for an arbitrary simplicial complex (with many 4-simplices). The semiclassical asymptotics of the amplitude is shown to correctly reproduce the four-dimensional Einstein-Regge action with a cosmological constant term.
NASA Astrophysics Data System (ADS)
Noguchi, Atsushi; Yamazaki, Rekishu; Ataka, Manabu; Fujita, Hiroyuki; Tabuchi, Yutaka; Ishikawa, Toyofumi; Usami, Koji; Nakamura, Yasunobu
2016-10-01
Cavity electro-(opto-)mechanics gives us a quantum tool to access mechanical modes in a massive object. Here we develop a quantum electromechanical system in which a vibrational mode of a SiN x membrane are coupled to a three-dimensional loop-gap superconducting microwave cavity. The tight confinement of the electric field across a mechanically compliant narrow-gap capacitor realizes the quantum strong coupling regime under a red-sideband pump field and the quantum ground state cooling of the mechanical mode. We also demonstrate strong coupling between two mechanical modes, which is induced by two-tone parametric drives and mediated by a virtual photon in the cavity.
Isotropically polarized speckle patterns.
Schmidt, Mikolaj K; Aizpurua, Javier; Zambrana-Puyalto, Xavier; Vidal, Xavier; Molina-Terriza, Gabriel; Sáenz, Juan José
2015-03-20
The polarization of the light scattered by an optically dense and random solution of dielectric nanoparticles shows peculiar properties when the scatterers exhibit strong electric and magnetic polarizabilities. While the distribution of the scattering intensity in these systems shows the typical irregular speckle patterns, the helicity of the incident light can be fully conserved when the electric and magnetic polarizabilities of the scatterers are equal. We show that the multiple scattering of helical beams by a random dispersion of "dual" dipolar nanospheres leads to a speckle pattern exhibiting a perfect isotropic constant polarization, a situation that could be useful in coherent control of light as well as in lasing in random media.
NASA Astrophysics Data System (ADS)
Achour, Jibril Ben; Geiller, Marc; Noui, Karim; Yu, Chao
2015-05-01
We study the role of the Barbero-Immirzi parameter γ and the choice of connection in the construction of (a symmetry-reduced version of) loop quantum gravity. We start with the four-dimensional Lorentzian Holst action that we reduce to three dimensions in a way that preserves the presence of γ . In the time gauge, the phase space of the resulting three-dimensional theory mimics exactly that of the four-dimensional one. Its quantization can be performed, and on the kinematical Hilbert space spanned by SU(2) spin network states the spectra of geometric operators are discrete and γ dependent. However, because of the three-dimensional nature of the theory, its SU(2) Ashtekar-Barbero Hamiltonian constraint can be traded for the flatness constraint of an s l (2 ,C ) connection, and we show that this latter has to satisfy a linear simplicitylike condition analogous to the one used in the construction of spin foam models. The physically relevant solution to this constraint singles out the noncompact subgroup SU(1, 1), which in turn leads to the disappearance of the Barbero-Immirzi parameter and to a continuous length spectrum, in agreement with what is expected from Lorentzian three-dimensional gravity.
Tsang, Mankei; Shapiro, Jeffrey H.; Lloyd, Seth
2009-05-15
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [M. Tsang et al., Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that postprocessing can further improve the estimation performance if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continuous optical phase measurements from the classical estimation theory perspective. In the case of delayed estimation, we find that the inferred uncertainty product can drop below that allowed by the Heisenberg uncertainty relation. Although this result seems counterintuitive, we argue that it does not violate any basic principle of quantum mechanics.
Haro, Jaume; Amorós, Jaume E-mail: jaume.amoros@upc.edu
2014-12-01
We consider the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology (LQC) for phenomenological potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding or contracting phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these potentials, numerically solving the dynamical perturbation equations we have seen that, for the particular F(T) model that we will name teleparallel version of LQC, and whose modified Friedmann equation coincides with the corresponding one in holonomy corrected LQC when one deals with the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, the corresponding equations obtained from the well-know perturbed equations in F(T) gravity lead to theoretical results that fit well with current observational data. More precisely, in this teleparallel version of LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Planck's experimental data. On the other hand, in the standard holonomy corrected LQC, using the perturbed equations obtained replacing the Ashtekar connection by a suitable sinus function and inserting some counter-terms in order to preserve the algebra of constrains, the theoretical value of the tensor/scalar ratio is smaller than in the teleparallel version, which means that there is always a set of solutions that matches with Planck's data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.
NASA Astrophysics Data System (ADS)
Haro, Jaume; Amorós, Jaume
2014-12-01
We consider the matter bounce scenario in F(T) gravity and Loop Quantum Cosmology (LQC) for phenomenological potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding or contracting phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these potentials, numerically solving the dynamical perturbation equations we have seen that, for the particular F(T) model that we will name teleparallel version of LQC, and whose modified Friedmann equation coincides with the corresponding one in holonomy corrected LQC when one deals with the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, the corresponding equations obtained from the well-know perturbed equations in F(T) gravity lead to theoretical results that fit well with current observational data. More precisely, in this teleparallel version of LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with Planck's experimental data. On the other hand, in the standard holonomy corrected LQC, using the perturbed equations obtained replacing the Ashtekar connection by a suitable sinus function and inserting some counter-terms in order to preserve the algebra of constrains, the theoretical value of the tensor/scalar ratio is smaller than in the teleparallel version, which means that there is always a set of solutions that matches with Planck's data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.
Semiclassical States Associated with Isotropic Submanifolds of Phase Space
NASA Astrophysics Data System (ADS)
Guillemin, V.; Uribe, A.; Wang, Z.
2016-12-01
We define classes of quantum states associated with isotropic submanifolds of cotangent bundles. The classes are stable under the action of semiclassical pseudo-differential operators and covariant under the action of semiclassical Fourier integral operators. We develop a symbol calculus for them; the symbols are symplectic spinors. We outline various applications.
Entanglement of Formation for Werner States and Isotropic States via Logical Gates
NASA Astrophysics Data System (ADS)
Bertini, Cesarino; Chiara, Maria Luisa Dalla; Leporini, Roberto
To what extent is a logical characterization of entanglement possible? We investigate some correlations that hold between the concept of entanglement of formation for Werner states and for isotropic states and the probabilistic behavior of some quantum logical gates.
Isotropic Monte Carlo Grain Growth
Mason, J.
2013-04-25
IMCGG performs Monte Carlo simulations of normal grain growth in metals on a hexagonal grid in two dimensions with periodic boundary conditions. This may be performed with either an isotropic or a misorientation - and incliantion-dependent grain boundary energy.
Indentation of Transversely Isotropic Materials
NASA Astrophysics Data System (ADS)
Bhat, Talapady Srivatsa
Instrumented indentation, as a tool for characterization of mechanical properties, has well been established in the past decades. Studies have been conducted to understand the behavior of isotropic materials under indentation and techniques to accurately predict isotropic material properties have also been reported. Further, within the isotropic regime, work has been done to predict the indentation hardness without having to investigate the area of contact during indentation. Studies have also reported the prospect of utilizing indentation to predict the fatigue behavior of isotropic materials. This dissertation is made with the intent of extending the use of indentation, as a characterization tool, to the anisotropic regime. The effect of transverse isotropy on the indentation response of materials is systematically studied here. Extensive computational analysis is performed to elucidate the underlying deformation mechanics of indentation of transversely isotropic materials. Owing to the anisotropy, indentation may be performed parallel or perpendicular to the plane of isotropy of the specimen. It is observed that the indentation response varies significantly for each of these cases. The two cases are treated as unique and an identical systematic analysis is carried for both. The indentation orientations shall henceforth be referred to as transverse and longitudinal indentation for indentation parallel and perpendicular to the plane of isotropy respectively. A technique is developed capable of extracting the elastic-plastic properties of transversely isotropic materials from interpretation of indentation response in either direction. The technique is rigorously tested for its robustness, accuracy and uniqueness of results. A sensitivity analysis is performed to determine how sensitive the technique is to errors in experimental results. Rigorous studies are performed to understand the variation in pile-up or sink-in during indentation with varying anisotropy in the
Transversely isotropic poroelasticity arising from thin isotropic layers
Berryman, J.G.
1996-11-01
Percolation phenomena play central roles in the field of poroelasticity, where two distinct sets of percolating continua intertwine. A connected solid frame forms the basis of the elastic behavior of a poroelastic medium in the presence of confining forces, while connected pores permit a percolating fluid (if present) to influence the mechanical response of the system from within. The present paper discusses isotropic and anisotropic poroelastic media and establishes general formulas for the behavior of transversely isotropic poroelasticity arising from laminations of isotropic components. The Backus averaging method is shown to provide elementary means of constructing general formulas. The results for confined fluids are then compared with the more general Gassmann formulas that must be satisfied by any anisotropic poroelastic medium and found to be in complete agreement.
Transversely isotropic elasticity and poroelasticity arising from thin isotropic layers
Berryman, J.G.
1997-07-01
Since the classic work of Postma [1955] and Backus [1962], much has been learned about elastic constants in vertical transversely isotropic (VTI) media when the anisotropy is due to fine layering of isotropic elastic materials. However, new results are still being discovered. For example, the P-wave anisotropy parameter c{sub 11}/c{sub 33} lies in the range 1/4 {<=} c{sub 11}/c{sub 33} {<=} <{lambda}+2{mu}><1/({lambda}+2{mu})>, when the layers are themselves composed of isotropic elastic materials with Lame constants {lambda} and {mu} and the vertical average of the layers is symbolized by <{center_dot}>. The lower bound corrects a result of Postma. For porous layers, a connected solid frame forms the basis of the elastic behavior of a poroelastic medium in the presence of confining forces, while connected pores permit a percolating fluid (if present) to influence the mechanical response of the system from within. For isotropic and anisotropic poroelastic media, we establish general formulas for the behavior of transversely isotropic poroelasticity arising from laminations of isotropic components. The Backus averaging method is shown to provide elementary means of constructing general formulas. The results for confined fluids are then compared with the more general Gassmann [1951] formulas that must be satisfied by any anisotropic poroelastic medium and found to be in complete agreement. Such results are important for applications to oil exploration using AVO (amplitude versus offset) since the presence or absence of a fluid component, as well as the nature of the fluid, is the critical issue and the ways in which the fluid influences seismic reflection data still need to be better understood.
Quantum nature of the big bang.
Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet
2006-04-14
Some long-standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big-bang singularity in loop quantum cosmology are significantly extended as follows: (i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the "emergent time" idea; (ii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously; (iii) the Hamiltonian constraint is solved numerically to show that the big bang is replaced by a big bounce. Thanks to the nonperturbative, background independent methods, unlike in other approaches the quantum evolution is deterministic across the deep Planck regime.
Bi-isotropic constitutive relations
NASA Astrophysics Data System (ADS)
Sihvola, A. H.; Lindell, I. V.
1991-03-01
The constitutive relations of general bi-isotropic media, requiring four material parameters, can be written in different ways to describe their electromagnetic behavior. This communication contains a two-way 'dictionary' between a proposed formulation of the constitutive relations with three other sets of relations, generalized from relations used for chiral materials.
Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward
2016-11-01
We study the effective cosmological dynamics, emerging as the hydrodynamics of simple condensate states, of a group field theory (GFT) model for quantum gravity coupled to a massless scalar field and reduced to its isotropic sector. The quantum equations of motion for these GFT condensate states are given in relational terms with respect to the scalar field, from which effective dynamics for spatially flat, homogeneous and isotropic space-times can be extracted. The result is a generalisation of the Friedmann equations, including quantum gravity modifications, in a specific regime of the theory corresponding to a Gross-Pitaevskii approximation where interactions are subdominant. The classical Friedmann equations of general relativity are recovered in a suitable semi-classical limit for some range of parameters of the microscopic dynamics. An important result is that the quantum geometries associated with these GFT condensate states are non-singular: a bounce generically occurs in the Planck regime. For some choices of condensate states, these modified Friedmann equations are very similar to those of loop quantum cosmology.
Regulative Loops, Step Loops and Task Loops
ERIC Educational Resources Information Center
VanLehn, Kurt
2016-01-01
This commentary suggests a generalization of the conception of the behavior of tutoring systems, which the target article characterized as having an outer loop that was executed once per task and an inner loop that was executed once per step of the task. A more general conception sees these two loops as instances of regulative loops, which…
Regulative Loops, Step Loops and Task Loops
ERIC Educational Resources Information Center
VanLehn, Kurt
2016-01-01
This commentary suggests a generalization of the conception of the behavior of tutoring systems, which the target article characterized as having an outer loop that was executed once per task and an inner loop that was executed once per step of the task. A more general conception sees these two loops as instances of regulative loops, which…
NASA Astrophysics Data System (ADS)
Bedir, Islam
The methods are developed of two-loop calculation of spectral density for the 3-point correlation function of an electromagnetic current and two axial currents which are the basis of the pion form factor analysis within the framework of QCD sum rules and local quark-hadron duality approach. The nature of various types of contributions is established which are related to particular regions of momentum integrations inside Feynman integrals. The trace factors accompanying all six two-loop diagrams are calculated and classified. To regularize particular loop integrals, the dimensional regularization technique has been used. The calculation involves such methods as infinite-momentum frame approach, alpha-representation method, Sudakov parametrization of the integration momentum and covariant calculation in momentum space. It is shown that final results of integration are given by logarithms and di-logarithm functions. For the diagram with the gluon correction to the electromagnetic vertex, it is shown that its large momentum transfer behavior is dominated by the Feynman mechanism, in which the active quark carries the bulk of the hadron momentum both before and after collision with virtual photon. For this diagram, the Sudakov double logarithmic terms were obtained that are known to convert into the Sudakov form factor after summation over all orders. Another type of double-logarithmic term was found in the contribution of the diagrams with the gluon correction to the axial-current vertices. This term appears as a power correction to the leading power behavior of this diagram governed by a short-distance re-scattering subprocess in which the exchanged gluon has large virtuality. This subprocess corresponds to the asymptotic perturbative QCD contribution. This observation shows that the two double-logarithmic terms have different nature. The methods developed in this dissertation may be applied to other two-loop calculations within the QCD sum rule method.
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Ramaswamy, V. G.; Vanstone, R. H.; Dame, L. T.; Laflen, J. H.
1984-01-01
The unified constitutive theories for application to typical isotropic cast nickel base supperalloys used for air-cooled turbine blades were evaluated. The specific modeling aspects evaluated were: uniaxial, monotonic, cyclic, creep, relaxation, multiaxial, notch, and thermomechanical behavior. Further development of the constitutive theories to model thermal history effects, refinement of the material test procedures, evaluation of coating effects, and verification of the models in an alternate material will be accomplished in a follow-on for this base program.
Spherical 3D isotropic wavelets
NASA Astrophysics Data System (ADS)
Lanusse, F.; Rassat, A.; Starck, J.-L.
2012-04-01
Context. Future cosmological surveys will provide 3D large scale structure maps with large sky coverage, for which a 3D spherical Fourier-Bessel (SFB) analysis in spherical coordinates is natural. Wavelets are particularly well-suited to the analysis and denoising of cosmological data, but a spherical 3D isotropic wavelet transform does not currently exist to analyse spherical 3D data. Aims: The aim of this paper is to present a new formalism for a spherical 3D isotropic wavelet, i.e. one based on the SFB decomposition of a 3D field and accompany the formalism with a public code to perform wavelet transforms. Methods: We describe a new 3D isotropic spherical wavelet decomposition based on the undecimated wavelet transform (UWT) described in Starck et al. (2006). We also present a new fast discrete spherical Fourier-Bessel transform (DSFBT) based on both a discrete Bessel transform and the HEALPIX angular pixelisation scheme. We test the 3D wavelet transform and as a toy-application, apply a denoising algorithm in wavelet space to the Virgo large box cosmological simulations and find we can successfully remove noise without much loss to the large scale structure. Results: We have described a new spherical 3D isotropic wavelet transform, ideally suited to analyse and denoise future 3D spherical cosmological surveys, which uses a novel DSFBT. We illustrate its potential use for denoising using a toy model. All the algorithms presented in this paper are available for download as a public code called MRS3D at http://jstarck.free.fr/mrs3d.html
NASA Astrophysics Data System (ADS)
Elbaz, Edgard
This book gives a new insight into the interpretation of quantum mechanics (stochastic, integral paths, decoherence), a completely new treatment of angular momentum (graphical spin algebra) and an introduction to Fermion fields (Dirac equation) and Boson fields (e.m. and Higgs) as well as an introduction to QED (quantum electrodynamics), supersymmetry and quantum cosmology.
A Transversely Isotropic Thermoelastic Theory
NASA Technical Reports Server (NTRS)
Arnold, S. M.
1989-01-01
A continuum theory is presented for representing the thermoelastic behavior of composites that can be idealized as transversely isotropic. This theory is consistent with anisotropic viscoplastic theories being developed presently at NASA Lewis Research Center. A multiaxial statement of the theory is presented, as well as plane stress and plane strain reductions. Experimental determination of the required material parameters and their theoretical constraints are discussed. Simple homogeneously stressed elements are examined to illustrate the effect of fiber orientation on the resulting strain distribution. Finally, the multiaxial stress-strain relations are expressed in matrix form to simplify and accelerate implementation of the theory into structural analysis codes.
Are random fractal clusters isotropic\\?
NASA Astrophysics Data System (ADS)
Family, Fereydoon; Vicsek, Tamás; Meakin, Paul
1985-08-01
We have studied the shape of large clusters in the lattice-animal, percolation, and growing-percolation models. By calculating the radius of gyration tensor we find that in these models the clusters have an anisotropic shape. The results suggest that the critical droplets in related isotropic equilibrium models, such as the Ising model, may also be anisotropic. We have also determined the leading nonanalytic correction-to-scaling exponent by analyzing the anisotropy data and find that for percolation in two dimensions e~=0.47. .AE
Nicolau, A.
1988-10-01
Loop unwinding is a known technique for reducing loop overhead, exposing parallelism, and increasing the efficiency of pipelining. Traditional loop unwinding is limited to the innermost loop in a group of nested loops and the amount of unwinding either is fixed or must be specified by the user, on a case by case basis. In this paper the authors present a general technique for automatically unwinding multiply nested loops, explain its advantages over other transformation techniques, and illustrate its practical effectiveness. Lopp Quantization could be beneficial by itself or coupled with other loop transformations.
NASA Astrophysics Data System (ADS)
Georgakopoulos, D.; Budovsky, I.; Hagen, T.; Sasaki, H.; Yamamori, H.
2012-12-01
We have developed a programmable Josephson voltage standard that can produce voltages up to 20 V with a resolution of better than 0.1 µV over the whole voltage range and better than 1 nV for voltages up to 10 mV. The standard has two superconductor-normal metal-superconductor junction arrays connected in series and driven by two radiofrequency oscillators. The cryogenic part of the standard is based on a cryocooler. The new standard agrees with the primary quantum voltage standard maintained at the National Measurement Institute, Australia, within 10 nV and forms the basis of an automated calibration system for digital multimeters and voltage references.
Isotropic Negative Thermal Expansion Metamaterials.
Wu, Lingling; Li, Bo; Zhou, Ji
2016-07-13
Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the three-dimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the three-dimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale.
Vortex knots in tangled quantum eigenfunctions.
Taylor, Alexander J; Dennis, Mark R
2016-07-29
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose-Einstein condensates.
Vortex knots in tangled quantum eigenfunctions
Taylor, Alexander J.; Dennis, Mark R.
2016-01-01
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose–Einstein condensates. PMID:27468801
Controlling elastic waves with isotropic materials
NASA Astrophysics Data System (ADS)
Chang, Zheng; Hu, Jin; Hu, Gengkai; Tao, Ran; Wang, Yue
2011-03-01
Design of functional devices with isotropic materials has significant advantages, as regards easy fabrication and broadband application. In this letter, we present a method to derive isotropic transformation material parameters for elastodynamics under local conformal transformation. The transformed material parameters are then applied to design a beam bender, a four-beam antenna and an approximate carpet cloak for elastic wave with isotropic materials, validated by the numerical simulations.
Measuring isotropic subsurface light transport.
Happel, Kathrin; Dörsam, Edgar; Urban, Philipp
2014-04-21
Subsurface light transport can affect the visual appearance of materials significantly. Measuring and modeling this phenomenon is crucial for accurately reproducing colors in printing or for rendering translucent objects on displays. In this paper, we propose an apparatus to measure subsurface light transport employing a reference material to cancel out adverse signals that may bias the results. In contrast to other approaches, the setup enables improved focusing on rough surfaces (e.g. uncoated paper). We derive a measurement equation that may be used to deduce the point spread function (PSF) of subsurface light transport. Main contributions are the usage of spectrally-narrowband exchangeable LEDs allowing spectrally-resolved measurements and an approach based on quadratic programming for reconstructing PSFs in the case of isotropic light transport.
Macroscopic simulation of isotropic permanent magnets
NASA Astrophysics Data System (ADS)
Bruckner, Florian; Abert, Claas; Vogler, Christoph; Heinrichs, Frank; Satz, Armin; Ausserlechner, Udo; Binder, Gernot; Koeck, Helmut; Suess, Dieter
2016-03-01
Accurate simulations of isotropic permanent magnets require to take the magnetization process into account and consider the anisotropic, nonlinear, and hysteretic material behaviour near the saturation configuration. An efficient method for the solution of the magnetostatic Maxwell equations including the description of isotropic permanent magnets is presented. The algorithm can easily be implemented on top of existing finite element methods and does not require a full characterization of the hysteresis of the magnetic material. Strayfield measurements of an isotropic permanent magnet and simulation results are in good agreement and highlight the importance of a proper description of the isotropic material.
Dielectrophoretic manipulation of nematic and isotropic droplets
NASA Astrophysics Data System (ADS)
Lee, Bomi; Song, Jang-Kun
2016-03-01
Dielectrophoresis can provide a delicate tool to control electrically neutral particles in colloid. The dielectrophoresis is usually applied to solid particles or heterogeneous liquid droplet in continuous liquid, but we devised and investigated the dielectrophoresis of isotropic droplets within nematic phase or vice versa. Using multi-components liquid crystal mixtures that exhibit relatively wide temperature range of nematic-isotropic coexistence, we achieved a field-induced phase separation between isotropic and nematic. We also fabricated the isotropic-nematic filaments that was achieved using a biased surface preference for either isotropic or nematic phase of the alignment layer [1]. The dielectrophoresis manipulations of isotropic and nematic droplets required much lower voltage compared to that for the electro wetting type devices. In addition, we observed the bi-directional actuation of isotropic droplets using anisotropic dielectric property of liquid crystal, which is not possible in usual dielectrophoresis. The bidirectional actuation was achieved by controlling the LC director within the cell so as to change the sign of the difference between the effective dielectric constant of nematic and isotropic liquid crystals. We simulated the bi-directional dielectrophoresis by performing the LC director calculation and the corresponding dielectrophoresis. The simulation results matched well with the experimental data. Thus, the bi-directional dielectrophoresis using isotropic and nematic droplets may open new possibility of electro- optical applications using liquid crystals.
Observation of transverse patterns in an isotropic microchip laser
Chen, Y.F.; Lan, Y.P.
2003-04-01
An isotropic microchip laser is used to study the characteristics of high-order wave functions in a two-dimensional (2D) quantum harmonic oscillator based on the identical functional forms. With a doughnut pump profile, the spontaneous transverse modes are found to, generally, be elliptic and hyperbolic transverse modes. Theoretical analyses reveal that the elliptic transverse modes are analogous to the coherent states of a 2D harmonic oscillator; the formation of hyperbolic transverse modes is a spontaneous mode locking between two identical Hermite-Gaussian modes.
Magnetic monopole in the loop representation
Leal, Lorenzo; Lopez, Alexander
2006-01-15
We quantize, within the Loop Representation formalism, the electromagnetic field in the presence of a static magnetic pole. It is found that the loop-dependent physical wave functionals of the quantum Maxwell theory become multivalued, through a topological phase factor depending on the solid angle subtended at the monopole by a surface bounded by the loop. It is discussed how this fact generalizes what occurs in ordinary quantum mechanics in multiply connected spaces.
Light-Steered Isotropic Semiconductor Micromotors.
Chen, Chuanrui; Mou, Fangzhi; Xu, Leilei; Wang, Shaofei; Guan, Jianguo; Feng, Zunpeng; Wang, Quanwei; Kong, Lei; Li, Wei; Wang, Joseph; Zhang, Qingjie
2017-01-01
Intelligent photoresponsive isotropic semiconductor micromotors are developed by taking advantage of the limited penetration depth of light to induce asymmetrical surface chemical reactions. Independent of the Brownian motion of themselves, the as-proposed isotropic micromotors are able to continuously move with both motion direction and speed just controlled by light, as well as precisely manipulate particles for nanoengineering.
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Chan, K. S.; Lindholm, U. S.; Bodner, S. R.
1988-01-01
The third and fourth years of a 4-year research program, part of the NASA HOST Program, are described. The program goals were: (1) to develop and validate unified constitutive models for isotropic materials, and (2) to demonstrate their usefulness for structural analysis of hot section components of gas turbine engines. The unified models selected for development and evaluation were those of Bodner-Partom and of Walker. The unified approach for elastic-viscoplastic constitutive equations is a viable method for representing and predicting material response characteristics in the range where strain rate and temperature dependent inelastic deformations are experienced. This conclusion is reached by extensive comparison of model calculations against the experimental results of a test program of two high temperature Ni-base alloys, B1900+Hf and Mar-M247, over a wide temperature range for a variety of deformation and thermal histories including uniaxial, multiaxial, and thermomechanical loading paths. The applicability of the Bodner-Partom and the Walker models for structural applications has been demonstrated by implementing these models into the MARC finite element code and by performing a number of analyses including thermomechanical histories on components of hot sections of gas turbine engines and benchmark notch tensile specimens. The results of the 4-year program have been published in four annual reports. The results of the base program are summarized in this report. The tasks covered include: (1) development of material test procedures, (2) thermal history effects, and (3) verification of the constitutive model for an alternative material.
How Isotropic is the Universe?
NASA Astrophysics Data System (ADS)
Saadeh, Daniela; Feeney, Stephen M.; Pontzen, Andrew; Peiris, Hiranya V.; McEwen, Jason D.
2016-09-01
A fundamental assumption in the standard model of cosmology is that the Universe is isotropic on large scales. Breaking this assumption leads to a set of solutions to Einstein's field equations, known as Bianchi cosmologies, only a subset of which have ever been tested against data. For the first time, we consider all degrees of freedom in these solutions to conduct a general test of isotropy using cosmic microwave background temperature and polarization data from Planck. For the vector mode (associated with vorticity), we obtain a limit on the anisotropic expansion of (σV/H )0 <4.7 ×10-11 (95% C.L.), which is an order of magnitude tighter than previous Planck results that used cosmic microwave background temperature only. We also place upper limits on other modes of anisotropic expansion, with the weakest limit arising from the regular tensor mode, (σT ,reg/H )0 <1.0 ×10-6 (95% C.L.). Including all degrees of freedom simultaneously for the first time, anisotropic expansion of the Universe is strongly disfavored, with odds of 121 000:1 against.
Constitutive modeling for isotropic materials
NASA Technical Reports Server (NTRS)
Lindholm, Ulric S.; Chan, Kwai S.
1986-01-01
The objective of the program is to evaluate and develop existing constitutive models for use in finite-element structural analysis of turbine engine hot section components. The class of constitutive equation studied is considered unified in that all inelastic deformation including plasticity, creep, and stress relaxation are treated in a single term rather than a classical separation of plasticity (time independent) and creep (time dependent) behavior. The unified theories employed also do not utilize the classical yield surface or plastic potential concept. The models are constructed from an appropriate flow law, a scalar kinetic relation between strain rate, temperature and stress, and evolutionary equations for internal variables describing strain or work hardening, both isotropic and directional (kinematic). This and other studies have shown that the unified approach is particularly suited for determining the cyclic behavior of superalloy type blade and vane materials and is entirely compatible with three-dimensional inelastic finite-element formulations. The behavior was examined of a second nickel-base alloy, MAR-M247, and compared it with the Bodner-Partom model, further examined procedures for determining the material-specific constants in the models, and exercised the MARC code for a turbine blade under simulated flight spectrum loading. Results are summarized.
How Isotropic is the Universe?
Saadeh, Daniela; Feeney, Stephen M; Pontzen, Andrew; Peiris, Hiranya V; McEwen, Jason D
2016-09-23
A fundamental assumption in the standard model of cosmology is that the Universe is isotropic on large scales. Breaking this assumption leads to a set of solutions to Einstein's field equations, known as Bianchi cosmologies, only a subset of which have ever been tested against data. For the first time, we consider all degrees of freedom in these solutions to conduct a general test of isotropy using cosmic microwave background temperature and polarization data from Planck. For the vector mode (associated with vorticity), we obtain a limit on the anisotropic expansion of (σ_{V}/H)_{0}<4.7×10^{-11} (95% C.L.), which is an order of magnitude tighter than previous Planck results that used cosmic microwave background temperature only. We also place upper limits on other modes of anisotropic expansion, with the weakest limit arising from the regular tensor mode, (σ_{T,reg}/H)_{0}<1.0×10^{-6} (95% C.L.). Including all degrees of freedom simultaneously for the first time, anisotropic expansion of the Universe is strongly disfavored, with odds of 121 000:1 against.
NASA Astrophysics Data System (ADS)
Giesel, Kristina
The following sections are included: * Canonical Quantization of General Relativity * General Relativity in Connection Variables * Holonomy-Flux Algebra and its Representation(s) * The Ashtekar-Lewandowski Representation and the Kinematical Hilbert Space of LQG * The Quantum Einstein's Equations of Loop Quantum Gravity * Geometric Operators and Their Properties * Summary * References
Kung, P.J.; Bracht, R.R.; Flynn, E.R.; Lewis, P.S.
1996-01-01
A double-washer dc superconducting quantum interference device (SQUID) gradiometer with a flux-locked loop (FLL) based on a digital signal processor (DSP) has been developed for biomagnetic applications. All of the analog electronics in the conventional FLL are replaced and implemented by the DSP except for the low-noise field-effect transistor preamplifier at the front end of the signal recovery components. The DSP performs the signal demodulation by synchronously sampling the recovered signals and applying the appropriate full wave rectification. The signals are then integrated, filtered, and applied to the output. At 4.2 K, the white flux noise of the gradiometer measured in a DSP FLL mode is about 4{mu}{phi}{sub 0}/{radical}Hz and the noise at 1 Hz is 13 {mu}{phi}{sub 0}/{radical}Hz. The corresponding noise levels in the gradiometer operated by the conventional FLL are 1.8 and 3{mu}{phi}{sub 0}/{radical}Hz. The poorer system performance in the DSP FLL compared to the analog FLL is mainly caused by the ambient field noise and interference signals picked up through the connecting cables. Additional noise is also added to the overall noise floor by the instruments employed in the DSP system in the present prototype setup. Further improvement in the noise characteristics and the dynamic behavior of the DSP SQUID gradiometer is expected when a better configuration of DSP with the associated I/O devices is implemented. Additional improvements of the DSP programs are expected by incorporating higher-order integration, adaptive control, and noise reduction schemes. {copyright} {ital 1996 American Institute of Physics.}
Non-linear dielectric effect in the isotropic phase above the isotropic-cholesteric phase transition
NASA Astrophysics Data System (ADS)
Mukherjee, Prabir K.; Chakraborty, Sumanta; Rzoska, Sylwester J.
2011-11-01
Using the Landau-de Gennes theory, the temperature, pressure and frequency dependence of the non-linear effect in the isotropic phase above the isotropic-cholesteric phase transition is calculated. The influence of pressure on the isotropic-cholesteric phase transition is discussed by varying the coupling between the orientational order parameter and the macroscopic polarization of polar cholesterics. Comparing the results of the calculations with existing data, we finally conclude that the model provides a description of the isotropic-cholesteric transition that takes all experimentally known features of the unusual negative and positive pretransitional effect in the isotropic phase of the system into account in a qualitatively correct way.
A spatially homogeneous and isotropic Einstein-Dirac cosmology
NASA Astrophysics Data System (ADS)
Finster, Felix; Hainzl, Christian
2011-04-01
We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.
Inertial currents in isotropic plasma
NASA Technical Reports Server (NTRS)
Heinemann, M.; Erickson, G. M.; Pontius, D. H., Jr.
1994-01-01
The magnetospheric convection electric field contributes to Birkeland currents. The effects of the field are to polarize the plasma by displacing the bounce paths of the ions from those of electrons, to redistribute the pressure so that it is not constant along magnetic field lines, and to enhance the pressure gradient by the gradient of the bulk speed. Changes in the polarization charge during the convection of the plasma are neutralized by electrons in the form of field-aligned currents that close through the ionosphere. The pressure drives field-aligned currents through its gradient in the same manner as in quasi-static plasmas, but with modifications that are important if the bulk speed is of the order of the ion thermal speed; the variations in the pressure along field lines are maintained by a weak parallel potential drop. These effects are described in terms of the field-aligned currents in steady state, isotropic, MHD plasma. Solutions are developed by taking the MHD limit ot two-fluid solutions and illustrated in the special case of Maxwellian plasma for which the temperature is constant along magnetic field lines. The expression for the Birkeland current density is a generalization of Vasyliunas' expression for the field-aligned current density in quasi-static plasma and provides a unifying expression when both pressure gradients and ion inertia operate simultaneously as sources of field-aligned currents. It contains a full account of different aspects of the ion flow (parallel and perpendicular velocity and vorticity) that contribute to the currents. Contributions of ion inertia to field-aligned currents will occur in regions of strong velocity shear, electric field reversal, or large gradients in the parallel velocity or number density, and may be important in the low-latitude boundary layer, plasma sheet boundary layer, and the inner edge region of the plasma sheet.
2016-09-15
A series of active regions stretched along the right side of the sun exhibited a wide variety of loops cascading above them (Sept. 12-14, 2016). The active region near the center has tightly coiled loops, while the region rotating over the right edge has some elongated and some very stretched loops above it. The loops are actually charged particles spiraling along magnetic field lines, observed here in a wavelength of extreme ultraviolet light. Near the middle of the video the Earth quickly passes in front of a portion of the sun as viewed by SDO. http://photojournal.jpl.nasa.gov/catalog/PIA16997
Isotropic versus anisotropic modeling of photorefractive solitons.
Belić, M R; Vujić, D; Stepken, A; Kaiser, F; Calvo, G F; Agulló-López, F; Carrascosa, M
2002-06-01
The question of the isotropic versus anisotropic modeling of incoherent spatial screening solitons in photorefractive crystals is addressed by a careful theoretical and numerical analysis. Isotropic, or local, models allow for an extended spiraling of two interacting scalar solitons, and for a prolonged propagation of vortex vector solitons, whereas anisotropic, nonlocal, models prevent such phenomena. In the context of Kukhtarev's material equations, the difference in behavior is traced to the continuity equation for the current density. We further show that neither an indefinite spiraling of two solitons nor stable propagation of vortex vector solitons is generally possible in both isotropic and anisotropic models. Such systems do not conserve angular momentum, even in the case of an isotropic change in the index of refraction.
One loop back reaction on power law inflation
NASA Astrophysics Data System (ADS)
Abramo, L. R.; Woodard, R. P.
1999-08-01
We consider quantum-mechanical corrections to a homogeneous, isotropic, and spatially flat geometry whose scale factor expands classically as a general power of the comoving time. The effects of both gravitons and the scalar inflaton are computed at one loop using the manifestly causal formalism of Schwinger [J. Math. Phys. 2, 407 (1961); Particles, Sources and Fields (Addison, Wesley, Reading, MA, 1970)] with the Feynman rules recently developed by Iliopoulos et al. [Nucl. Phys. B 534, 419 (1998)]. We find no significant effect, in marked contrast to the result obtained by Mukhanov and co-workers [Phys. Rev. Lett. 78, 1624 (1998); Phys. Rev. D 56, 3248 (1997)] for chaotic inflation based on a quadratic potential. By applying the canonical technique of Mukhanov and co-workers to the exponential potentials of power law inflation, we show that the two methods produce the same results, within the approximations employed, for these backgrounds. We therefore conclude that the shape of the inflaton potential can have an enormous impact on the one loop back reaction.
Time delay anisotropy in photoelectron emission from isotropic helium
NASA Astrophysics Data System (ADS)
Heuser, S.; Jiménez-Gálan, Á.; Cirelli, C.; Sabbar, M.; Boge, R.; Lucchini, M.; Gallmann, L.; Ivanov, I.; Kheifets, A.; Dahlström, J. M.; Lindroth, E.; Argenti, L.; Martín, F.; Keller, U.
2015-09-01
Time delays of electrons emitted from an isotropic initial state and leaving behind an isotropic ion are assumed to be angle-independent. Using an interferometric method involving XUV attosecond pulse trains and an IR probe field in combination with a detection scheme, which allows for full 3D momentum resolution, we show that measured time delays between electrons liberated from the $1s^2$ spherically symmetric ground state of helium depend on the emission direction of the electrons relative to the linear polarization axis of the ionizing XUV light. Such time-delay anisotropy, for which we measure values as large as 60 attoseconds, is caused by the interplay between final quantum states with different symmetry and arises naturally whenever the photoionization process involves the exchange of more than one photon in the field of the parent-ion. With the support of accurate theoretical models, the angular dependence of the time delay is attributed to small phase differences that are induced in the laser-driven continuum transitions to the final states. Since most measurement techniques tracing attosecond electron dynamics involve the exchange of at least two photons, this is a general, significant, and initially unexpected effect that must be taken into account in all such photoionization measurements.
Interacting Generalized Ghost Dark Energy in Non-isotropic Background
NASA Astrophysics Data System (ADS)
Barati, F.
2016-04-01
In this work, the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity is investigated. At first, the non-interacting generalized ghost dark energy in a Bianchi type I (BI) background is discussed. Then the equation of state parameter, ω D = p D / ρ D , the deceleration parameter, and the evolution equation of the generalized ghost dark energy are obtained. It was found that, in this case, ω D cannot cross the phantom line (ω D >-1) and eventually the universe approaches a de-Sitter phase of expansion (ω D →-1). Then, this investigation was extended to the interacting ghost dark energy in a non-isotropic universe. It was found that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (ω D <-1) provided the parameters of the model are chosen suitably. It was considered a specific model which permits the standard continuity equation in this theory. Besides ΩΛ and Ω m in standard Einstein cosmology, another density parameter, Ω σ , is expected by the anisotropy. The anisotropy of the universe decreases and the universe transits to an isotropic flat FRW universe accommodating the present acceleration.
Static spherically symmetric wormholes with isotropic pressure
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2016-06-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p = ωρ for the isotropic pressure, independently of the form of the redshift function ϕ (r). We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Efficient modeling in transversely isotropic inhomogeneous media
Alkhalifah, T.
1993-11-01
An efficient modeling technique for transversely isotropic, inhomogeneous media, is developed using a mix of analytical equations and numerical calculations. The analytic equation for the raypath in a factorized transversely isotropic (FTI) media with linear velocity variation, derived by Shearer and Chapman, is used to trace between two points. In addition, I derive an analytical equation for geometrical spreading in FTI media that aids in preserving program efficiency; however, the traveltime is calculated numerically. I then generalize the method to treat general transversely isotropic (TI) media that are not factorized anisotropic inhomogeneous by perturbing the FTI traveltimes, following the perturbation ideas of Cerveny and Filho. A Kirchhoff-summation-based program relying on Trorey`s (1970) diffraction method is used to generate synthetic seismograms for such a medium. For the type of velocity models treated, the program is much more efficient than finite-difference and general ray-trace modeling techniques.
Negative Poisson's ratio materials via isotropic interactions.
Rechtsman, Mikael C; Stillinger, Frank H; Torquato, Salvatore
2008-08-22
We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.
The Two Isotropic Asymptotes of Fiber Composites,
1988-03-01
Voigt and Reuss models of summed stiffness and compliance. The compliance quasi-isotropic asymptote, which >’-:’ has evidently not been discussed in the...i,j,e)de o0 The resulting pseudo -isotropic compliance (series-model) Hooke’s law matrix is similar but not identical to Eq. (3): W(1) W(4) 0 a aIE...given by 1 W( ) 14) E : - Vc Wc 4W(5) 2[W(1) - W()] (8) c W() W(14 12 Direct formulas for the pseudo -isctrcpic moduli, in terms of the ply 1s natural
Quantum nature of the big bang: An analytical and numerical investigation
Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet
2006-06-15
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors and significantly extend the known results on the resolution of the big bang singularity. Specifically, the following results are established for the homogeneous isotropic model with a massless scalar field: (i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the 'emergent time' idea; (ii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously; (iii) the Hamiltonian constraint is solved numerically to show that the big bang is replaced by a big bounce. Thanks to the nonperturbative, background independent methods, unlike in other approaches the quantum evolution is deterministic across the deep Planck regime. Our constructions also provide a conceptual framework and technical tools which can be used in more general models. In this sense, they provide foundations for analyzing physical issues associated with the Planck regime of loop quantum cosmology as a whole.
Biomimetic Isotropic Nanostructures for Structural Coloration
Forster, Jason D.; Noh, Heeso; Liew, Seng Fatt; Saranathan, Vinodkumar; Schreck, Carl F.; Yang, Lin; Park, Jin-Gyu; Prum, Richard O.; Mochrie, Simon G.J.; O'Hern, Corey S.; Cao, Hui; Dufresne, Eric R.
2010-08-09
The self-assembly of films that mimic color-producing nanostructures in bird feathers is described. These structures are isotropic and have a characteristic length-scale comparable to the wavelength of visible light. Structural colors are produced when wavelength-independent scattering is suppressed by limiting the optical path length through geometry or absorption.
Using CMB data to constrain non-isotropic Planck-scale modifications to Electrodynamics
Gubitosi, Giulia; Migliaccio, Marina; Pagano, Luca; Amelino-Camelia, Giovanni; Melchiorri, Alessandro; Natoli, Paolo; Polenta, Gianluca E-mail: Marina.Migliaccio@roma2.infn.it E-mail: giovanni.amelino-camelia@roma1.infn.it E-mail: paolo.natoli@roma2.infn.it
2011-11-01
We develop a method to constrain non-isotropic features of Cosmic Microwave Background (CMB) polarization, of a type expected to arise in some models describing quantum gravity effects on light propagation. We describe the expected signatures of this kind of anomalous light propagation on CMB photons, showing that it will produce a non-isotropic birefringence effect, i.e. a rotation of the CMB polarization direction whose observed amount depends in a peculiar way on the observation direction. We also show that the sensitivity levels expected for CMB polarization studies by the Planck satellite are sufficient for testing these effects if, as assumed in the quantum-gravity literature, their magnitude is set by the minute Planck length.
Transversely Isotropic Elasticity Imaging of Cancellous Bone
Shore, Spencer W.; Barbone, Paul E.; Oberai, Assad A.; Morgan, Elise F.
2012-01-01
To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ε12 is necessary to reconstruct C1212), and the application of regularization is shown to improve accuracy. Finally, the effects
Transversely isotropic elasticity imaging of cancellous bone.
Shore, Spencer W; Barbone, Paul E; Oberai, Assad A; Morgan, Elise F
2011-06-01
To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ɛ₁₂ is necessary to reconstruct C₁₂₁₂), and the application of regularization is shown to improve accuracy. Finally
2017-03-16
When an active region rotated over to the edge of the sun, it presented us with a nice profile view of its elongated loops stretching and swaying above it (Mar. 8-9, 2017). These loops are actually charged particles (made visible in extreme ultraviolet light) swirling along the magnetic field lines of the active region. The video covers about 30 hours of activity. Also of note is a darker twisting mass of plasma to the left of the active region being pulled and spun about by magnetic forces. Video is available at http://photojournal.jpl.nasa.gov/catalog/PIA21562
Interactively variable isotropic resolution in computed tomography.
Lapp, Robert M; Kyriakou, Yiannis; Kachelriess, Marc; Wilharm, Sylvia; Kalender, Willi A
2008-05-21
An individual balancing between spatial resolution and image noise is necessary to fulfil the diagnostic requirements in medical CT imaging. In order to change influencing parameters, such as reconstruction kernel or effective slice thickness, additional raw-data-dependent image reconstructions have to be performed. Therefore, the noise versus resolution trade-off is time consuming and not interactively applicable. Furthermore, isotropic resolution, expressed by an equivalent point spread function (PSF) in every spatial direction, is important for the undistorted visualization and quantitative evaluation of small structures independent of the viewing plane. Theoretically, isotropic resolution can be obtained by matching the in-plane and through-plane resolution with the aforementioned parameters. Practically, however, the user is not assisted in doing so by current reconstruction systems and therefore isotropic resolution is not commonly achieved, in particular not at the desired resolution level. In this paper, an integrated approach is presented for equalizing the in-plane and through-plane spatial resolution by image filtering. The required filter kernels are calculated from previously measured PSFs in x/y- and z-direction. The concepts derived are combined with a variable resolution filtering technique. Both approaches are independent of CT raw data and operate only on reconstructed images which allows for their application in real time. Thereby, the aim of interactively variable, isotropic resolution is achieved. Results were evaluated quantitatively by measuring PSFs and image noise, and qualitatively by comparing the images to direct reconstructions regarded as the gold standard. Filtered images matched direct reconstructions with arbitrary reconstruction kernels with standard deviations in difference images of typically between 1 and 17 HU. Isotropic resolution was achieved within 5% of the selected resolution level. Processing times of 20-100 ms per frame
NASA Astrophysics Data System (ADS)
Oriti, Daniele
2009-03-01
Preface; Part I. Fundamental Ideas and General Formalisms: 1. Unfinished revolution C. Rovelli; 2. The fundamental nature of space and time G. 't Hooft; 3. Does locality fail at intermediate length scales R. Sorkin; 4. Prolegomena to any future quantum gravity J. Stachel; 5. Spacetime symmetries in histories canonical gravity N. Savvidou; 6. Categorical geometry and the mathematical foundations of quantum gravity L. Crane; 7. Emergent relativity O. Dreyer; 8. Asymptotic safety R. Percacci; 9. New directions in background independent quantum gravity F. Markopoulou; Questions and answers; Part II: 10. Gauge/gravity duality G. Horowitz and J. Polchinski; 11. String theory, holography and quantum gravity T. Banks; 12. String field theory W. Taylor; Questions and answers; Part III: 13. Loop Quantum Gravity T. Thiemann; 14. Covariant loop quantum gravity? E. LIvine; 15. The spin foam representation of loop quantum gravity A. Perez; 16. 3-dimensional spin foam quantum gravity L. Freidel; 17. The group field theory approach to quantum gravity D. Oriti; Questions and answers; Part IV. Discrete Quantum Gravity: 18. Quantum gravity: the art of building spacetime J. Ambjørn, J. Jurkiewicz and R. Loll; 19. Quantum Regge calculations R. Williams; 20. Consistent discretizations as a road to quantum gravity R. Gambini and J. Pullin; 21. The causal set approach to quantum gravity J. Henson; Questions and answers; Part V. Effective Models and Quantum Gravity Phenomenology: 22. Quantum gravity phenomenology G. Amelino-Camelia; 23. Quantum gravity and precision tests C. Burgess; 24. Algebraic approach to quantum gravity II: non-commutative spacetime F. Girelli; 25. Doubly special relativity J. Kowalski-Glikman; 26. From quantum reference frames to deformed special relativity F. Girelli; 27. Lorentz invariance violation and its role in quantum gravity phenomenology J. Collins, A. Perez and D. Sudarsky; 28. Generic predictions of quantum theories of gravity L. Smolin; Questions and
Warne, Larry Kevin; Lucero, Larry Martin; Langston, William L.; Salazar, Robert Austin; Coleman, Phillip Dale; Basilio, Lorena I.; Bacon, Larry Donald
2012-05-01
This report estimates inductively-coupled energy to a low-impedance load in a loop-to-loop arrangement. Both analytical models and full-wave numerical simulations are used and the resulting fields, coupled powers and energies are compared. The energies are simply estimated from the coupled powers through approximations to the energy theorem. The transmitter loop is taken to be either a circular geometry or a rectangular-loop (stripline-type) geometry that was used in an experimental setup. Simple magnetic field models are constructed and used to estimate the mutual inductance to the receiving loop, which is taken to be circular with one or several turns. Circuit elements are estimated and used to determine the coupled current and power (an equivalent antenna picture is also given). These results are compared to an electromagnetic simulation of the transmitter geometry. Simple approximate relations are also given to estimate coupled energy from the power. The effect of additional loads in the form of attached leads, forming transmission lines, are considered. The results are summarized in a set of susceptibility-type curves. Finally, we also consider drives to the cables themselves and the resulting common-to-differential mode currents in the load.
Apparent anisotropy in inhomogeneous isotropic media
NASA Astrophysics Data System (ADS)
Lin, Fan-Chi; Ritzwoller, Michael H.
2011-09-01
Surface waves propagating through a laterally inhomogeneous medium undergo wavefield complications such as multiple scattering, wave front healing, and backward scattering. Unless accounted for accurately, these effects will introduce a systematic isotropic bias in estimates of azimuthal anisotropy. We demonstrate with synthetic experiments that backward scattering near an observing station will introduce an apparent 360° periodicity into the azimuthal distribution of anisotropy near strong lateral variations in seismic wave speeds that increases with period. Because it violates reciprocity, this apparent 1ψ anisotropy, where ψ is the azimuthal angle, is non-physical for surface waves and is, therefore, a useful indicator of isotropic bias. Isotropic bias of the 2ψ (180° periodicity) component of azimuthal anisotropy, in contrast, is caused mainly by wave front healing, which results from the broad forward scattering part of the surface wave sensitivity kernel. To test these predictions, we apply geometrical ray theoretic (eikonal) tomography to teleseismic Rayleigh wave measurements across the Transportable Array component of USArray to measure the directional dependence of phase velocities between 30 and 80 s period. Eikonal tomography accounts for multiple scattering (ray bending) but not finite frequency effects such as wave front healing or backward scattering. At long periods (>50 s), consistent with the predictions from the synthetic experiments, a significant 1ψ component of azimuthal anisotropy is observed near strong isotropic structural contrasts with fast directions that point in the direction of increasing phase speeds. The observed 2ψ component of azimuthal anisotropy is more weakly correlated with synthetic predictions of isotropic bias, probably because of the imprint of intrinsic structural anisotropy. The observation of a 1ψ component of azimuthal anisotropy is a clear indicator of isotropic bias in the inversion caused by unmodelled
ISOTROPIC INELASTIC COLLISIONS IN A MULTITERM ATOM WITH HYPERFINE STRUCTURE
Belluzzi, Luca; Landi Degl’Innocenti, Egidio; Bueno, Javier Trujillo
2015-10-10
A correct modeling of the scattering polarization profiles observed in some spectral lines of diagnostic interest, the sodium doublet being one of the most important examples, requires taking hyperfine structure (HFS) and quantum interference between different J-levels into account. An atomic model suitable for taking these physical ingredients into account is the so-called multiterm atom with HFS. In this work, we introduce and study the transfer and relaxation rates due to isotropic inelastic collisions with electrons, which enter the statistical equilibrium equations (SEE) for the atomic density matrix of this atomic model. Under the hypothesis that the electron–atom interaction is described by a dipolar operator, we provide useful relations between the rates describing the transfer and relaxation of quantum interference between different levels (whose numerical values are in most cases unknown) and the usual rates for the atomic level populations, for which experimental data and/or approximate theoretical expressions are generally available. For the particular case of a two-term atom with HFS, we present an analytical solution of the SEE for the spherical statistical tensors of the upper term, including both radiative and collisional processes, and we derive the expression of the emission coefficient in the four Stokes parameters. Finally, an illustrative application to the Na i D{sub 1} and D{sub 2} lines is presented.
Isotropic Inelastic Collisions in a Multiterm Atom with Hyperfine Structure
NASA Astrophysics Data System (ADS)
Belluzzi, Luca; Landi Degl'Innocenti, Egidio; Trujillo Bueno, Javier
2015-10-01
A correct modeling of the scattering polarization profiles observed in some spectral lines of diagnostic interest, the sodium doublet being one of the most important examples, requires taking hyperfine structure (HFS) and quantum interference between different J-levels into account. An atomic model suitable for taking these physical ingredients into account is the so-called multiterm atom with HFS. In this work, we introduce and study the transfer and relaxation rates due to isotropic inelastic collisions with electrons, which enter the statistical equilibrium equations (SEE) for the atomic density matrix of this atomic model. Under the hypothesis that the electron-atom interaction is described by a dipolar operator, we provide useful relations between the rates describing the transfer and relaxation of quantum interference between different levels (whose numerical values are in most cases unknown) and the usual rates for the atomic level populations, for which experimental data and/or approximate theoretical expressions are generally available. For the particular case of a two-term atom with HFS, we present an analytical solution of the SEE for the spherical statistical tensors of the upper term, including both radiative and collisional processes, and we derive the expression of the emission coefficient in the four Stokes parameters. Finally, an illustrative application to the Na i D1 and D2 lines is presented.
WYPIWYG hyperelasticity for isotropic, compressible materials
NASA Astrophysics Data System (ADS)
Crespo, José; Latorre, Marcos; Montáns, Francisco Javier
2016-10-01
Nowadays the most common approach to model elastic behavior at large strains is through hyperelasticity. Hyperelastic models usually specify the shape of the stored energy function. This shape is modulated by some material parameters that are computed so the predicted stresses best fit the experimental data. Many stored energy functions have been proposed in the literature for isotropic and anisotropic materials, either compressible or incompressible. What-You-Prescribe-Is-What-You-Get (WYPIWYG) formulations present a different approach which may be considered an extension of the infinitesimal framework. The shape of the stored energy is not given beforehand but computed numerically from experimental data solving the equilibrium equations. The models exactly fit the experimental data without any material parameter. WYPIWYG procedures have comparable efficiency in finite element procedures as classical hyperelasticity. In this work we present a WYPIWYG numerical procedure for compressible isotropic materials and we motivate the formulation through an equivalent infinitesimal model.
Polyakov loop modeling for hot QCD
NASA Astrophysics Data System (ADS)
Fukushima, Kenji; Skokov, Vladimir
2017-09-01
We review theoretical aspects of quantum chromodynamics (QCD) at finite temperature. The most important physical variable to characterize hot QCD is the Polyakov loop, which is an approximate order parameter for quark deconfinement in a hot gluonic medium. Additionally to its role as an order parameter, the Polyakov loop has rich physical contents in both perturbative and non-perturbative sectors. This review covers a wide range of subjects associated with the Polyakov loop from topological defects in hot QCD to model building with coupling to the Polyakov loop.
Conservation law for linked cosmic string loops
NASA Astrophysics Data System (ADS)
Bekenstein, Jacob D.
1992-05-01
Taking a cue from the connection between fluid helicity and the linkage between closed vortices in ordinary turbulent flow, we examine topological restrictions on the linkage of cosmic string loops (or superfluid quantum vortex rings). The analog of helicity in these cases vanishes, but loops (and vortex rings) can link together, the extent of linkage (knotting included) being related to the contorsion of the loops or rings by a topological conservation law. This law is respected by intercommunication. One consequence is that total loop contorsion is quantized in integers.
Infinite Products of Random Isotropically Distributed Matrices
NASA Astrophysics Data System (ADS)
Il'yn, A. S.; Sirota, V. A.; Zybin, K. P.
2017-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
Xu Zhe; Greiner, Carsten
2007-08-15
To describe momentum isotropization of gluon matter produced in ultrarelativistic heavy-ion collisions, the transport rate of gluon drift and the transport collision rates of elastic (gg{r_reversible}gg) as well as inelastic (gg{r_reversible}ggg) perturbative quantum chromodynamics- (pQCD) scattering processes are introduced and calculated within the kinetic parton cascade Boltzmann approach of multiparton scatterings (BAMPS), which simulates the space-time evolution of partons. We define isotropization as the development of an anisotropic system as it reaches isotropy. The inverse of the introduced total transport rate gives the correct time scale of the momentum isotropization. The contributions of the various scattering processes to the momentum isotropization can be separated into the transport collision rates. In contrast to the transport cross section, the transport collision rate has an indirect but correctly implemented relationship with the collision-angle distribution. Based on the calculated transport collision rates from BAMPS for central Au+Au collisions at Relativistic Heavy Ion Collider energies, we show that pQCD gg{r_reversible}ggg bremsstrahlung processes isotropize the momentum five times more efficiently than elastic scatterings. The large efficiency of the bremsstrahlung stems mainly from its large momentum deflection. Due to kinematics, 2{yields}N (N>2) production processes allow more particles to become isotropic in momentum space and thus kinetically equilibrate more quickly than their back reactions or elastic scatterings. We also show that the relaxation time in the relaxation time approximation, which is often used, is strongly momentum dependent and thus cannot serve as a global quantity that describes kinetic equilibration.
DNS of Shock / Isotropic Turbulence Interaction
NASA Astrophysics Data System (ADS)
Grube, Nathan; Taylor, Ellen; Martín, Pino
2010-11-01
We discuss DNS of Shock / Isotropic Turbulence Interactions (SITI). We vary the incoming turbulence Mach number up to 0.8 and the convective Mach number up to 5 in order to determine their effects on the interaction. These cases are challenging due to the presence of shocklets in the incoming turbulence as well as significant motion of the main shock. Shock-capturing must be used at all points while still maintaining low enough numerical dissipation to preserve the turbulent fluctuations. We use the linearly- and nonlinearly-optimized Weighted Essentially Non-Oscillatory (WENO) method[1,2]. Particular attention is paid to the inflow boundary condition, where we find the use of snapshots of "frozen" turbulence from decaying isotropic box simulations to be unsatisfactory. We instead use time-varying inflow data generated by a separate forced isotropic turbulence simulation with a specified convection speed. This allows us to access flow conditions where the assumptions of Taylor's Hypothesis are not met. 1.) Mart'in, M.P., Taylor, E.M., Wu, M., and Weirs, V.G., JCP 220(1) 270-89, 2006. 2.) Taylor, E.M., Wu, M., and Mart'in, M.P., JCP 223(1) 384-97, 2007.
Isotropic Contraction Of Mercury Due To Despinning
NASA Astrophysics Data System (ADS)
Matsuyama, Isamu; Bills, B. G.
2009-09-01
Mercury's slow rotation period of 59 days is presumably the result of solar tides driving its initial rotational state to the present 3:2 spin-orbit resonance. The observed large gravity coefficients can be explained as due to a remnant rotational bulge recording an initial rotation period of a few days (Matsuyama and Nimmo 2009). Despinning changes the shape of the rotational bulge, generating both compressional and extensional stresses (Melosh 1977). However, Mercury's surface is dominated by compressional tectonic features (Watters et al. 1998), and the inferred global contraction has been explained as due to thermal cooling (Solomon 1976). In addition to non-isotropic changes associated with the rotational flattening, despinning causes isotropic contraction of the entire planet. We consider the effect of the compressional stresses generated by this isotropic contraction on the predicted tectonic pattern. References Matsuyama and Nimmo. Gravity and tectonic patterns of Mercury: Effect of tidal deformation, spin-orbit resonance, nonzero eccentricity, despinning, and reorientation. J. Geophys. Res. (2009) vol. 114 pp. E01010 Melosh. Global tectonics of a despun planet. Icarus (1977) vol. 31 pp. 221-243 Solomon. Some aspects of core formation in Mercury. Icarus (1976) vol. 28 pp. 509-521 Watters et al. Topography of lobate scarps on Mercury: New constraints on the planet's contraction. Geology (1998) vol. 26 pp. 991-994
Non-singular dislocation loops in gradient elasticity
NASA Astrophysics Data System (ADS)
Lazar, Markus
2012-04-01
Using gradient elasticity, we give in this Letter the non-singular fields produced by arbitrary dislocation loops in isotropic media. We present the ‘modified’ Mura, Peach-Koehler and Burgers formulae in the framework of gradient elasticity theory.
Non-anticommutative quantum gravity
NASA Astrophysics Data System (ADS)
Moffat, J. W.
2015-06-01
A calculation of the one loop gravitational self-energy graph in non-anticommutative quantum gravity reveals that graviton loops are damped by internal momentum dependent factors in the modified propagator and the vertex functions. The non-anticommutative quantum gravity perturbation theory is finite for matter-free gravity and for matter interactions.
Linearized holographic isotropization at finite coupling
NASA Astrophysics Data System (ADS)
Atashi, Mahdi; Fadafan, Kazem Bitaghsir; Jafari, Ghadir
2017-06-01
We study holographic isotropization of an anisotropic homogeneous non-Abelian strongly coupled plasma in the presence of Gauss-Bonnet corrections. It was verified before that one can linearize Einstein's equations around the final black hole background and simplify the complicated setup. Using this approach, we study the expectation value of the boundary stress tensor. Although we consider small values of the Gauss-Bonnet coupling constant, it is found that finite coupling leads to significant increasing of the thermalization time. By including higher order corrections in linearization, we extend the results to study the effect of the Gauss-Bonnet coupling on the entropy production on the event horizon.
Shear elasticity of isotropic magnetic gels
NASA Astrophysics Data System (ADS)
Lopez-Lopez, M. T.; Borin, D. Yu.; Zubarev, A. Yu.
2017-08-01
The paper deals with a theoretical study of the effective shear modulus of a magnetic gel, consisting of magnetizable particles randomly and isotropically distributed in an elastic matrix. The effect of an external magnetic field on the composite modulus is the focus of our consideration. We take into account that magnetic interaction between the particles can induce their spatial rearrangement and lead to internal anisotropy of the system. Our results show that, if this magnetically induced anisotropy is insignificant, the applied field reduces the total shear modulus of the composite. Strong anisotropy can qualitatively change the magnetomechanic effect and induce an increase of this modulus with the field.
Isotropic homogeneous universe with viscous fluid
Santos, N.O.; Dias, R.S.; Banerjee, A.
1985-04-01
Exact solutions are obtained for the isotropic homogeneous cosmological model with viscous fluid. The fluid has only bulk viscosity and the viscosity coefficient is taken to be a power function of the mass density. The equation of state assumed obeys a linear relation between mass density and pressure. The models satisfying Hawking's energy conditions are discussed. Murphy's model is only a special case of this general set of solutions and it is shown that Murphy's conclusion that the introduciton of bulk viscosity can avoid the occurrence of space-time singularity at finite past is not, in general, valid.
Small scale dynamics of isotropic viscoelastic turbulence
NASA Astrophysics Data System (ADS)
Nguyen, M. Quan; Delache, Alexandre; Simoëns, Serge; Bos, Wouter J. T.; El Hajem, Mamoud
2016-12-01
The comparison of the results of direct numerical simulations of isotropic turbulence of Newtonian and viscoelastic fluid provides evidence that viscoelasticity modifies qualitatively the behavior of the smallest scales: we observe a power law in the far dissipation range of the fluid kinetic energy spectrum and we show that it is a robust feature, roughly independent of the large scale dynamics. A detailed analysis of the energy transfer shows that at these scales energy is injected into the fluid flow through polymer relaxation. It is further shown that a part of the total energy is transferred among scales through an interaction of the velocity field with the polymer field.
Isotropization of nematic liquid crystals by TMDSC
Chen, Wei; Dadmun, M.; Zhang, Ge; Boller, A.; Wunderlich, B. |
1997-12-01
Temperature-modulated differential scanning calorimetry (TMDSC) and traditional DSC are used to study the transition between the nematic liquid crystalline state and the isotropic liquid for two small molecules [4,4{prime}-azoxyanisole and N,N`-bis(4-n-octyloxybenzal)-1,4-phenylenediamine] and one macromolecule (4,4{prime}-dihydroxy-{alpha}-methylstilbene copolymerized with a 1:1 molar mixture of 1,7-dibromoheptane and 1,9-dibromononane). The DSC measurements with 4,4{prime}-azoxyanisole were used for temperature calibration with varying heating and cooling rates. Quasi-isothermal TMDSC with small temperature amplitude and standard TMDSC with underlying heating and cooling rates were utilized to analyze the breadth of the transitions. It could be verified that the isotropization transition of a nematic liquid crystal is, indeed, reversible for all three molecules. The nature of the transition changes, however, from relatively sharp, for small, rigid molecules, to about three kelvins wide for the small molecule with flexible ends, to as broad as 20 K for the macromolecule. It was also demonstrated that quantitative heats of fusion of sharp transitions can be extracted from TMDSC, but only from the time-domain heat-flow signal.
Cyclic networks of quantum gates
NASA Astrophysics Data System (ADS)
Cabauy, Peter
In this thesis we first give an introduction to the basic aspects of quantum computation followed by an analysis of networks of quantum logic gates where the qubit lines are loops (cyclic). Thus far, investigations into cyclic networks of quantum logic gates have not been examined (as far as we know) by the quantum information community. In our investigations of cyclic quantum networks we have studied simple, one and two qubit systems. The analysis includes: classifying networks into groups, the dynamics of the qubits in a cyclic quantum network, and the perturbation effects of an external qubit acting on a cyclic quantum network. The analysis will be followed by a discussion on quantum algorithms and quantum information processing with cyclic quantum networks, a novel implementation of a cyclic network quantum memory and a discussion of quantum sensors via cyclic quantum networks.
NASA Astrophysics Data System (ADS)
Freidel, Laurent; Perez, Alejandro; Pranzetti, Daniele
2017-05-01
In this work we study canonical gravity in finite regions for which we introduce a generalization of the Gibbons-Hawking boundary term including the Immirzi parameter. We study the canonical formulation on a spacelike hypersurface with a boundary sphere and show how the presence of this term leads to an unprecedented type of degrees of freedom coming from the restoration of the gauge and diffeomorphism symmetry at the boundary. In the presence of a loop quantum gravity state, these boundary degrees of freedom localize along a set of punctures on the boundary sphere. We demonstrate that these degrees of freedom are effectively described by auxiliary strings with a three-dimensional internal target space attached to each puncture. We show that the string currents represent the local frame field, that the string angular momenta represent the area flux, and that the string stress tensor represents the two-dimensional metric on the boundary of the region of interest. Finally, we show that the commutators of these broken diffeomorphism charges of quantum geometry satisfy, at each puncture, a Virasoro algebra with central charge c =3 . This leads to a description of the boundary degrees of freedom in terms of a CFT structure with central charge proportional to the number of loop punctures. The boundary S U (2 ) gauge symmetry is recovered via the action of the U (1 )3 Kac-Moody generators (associated with the string current) in a way that is the exact analog of an infinite dimensional generalization of the Schwinger spin representation. We finally show that this symmetry is broken by the presence of background curvature.
Accelerating the loop expansion
Ingermanson, R.
1986-07-29
This thesis introduces a new non-perturbative technique into quantum field theory. To illustrate the method, I analyze the much-studied phi/sup 4/ theory in two dimensions. As a prelude, I first show that the Hartree approximation is easy to obtain from the calculation of the one-loop effective potential by a simple modification of the propagator that does not affect the perturbative renormalization procedure. A further modification then susggests itself, which has the same nice property, and which automatically yields a convex effective potential. I then show that both of these modifications extend naturally to higher orders in the derivative expansion of the effective action and to higher orders in the loop-expansion. The net effect is to re-sum the perturbation series for the effective action as a systematic ''accelerated'' non-perturbative expansion. Each term in the accelerated expansion corresponds to an infinite number of terms in the original series. Each term can be computed explicitly, albeit numerically. Many numerical graphs of the various approximations to the first two terms in the derivative expansion are given. I discuss the reliability of the results and the problem of spontaneous symmetry-breaking, as well as some potential applications to more interesting field theories. 40 refs.
Loop Optimization for Tensor Network Renormalization
NASA Astrophysics Data System (ADS)
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
2017-03-01
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model.
Loop Optimization for Tensor Network Renormalization.
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
2017-03-17
We introduce a tensor renormalization group scheme for coarse graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to deform a 2D tensor network into small loops and then optimize the tensors on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model.
Quantum Computation Toward Quantum Gravity
NASA Astrophysics Data System (ADS)
Zizzi, P. A.
2001-08-01
The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin -1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.
Long distance quantum communication using quantum error correction
NASA Technical Reports Server (NTRS)
Gingrich, R. M.; Lee, H.; Dowling, J. P.
2004-01-01
We describe a quantum error correction scheme that can increase the effective absorption length of the communication channel. This device can play the role of a quantum transponder when placed in series, or a cyclic quantum memory when inserted in an optical loop.
Long distance quantum communication using quantum error correction
NASA Technical Reports Server (NTRS)
Gingrich, R. M.; Lee, H.; Dowling, J. P.
2004-01-01
We describe a quantum error correction scheme that can increase the effective absorption length of the communication channel. This device can play the role of a quantum transponder when placed in series, or a cyclic quantum memory when inserted in an optical loop.
Real wave propagation in the isotropic-relaxed micromorphic model.
Neff, Patrizio; Madeo, Angela; Barbagallo, Gabriele; d'Agostino, Marco Valerio; Abreu, Rafael; Ghiba, Ionel-Dumitrel
2017-01-01
For the recently introduced isotropic-relaxed micromorphic generalized continuum model, we show that, under the assumption of positive-definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than the positive definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, whereas it does in isotropic linear elasticity.
Scattering from isotropic plasma coated nihility sphere
NASA Astrophysics Data System (ADS)
Hussan, M. M.; Ghaffar, A.; Alkanhal, Majeed A. S.; Naz, M. Y.; Ur Rehman, Sajjad; Khan, Y.
2017-06-01
In this study, it is observed that when an isotropic collisional plasma coating layer is produced on a nihility sphere, its back scattering efficiency becomes non-zero. Field equations, at each interface, are expanded in terms of spherical wave vector functions (SWVFs) by enforcing the extended classical wave scattering theory. Electromagnetic boundary conditions are applied at both interfaces, i.e., free space-plasma and plasma layer-nihility sphere core to obtain the scattering coefficients. The obtained scattering coefficients are used to calculate the forward scattering, back scattering, and extinction efficiencies. The obtained computational results show that an increase in collisional frequency causes a decrease in both forward and backscattered efficiencies and an increase in extinction efficiency. Furthermore, the numerical results indicate that an increase in plasma density causes an increase in both forward and backscattered efficiencies and a decrease in extinction efficiency.
Constitutive model development for isotropic materials
NASA Technical Reports Server (NTRS)
Kaufman, A.
1982-01-01
The objective is to develop a unified constitutive model for finite-element structural analysis of turbine engine hot section components. This effort constitutes a different approach for nonlinear finite-element computer codes which were heretofore based on classical inelastic methods. A unified constitutive theory will avoid the simplifying assumptions of classical theory and should more accurately represent the behavior of superalloy materials under cyclic loading conditions and high temperature environments. Model development will be directed toward isotropic, cast nickel-base alloys used for aircooled turbine blades and vanes. The contractor will select a base material for model development and an alternate material for verification purposes from a list of three alloys specified by NASA. The candidate alloys represent a cross-section of turbine blade and vane materials of interest to both large and small size engine manufacturers. Material stock for the base and alternate materials will be supplied to the Contractor by the government.
Isotropic MD simulations of dynamic brittle fracture
Espanol, P.; Rubio, M.A.; Zuniga, I.
1996-12-01
The authors present results obtained by molecular dynamics simulations on the propagation of fast cracks in triangular 2D lattices. Their aim is to simulate Mode 1 fracture of brittle isotropic materials. They propose a force law that respects the isotropy of the material. The code yields the correct imposed sound c{sub {parallel}}, shear c{sub {perpendicular}} and surface V{sub R} wave speeds. Different notch lengths are systematically studied. They observed that initially the cracks are linear and always branch at a particular critical velocity c* {approx} 0.8V{sub R} and that this occurs when the crack tip reaches the position of a front emitted from the initial crack tip and propagating at a speed c = 0.68V{sub R}.
Isotropic cosmological singularities: other matter models
NASA Astrophysics Data System (ADS)
Tod, K. P.
2003-02-01
Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied, the existence and uniqueness of cosmological models with data at the singularity has been established (Anguige K and Tod K P 1999 Ann. Phys., NY 276 257-93, 294-320, Anguige K 2000 Ann. Phys., NY 285 395-419). These were cosmologies with, as source, either perfect fluids with linear equations of state or massless, collisionless particles. In this paper, we consider how to extend these results to a variety of other matter models. These are scalar fields, massive collisionless matter, the Yang-Mills plasma given by Choquet-Bruhat (Choquet-Bruhat Y 1996 Yang-Mills plasmas Global Structure and Evolution in General Relativity (Springer Lecture Notes in Physics vol 460) ed S Cotsakis and G W Gibbons (Berlin: Springer)) and matter satisfying the Einstein-Boltzmann equation.
Can we remove the systematic error due to isotropic inhomogeneities?
NASA Astrophysics Data System (ADS)
Negishi, Hiroyuki; Nakao, Ken-ichi
2017-01-01
Usually, we assume that there is no inhomogeneity isotropic in terms of our location in our Universe. This assumption has not been observationally confirmed yet in sufficient accuracy, and we need to consider the possibility that there are non-negligible large-scale isotropic inhomogeneities in our Universe. The existence of large-scale isotropic inhomogeneities affects the determination of cosmological parameters. In particular, from only the distance-redshift relation, we cannot distinguish the inhomogeneous isotropic universe model from the homogeneous isotropic one, because of the ambiguity in the cosmological parameters. In this paper, in order to avoid such ambiguity, we consider three observables—the distance-redshift relation, the fluctuation spectrum of the cosmic microwave background radiation, and the scale of the baryon acoustic oscillation—and compare these observables in two universe models. One is the inhomogeneous isotropic universe model with the cosmological constant, and the other is the homogeneous isotropic universe model with dark energy other than the cosmological constant. We show that these two universe models cannot predict the same observational data of all three observables but the same ones of only two of three, as long as the perturbations are adiabatic. In principle, we can distinguish the inhomogeneous isotropic universe from the homogeneous isotropic one through the appropriate three observables, if the perturbations are adiabatic.
Viscous propulsion in active transversely isotropic media
NASA Astrophysics Data System (ADS)
Cupples, G.; Dyson, R. J.; Smith, D. J.
2017-02-01
Taylor's swimming sheet is a classical model of microscale propulsion and pumping. Many biological fluids and substances are fibrous, having a preferred direction in their microstructure; for example cervical mucus is formed of polymer molecules which create an oriented fibrous network. Moreover, suspensions of elongated motile cells produce a form of active oriented matter. To understand how these effects modify viscous propulsion, we extend Taylor's classical model of small-amplitude zero-Reynolds-number propulsion of a 'swimming sheet' via the transversely-isotropic fluid model of Ericksen, which is linear in strain rate and possesses a distinguished direction. The energetic costs of swimming are significantly altered by all rheological parameters and the initial fibre angle. Propulsion in a passive transversely-isotropic fluid produces an enhanced mean rate of working, independent of the initial fibre orientation, with an approximately linear dependence of energetic cost on the extensional and shear enhancements to the viscosity caused by fibres. In this regime the mean swimming velocity is unchanged from the Newtonian case. The effect of the constant term in Ericksen's model for the stress, which can be identified as a fibre tension or alternatively a stresslet characterising an active fluid, is also considered. This stress introduces an angular dependence and dramatically changes the streamlines and flow field; fibres aligned with the swimming direction increase the energetic demands of the sheet. The constant fibre stress may result in a reversal of the mean swimming velocity and a negative mean rate of working if sufficiently large relative to the other rheological parameters.
Velocity analysis for transversely isotropic media
Alkhalifah, T.; Tsvankin, I.
1994-08-01
The main difficulty in extending seismic processing to anisotropic media is the recovery of anisotropic velocity fields from surface reflection data. Velocity analysis for transversely isotropic (TI) media can be done by inverting the dependence of P-wave moveout velocities on the ray parameter. P-wave NMO velocity in homogeneous TI media with a vertical symmetry axis depends just on the zero-dip value V{sub nmo} and a new effective parameter {eta} that reduces to the difference between Thomsen parameters {epsilon} and {delta} in the limit of weak anisotropy. It is possible to obtain {eta} and reconstruct the NMO velocity as a function of ray parameter using moveout velocities for two different dips. Moreover, V{sub nmo}(0) and {eta} determine not only the NMO velocity, but also also long-spread (nonhyperbollic) P-wave moveout for horizontal reflectors and time-migration impulse response. Inversion of dip-moveout information allows performance of all time-processing steps in TI media using only surface P-wave data. Isotropic time-processing methods remain entirely valid for elliptical anisotropy ({epsilon} = {delta}). Accurate time-to-depth conversion, however, requires the vertical velocity V{sub P0} be resolved independently. If I-P0 is known, then allisotropies {epsilon} and {delta} can be found by inverting two P-wave NMO velocities corresponding to a horizontal and a dipping reflector. If no information is available, all three parameters (V {sub P0}, {epsilon}, and {delta}) can be obtained by combining inversion results with shear-wave information. such as the P-SV or SV-SV wave NMO velocities for a horizontal reflector. Generalization of Tsvankin`s single-layer NMO equation for layered anisotropic media with a dipping reflector provides a basis for extending anisotropic velocity analysis to vertically inhomogeneous media. The influence of a stratified overburden on moveout velocity can be stripped through a Dix-type differentiation procedure.
ERIC Educational Resources Information Center
Jefimenko, Oleg
1974-01-01
Discusses the design of a modified loop-the-loop apparatus in which a water stream is used to illustrate centripetal forces and phenomena of high-velocity hydrodynamics. Included are some procedures of carrying out lecture demonstrations. (CC)
ERIC Educational Resources Information Center
Jefimenko, Oleg
1974-01-01
Discusses the design of a modified loop-the-loop apparatus in which a water stream is used to illustrate centripetal forces and phenomena of high-velocity hydrodynamics. Included are some procedures of carrying out lecture demonstrations. (CC)
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
3D phase-field modelling of dislocation loop sink strengths
NASA Astrophysics Data System (ADS)
Thuinet, L.; Rouchette, H.; Legris, A.
2017-01-01
This work presents a 3D phase-field model to correctly evaluate dislocation loop sink strength. This method is applied to a wide range of microstructures (dislocation loops of various types with isotropic or anisotropic elasticity, like in Zr, cohabitation of different types of loop in the same calculation domain), which allows to exhibit several original results. Among them, in the case of isotropic elasticity, our model shows that the sink strength of vacancy loops is higher than that of interstitial ones for low loop radii. In the case of Zr, the effect on sink biases of the shape anisotropy of self-interstitial atoms, already exhibited in the case of straight dislocations, is enhanced for loops and stabilizes basal vacancy and prism-plane interstitial ones. Moreover, isotropic elastic interactions promote the coexistence of parallel vacancy and interstitial loops. This result is still valid in the case of prism-plane loops in Zr, which could provide explanations to several experimental facts.
Active Colloids in Isotropic and Anisotropic Electrolytes
NASA Astrophysics Data System (ADS)
Peng, Chenhui
Electrically driven flows of fluids with respect to solid surfaces (electro-osmosis) and transport of particles in fluids (electrophoresis), collectively called electrokinetics, is a technologically important area of modern science. In this thesis, we study the electrokinetic phenomena in both isotropic and anisotropic fluids. A necessary condition of electrokinetics is separation of electric charges in space. In classic linear electrokinetics, with an isotropic electrolyte such as water, the charges are separated through dissociation of ionic groups at the solid-fluid interface; presence of the electric field is not required. In the nonlinear electrokinetics, the charges are separated with the assistance of the electric field. In the so-called induced-charge electro-osmosis (ICEO) the electric field separates charges near strongly polarizable surfaces such as metals. We establish the patterns of electro-osmotic velocities caused by nonlinear ICEO around an immobilized metallic and Janus (metallic-dielectric) spheres placed in water. In the case of the Janus particles, the flows are asymmetric, which results in pumping of water around the particle if it is immobilized, or in electrophoresis is the particle is free. When the isotropic electrolyte such as water is replaced with a LC electrolyte, the mechanism of the field-assisted charge separation becomes very different. Namely, the charges are separated at the director gradients, thanks to the anisotropy of electric conductivity and dielectric permittivity of the LC. These distortions can be created by the colloidal particles placed in the LC. We demonstrate the occurrence of nonlinear LC-enabled electro-osmosis (LCEO) by studying the flow patterns around colloidal spheres with different surface anchoring. LCEO velocities grow with the square of the electric field, which allows one to use an AC field to drive steady flows and to avoid electrode damage. Director distortions needed to trigger the LCEO can also be
Theoretical and experimental plastic strain ratios in planar isotropic textures
NASA Astrophysics Data System (ADS)
Kim, Insoo
1996-06-01
The plastic strain ratios of planar isotropic sheet specimens were studied by using unidirectionally solidified commercial Al. Sn and Al-Cu alloy sheets and Cu sheets electrodeposited under the various electrolysis conditions. The measured plastic strain ratios of [100] planar isotropic sheets by using unidirectionally solidified Al and Al-Cu alloy are about 0.17-0.52, that of [110] planar isotropic sheets using unidirectionally solidified Sn(BCT) are about 2.5, that of [110] planar isotropic sheets using electrodeposited Cu are 1.38-2.05 and that of [111] planar isotropic sheets using electrodeposited Cu are 2.61-2.85. There is a substantial discrepancy between the experimental plastic strain ratios which are measured from planar isotropic sheets and theoretical plastic strain ratios which are calculated by Backofen method and Bunge method, but the measured plastic strain ratio of [100] planar isotropic sheet using unidirectionally solidified Al and Al-Cu alloy is in good agreement with Bunge method and the measured plastic strain ratio of [110] and [111] planar isotropic sheets using electrodeposited Cu are in good agreement with Backofen method.
On the decay of homogeneous isotropic turbulence
NASA Astrophysics Data System (ADS)
Skrbek, L.; Stalp, Steven R.
2000-08-01
Decaying homogeneous, isotropic turbulence is investigated using a phenomenological model based on the three-dimensional turbulent energy spectra. We generalize the approach first used by Comte-Bellot and Corrsin [J. Fluid Mech. 25, 657 (1966)] and revised by Saffman [J. Fluid Mech. 27, 581 (1967); Phys. Fluids 10, 1349 (1967)]. At small wave numbers we assume the spectral energy is proportional to the wave number to an arbitrary power. The specific case of power 2, which follows from the Saffman invariant, is discussed in detail and is later shown to best describe experimental data. For the spectral energy density in the inertial range we apply both the Kolmogorov -5/3 law, E(k)=Cɛ2/3k-5/3, and the refined Kolmogorov law by taking into account intermittency. We show that intermittency affects the energy decay mainly by shifting the position of the virtual origin rather than altering the power law of the energy decay. Additionally, the spectrum is naturally truncated due to the size of the wind tunnel test section, as eddies larger than the physical size of the system cannot exist. We discuss effects associated with the energy-containing length scale saturating at the size of the test section and predict a change in the power law decay of both energy and vorticity. To incorporate viscous corrections to the model, we truncate the spectrum at an effective Kolmogorov wave number kη=γ(ɛ/v3)1/4, where γ is a dimensionless parameter of order unity. We show that as the turbulence decays, viscous corrections gradually become more important and a simple power law can no longer describe the decay. We discuss the final period of decay within the framework of our model, and show that care must be taken to distinguish between the final period of decay and the change of the character of decay due to the saturation of the energy containing length scale. The model is applied to a number of experiments on decaying turbulence. These include the downstream decay of turbulence in
Bojowald, Martin
2008-06-06
When quantum gravity is used to discuss the big bang singularity, the most important, though rarely addressed, question is what role genuine quantum degrees of freedom play. Here, complete effective equations are derived for isotropic models with an interacting scalar to all orders in the expansions involved. The resulting coupling terms show that quantum fluctuations do not affect the bounce much. Quantum correlations, however, do have an important role and could even eliminate the bounce. How quantum gravity regularizes the big bang depends crucially on properties of the quantum state.
Nonlinear elastic inclusions in isotropic solids
Yavari, Arash; Goriely, Alain
2013-01-01
We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder. PMID:24353470
Crossover from isotropic to directed percolation
NASA Astrophysics Data System (ADS)
Zhou, Zongzheng; Yang, Ji; Ziff, Robert M.; Deng, Youjin
2012-08-01
We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as p↓=ppd and p↑=p(1-pd), with p representing the average occupation probability and pd controlling the anisotropy. The Leath-Alexandrowicz method is used to grow a cluster from an active seed site. We call this model with two main growth directions biased directed percolation (BDP). Standard isotropic percolation (IP) and DP are the two limiting cases of the BDP model, corresponding to pd=1/2 and pd=0,1 respectively. In this work, besides IP and DP, we also consider the 1/2
Spectra and statistics in compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Wang, Jianchun; Gotoh, Toshiyuki; Watanabe, Takeshi
2017-01-01
Spectra and one-point statistics of velocity and thermodynamic variables in isotropic turbulence of compressible fluid are examined by using numerical simulations with solenoidal forcing at the turbulent Mach number Mt from 0.05 to 1.0 and at the Taylor Reynolds number Reλ from 40 to 350. The velocity field is decomposed into a solenoidal component and a compressible component in terms of the Helmholtz decomposition, and the compressible velocity component is further decomposed into a pseudosound component, namely, the hydrodynamic component associated with the incompressible field and an acoustic component associated with sound waves. It is found that the acoustic mode dominates over the pseudosound mode at turbulent Mach numbers Mt≥0.4 in our numerical simulations. At turbulent Mach numbers Mt≤0.4 , there exists a critical wave number kc beyond which the pseudosound mode dominates while the acoustic mode dominates at small wave numbers k
Scaling and intermittency in compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Wang, Jianchun; Gotoh, Toshiyuki; Watanabe, Takeshi
2017-05-01
Scaling and intermittency in compressible isotropic turbulence at the turbulent Mach number Mt ranging from 0.5 to 1.0 are studied by using numerical simulations with solenoidal forcing. Linear relations between the structure functions of the compressible velocity component and those of thermodynamic variables are modeled based on the shock jump conditions and are verified by numerical simulations. At a turbulent Mach number around 1.0, the relative scaling exponent of the structure functions saturates with an increase of the order. After proper normalization, the tails of the probability density functions (PDFs) of the increments of the compressible velocity component and thermodynamic variables overlap one another for different separations. Moreover, we study the conditional PDFs of the increments with respect to the shocklet. Linear relations between the tails of unconditional PDFs and conditional PDFs are established. The shocklet plays an important role in the determination of the PDF tails. The compressible velocity increment is decomposed into a negative component and a positive component. The negative component of the compressible velocity increment exhibits a scaling behavior with the saturation of the scaling exponent at high orders, which is similar to the Burgers turbulence, while the positive component of the compressible velocity increment exhibits a power-law scaling behavior, which is similar to the incompressible turbulence.
Constitutive modeling for isotropic materials (HOST)
NASA Technical Reports Server (NTRS)
Lindholm, Ulric S.; Chan, Kwai S.; Bodner, S. R.; Weber, R. M.; Walker, K. P.; Cassenti, B. N.
1984-01-01
The results of the first year of work on a program to validate unified constitutive models for isotropic materials utilized in high temperature regions of gas turbine engines and to demonstrate their usefulness in computing stress-strain-time-temperature histories in complex three-dimensional structural components. The unified theories combine all inelastic strain-rate components in a single term avoiding, for example, treating plasticity and creep as separate response phenomena. An extensive review of existing unified theories is given and numerical methods for integrating these stiff time-temperature-dependent constitutive equations are discussed. Two particular models, those developed by Bodner and Partom and by Walker, were selected for more detailed development and evaluation against experimental tensile, creep and cyclic strain tests on specimens of a cast nickel base alloy, B19000+Hf. Initial results comparing computed and test results for tensile and cyclic straining for temperature from ambient to 982 C and strain rates from 10(exp-7) 10(exp-3) s(exp-1) are given. Some preliminary date correlations are presented also for highly non-proportional biaxial loading which demonstrate an increase in biaxial cyclic hardening rate over uniaxial or proportional loading conditions. Initial work has begun on the implementation of both constitutive models in the MARC finite element computer code.
Near isotropic behavior of turbulent thermal convection
NASA Astrophysics Data System (ADS)
Nath, Dinesh; Pandey, Ambrish; Kumar, Abhishek; Verma, Mahendra K.
2016-10-01
We investigate the anisotropy in turbulent convection in a three-dimensional (3D) box using direct numerical simulation. We compute the anisotropic parameter A =u⊥2/(2 u∥2) , where u⊥ and u∥ are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number Pr ≈1 , but the anisotropy increases with the Prandtl number. For Pr =∞ ,A ≈0.3 , anisotropy is not very significant even in extreme cases. We also observe that u∥ feeds energy to u⊥ via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al. [Phys. Rev. E 90, 023016 (2014), 10.1103/PhysRevE.90.023016] for turbulent convection.
Microplane constitutive model for porous isotropic rocks
NASA Astrophysics Data System (ADS)
Baant, Zdenk P.; Zi, Goangseup
2003-01-01
The paper deals with constitutive modelling of contiguous rock located between rock joints. A fully explicit kinematically constrained microplane-type constitutive model for hardening and softening non-linear triaxial behaviour of isotropic porous rock is developed. The microplane framework, in which the constitutive relation is expressed in terms of stress and strain vectors rather than tensors, makes it possible to model various microstructural physical mechanisms associated with oriented internal surfaces, such as cracking, slip, friction and splitting of a particular orientation. Formulation of the constitutive relation is facilitated by the fact that it is decoupled from the tensorial invariance restrictions, which are satisfied automatically. In its basic features, the present model is similar to the recently developed microplane model M4 for concrete, but there are significant improvements and modifications. They include a realistic simulation of (1) the effects of pore collapse on the volume changes during triaxial loading and on the reduction of frictional strength, (2) recovery of frictional strength during shearing, and (3) the shear-enhanced compaction in triaxial tests, manifested by a deviation from the hydrostatic stress-strain curve. The model is calibrated by optimal fitting of extensive triaxial test data for Salem limestone, and good fits are demonstrated. Although these data do not cover the entire range of behaviour, credence in broad capabilities of the model is lend by its similarity to model M4 for concrete - an artificial rock. The model is intended for large explicit finite-element programs.
Constitutive modeling for isotropic materials (HOST)
NASA Technical Reports Server (NTRS)
Lindholm, U. S.; Chan, K. S.; Bodner, S. R.; Weber, R. M.; Walker, K. P.; Cassenti, B. N.
1985-01-01
This report presents the results of the second year of work on a problem which is part of the NASA HOST Program. Its goals are: (1) to develop and validate unified constitutive models for isotropic materials, and (2) to demonstrate their usefulness for structural analyses of hot section components of gas turbine engines. The unified models selected for development and evaluation are that of Bodner-Partom and Walker. For model evaluation purposes, a large constitutive data base is generated for a B1900 + Hf alloy by performing uniaxial tensile, creep, cyclic, stress relation, and thermomechanical fatigue (TMF) tests as well as biaxial (tension/torsion) tests under proportional and nonproportional loading over a wide range of strain rates and temperatures. Systematic approaches for evaluating material constants from a small subset of the data base are developed. Correlations of the uniaxial and biaxial tests data with the theories of Bodner-Partom and Walker are performed to establish the accuracy, range of applicability, and integability of the models. Both models are implemented in the MARC finite element computer code and used for TMF analyses. Benchmark notch round experiments are conducted and the results compared with finite-element analyses using the MARC code and the Walker model.
Isotropical conductive adhesives filled with silver nanowires
NASA Astrophysics Data System (ADS)
Tao, Y.; Xia, Y. P.; Zhang, G. Q.; Wu, H. P.; Tao, G. L.
2009-07-01
In this study, a solution-phase method was demonstrated to generate silver (Ag) nanowires with diameters in the range of 30~50nm and lengths of up to ~50μm, which was proceed by reducing silver nitrate with ethylene glycol in the presence of poly(vinyl pyrrolidone) (PVP). Fundamental material characterizations including X-ray diffraction transmission electro microscopy (TEM) and scanning electro microscopy (SEM) were conducted on these Ag nanowires. A novel kind of isotropical conductive adhesives (ICA) was prepared by using these Ag nanowires as conductive filler. Electrical property including bulk resistivity and mechanical property including shear strength were investigated and compared with that of conventional ICA filled with micrometer-sized Ag particles or nanometer-sized Ag particles. The average diameter of these Ag particles is about 1μm and 100 nm respectively. The results shown that ICA filled Ag nanowires exhibited higher conductivity, higher shear strength and low percolation threshold value than traditional ICA. Possible conductive mechanism was discussed based on theory calculation.
Centrifugal acceleration in the isotropic photon field
NASA Astrophysics Data System (ADS)
Bakhtadze, G. G.; Berezhiani, V. I.; Osmanov, Z.
In this paper, we study centrifugal acceleration of particles moving along a prescribed rotating curved trajectories. We consider the physical system embedded in an isotropic photon field and study the influence of the photon drag force on the acceleration process. For this purpose, we study three major configurations of the field lines: the straight line, the Archimede spiral and the dipolar field line configuration. By analyzing dynamics of particles sliding along the field lines in the equatorial plane, we have found several interesting features of motion. In particular, it has been shown that for rectilinear field lines, the particles reach the light cylinder (area where the linear velocity of rotation exactly equals the speed of light) zone relatively slowly for bigger drag forces. Considering the Archimedes’ spiral, we have found that in cases when the field lines lag behind the rotation, the particles achieve the force-free regime of dynamics regardless of the drag force. Unlike this scenario, when the spiral is oriented in an opposite direction, the particles do not reach the force free regime, but tend to stable equilibrium locations.
Isotropic microscale mechanical properties of coral skeletons
Pasquini, Luca; Molinari, Alan; Fantazzini, Paola; Dauphen, Yannicke; Cuif, Jean-Pierre; Levy, Oren; Dubinsky, Zvy; Caroselli, Erik; Prada, Fiorella; Goffredo, Stefano; Di Giosia, Matteo; Reggi, Michela; Falini, Giuseppe
2015-01-01
Scleractinian corals are a major source of biogenic calcium carbonate, yet the relationship between their skeletal microstructure and mechanical properties has been scarcely studied. In this work, the skeletons of two coral species: solitary Balanophyllia europaea and colonial Stylophora pistillata, were investigated by nanoindentation. The hardness HIT and Young's modulus EIT were determined from the analysis of several load–depth data on two perpendicular sections of the skeletons: longitudinal (parallel to the main growth axis) and transverse. Within the experimental and statistical uncertainty, the average values of the mechanical parameters are independent on the section's orientation. The hydration state of the skeletons did not affect the mechanical properties. The measured values, EIT in the 76–77 GPa range, and HIT in the 4.9–5.1 GPa range, are close to the ones expected for polycrystalline pure aragonite. Notably, a small difference in HIT is observed between the species. Different from corals, single-crystal aragonite and the nacreous layer of the seashell Atrina rigida exhibit clearly orientation-dependent mechanical properties. The homogeneous and isotropic mechanical behaviour of the coral skeletons at the microscale is correlated with the microstructure, observed by electron microscopy and atomic force microscopy, and with the X-ray diffraction patterns of the longitudinal and transverse sections. PMID:25977958
Shocklet statistics in compressible isotropic turbulence
NASA Astrophysics Data System (ADS)
Wang, Jianchun; Gotoh, Toshiyuki; Watanabe, Takeshi
2017-02-01
Shocklet statistics in compressible isotropic turbulence are studied by using numerical simulations with solenoidal forcing, at the turbulent Mach number Mt ranging from 0.5 up to 1.0 and at the Taylor Reynolds number Reλ ranging from 110 to 250. A power-law region of the probability density function (PDF) of the shocklet strength Mn-1 (Mn is the normal shock Mach number) is observed. The magnitude of the power-law exponent is found to decrease with the increase of Mt. We show that the most probable shocklet strength is proportional to Mt3, and the shocklet thickness corresponding to the most probable shock Mach number is proportional to Mt-2 in our numerical simulations. The PDFs of the jumps of the velocity and thermodynamic variables across a shocklet exhibit a similar power-law scaling. The statistics of the jumps of the velocity and thermodynamic variables are further investigated by conditioned average. Nonlinear models for the conditional average of the jumps of the velocity and thermodynamic variables are developed and verified.
Analytical investigation of stratified isotropic media
NASA Astrophysics Data System (ADS)
Vytovtov, Konstantin A.
2005-04-01
A rigorous analytical approach for investigating a stratified medium with an arbitrary finite number of homogeneous isotropic layers in a period is developed. The approach is based on the translation matrix method. It is well known that the translation matrix for a period must be found as the product of the layer matrices. It is proved that this matrix can be represented as a finite sum of trigonometric matrices, and thus the dispersion relation of a stratified medium is written in an analytical form. All final expressions are obtained in terms of the constitutive parameters. To this author's knowledge, this is the first time that the new sign function that allows us to develop the presented analytical results has been described. The condition of the existence of a wave with an arbitrary period divisible by a structure period is found in analytical form. It is proved that changing the layer arrangement within the period does not affect the structure of the transmission and absorption bands.
Loop gravity: An application and an extension
NASA Astrophysics Data System (ADS)
Taveras, Victor Manuel
In this thesis we address two issues in the area of loop quantum gravity. The first concerns the semiclassical limit in loop quantum cosmology via the use of so-called effective equations. In loop quantum cosmology the quantum dynamics is well understood. We can approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen semiclassical states. This submanifold is isomorphic with the classical phase space and the projected dynamical flow provides effective equations incorporating the leading quantum corrections to the classical equations of motion. Numerical work has been done in the full theory using quantum states which are semiclassical at late times. These states follow the classical trajectory until the density is on the order of 1% of the Planck density then deviate strongly from the classical trajectory. The effective equations we obtain reproduce this behavior to surprising accuracy. The second issue concerns generalizations of the classical action which is the starting point for loop quantum gravity. In loop quantum gravity one begins with the Einstein-Hilbert action, modified by the addition of the so-called Holst term. Classically, this term does not affect the equations of motion, but it leads to a well-known quantization ambiguity in the quantum theory parametrized by the Barbero-Immirzi parameter, which rescales the eigenvalues of the area and volume operators. We consider the theory obtained by promoting the Barbero-Immirzi parameter to a field. The resulting theory, called Modified Holst Gravity, is equivalent to General Relativity coupled to a pseudo-scalar field. However, this theory turns out to have an unconventional kinetic term for the Barbero-Immirzi field and a rather unnatural coupling with fermions. We then propose a further generalization of the Holst action, which we call Modified Nieh-Yan Gravity, which yields a theory of gravity
Looping: An Empirical Evaluation
ERIC Educational Resources Information Center
Cistone, Peter; Shneyderman, Aleksandr
2004-01-01
Looping is the practice in which a teacher instructs the same group of students for at least two school years, following them from one grade level to the next. Once a "loop" of two or more years is completed, the teacher may start a new loop teaching a new group of students. This evaluation study of the practice of looping in a large…
Quark and Gluon Form Factors to Three Loops
Baikov, P. A.; Smirnov, V. A.; Chetyrkin, K. G.; Smirnov, A. V.; Steinhauser, M.
2009-05-29
We compute the form factors of the photon-quark-anti-quark vertex and the effective vertex of a Higgs-boson and two gluons to three-loop order within massless perturbative quantum chromodynamics. These results provide building blocks for many third-order cross sections. Furthermore, this is the first calculation of complete three-loop vertex corrections.
A note on local unitary equivalence of isotropic-like states
NASA Astrophysics Data System (ADS)
Zhang, Ting-Gui; Hua, Bo-Bo; Li, Ming; Zhao, Ming-Jing; Yang, Hong
2015-12-01
We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition. Project supported by the National Natural Science Foundation of China (Grant Nos. 11401032, 61473325, 11501153, 11105226, 11275131, and 11401106), the Fundamental Research Funds for the Central Universities, China (Grant Nos. 15CX08011A and 24720122013), the Natural Science Foundation of Hainan Province, China (Grant Nos. 20151005 and 20151010), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.
Minisuperspace model of Machian resolution of Problem of Time. I. Isotropic case
NASA Astrophysics Data System (ADS)
Anderson, Edward
2014-05-01
A local resolution to the Problem of Time that is Machian and was previously demonstrated for relational mechanics models is here shown to work for a more widely studied quantum cosmological model. I.e., closed isotropic minisuperspace GR with minimally coupled scalar field matter. This resolution uses work firstly along the lines of Barbour's at the classical level. Secondly, it uses a Machianized version of the semiclassical approach to quantum cosmology (the resolution given is not more than semiclassical). Finally, it uses a Machianized version of a combined semiclassical histories timeless records scheme along the lines of Halliwell's work. This program's goal is the treatment of inhomogeneous perturbations about the present paper's model. This draws both from this paper's minisuperspace work and from qualitative parallels with relational particle mechanics, since both have nontrivial notions of inhomogeneity/structure (clumping) as well as nontrivial linear constraints.
Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation
NASA Astrophysics Data System (ADS)
Fathi, M.; Jalalzadeh, S.
2017-07-01
How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in Fathi et al. (Eur. Phys. J. C 76, 527 2016). In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.
The preprocessed doacross loop
NASA Technical Reports Server (NTRS)
Saltz, Joel H.; Mirchandaney, Ravi
1990-01-01
Dependencies between loop iterations cannot always be characterized during program compilation. Doacross loops typically make use of a-priori knowledge of inter-iteration dependencies to carry out required synchronizations. A type of doacross loop is proposed that allows the scheduling of iterations of a loop among processors without advance knowledge of inter-iteration dependencies. The method proposed for loop iterations requires that parallelizable preprocessing and postprocessing steps be carried out during program execution.
Ganther, Jr., Kenneth R.; Snapp, Lowell D.
2002-09-10
A flux locked loop for providing an electrical feedback signal, the flux locked loop employing radio-frequency components and technology to extend the flux modulation frequency and tracking loop bandwidth. The flux locked loop of the present invention has particularly useful application in read-out electronics for DC SQUID magnetic measurement systems, in which case the electrical signal output by the flux locked loop represents an unknown magnetic flux applied to the DC SQUID.
NASA Astrophysics Data System (ADS)
Sever, Amit; Vieira, Pedro; Wang, Tianheng
2011-11-01
We extend the Operator Product Expansion for Null Polygon Wilson loops to the Mason-Skinner-Caron-Huot super loop dual to non MHV gluon amplitudes. We explain how the known tree level amplitudes can be promoted into an infinite amount of data at any loop order in the OPE picture. As an application, we re-derive all one loop NMHV six gluon amplitudes by promoting their tree level expressions. We also present some new all loops predictions for these amplitudes.
Dirac Loops in Carbon Allotropes
NASA Astrophysics Data System (ADS)
Mullen, Kieran; Uchoa, Bruno; Glatzhofer, D.
2015-03-01
We propose a family of structures that have ``Dirac loops'': closed lines in momentum space with Dirac-like quasiparticles, on which the density of states vanishes linearly with energy. The structures all possess the planar trigonal connectivity present in graphene, but are three dimensional. We discuss the consequences of their multiply-connected Fermi surface for transport, including the presence of three dimensional Integer Quantum Hall effect. In the presence of spin-orbit coupling, we show that those structures may have topological surface states. We discuss the feasibility of realizing the structures as an allotrope of carbon. Work supported by NSF Grants DMR-1310407 and DMR-1352604.
The radiated noise from isotropic turbulence revisited
NASA Technical Reports Server (NTRS)
Lilley, Geoffrey M.
1993-01-01
The noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers, as derived by Proudman (1952), was the first application of Lighthill's Theory of Aerodynamic Noise to a complete flow field. The theory presented by Proudman involves the assumption of the neglect of retarded time differences and so replaces the second-order retarded-time and space covariance of Lighthill's stress tensor, Tij, and in particular its second time derivative, by the equivalent simultaneous covariance. This assumption is a valid approximation in the derivation of the second partial derivative of Tij/derivative of t exp 2 covariance at low Mach numbers, but is not justified when that covariance is reduced to the sum of products of the time derivatives of equivalent second-order velocity covariances as required when Gaussian statistics are assumed. The present paper removes these assumptions and finds that although the changes in the analysis are substantial, the change in the numerical result for the total acoustic power is small. The present paper also considers an alternative analysis which does not neglect retarded times. It makes use of the Lighthill relationship, whereby the fourth-order Tij retarded-time covariance is evaluated from the square of similar second order covariance, which is assumed known. In this derivation, no statistical assumptions are involved. This result, using distributions for the second-order space-time velocity squared covariance based on the Direct Numerical Simulation (DNS) results of both Sarkar and Hussaini(1993) and Dubois(1993), is compared with the re-evaluation of Proudman's original model. These results are then compared with the sound power derived from a phenomenological model based on simple approximations to the retarded-time/space covariance of Txx. Finally, the recent numerical solutions of Sarkar and Hussaini(1993) for the acoustic power are compared with the results obtained from the analytic solutions.
Investigating source processes of isotropic events
NASA Astrophysics Data System (ADS)
Chiang, Andrea
explosion. In contrast, recovering the announced explosive yield using seismic moment estimates from moment tensor inversion remains challenging but we can begin to put error bounds on our moment estimates using the NSS technique. The estimation of seismic source parameters is dependent upon having a well-calibrated velocity model to compute the Green's functions for the inverse problem. Ideally, seismic velocity models are calibrated through broadband waveform modeling, however in regions of low seismicity velocity models derived from body or surface wave tomography may be employed. Whether a velocity model is 1D or 3D, or based on broadband seismic waveform modeling or the various tomographic techniques, the uncertainty in the velocity model can be the greatest source of error in moment tensor inversion. These errors have not been fully investigated for the nuclear discrimination problem. To study the effects of unmodeled structures on the moment tensor inversion, we set up a synthetic experiment where we produce synthetic seismograms for a 3D model (Moschetti et al., 2010) and invert these data using Green's functions computed with a 1D velocity mode (Song et al., 1996) to evaluate the recoverability of input solutions, paying particular attention to biases in the isotropic component. The synthetic experiment results indicate that the 1D model assumption is valid for moment tensor inversions at periods as short as 10 seconds for the 1D western U.S. model (Song et al., 1996). The correct earthquake mechanisms and source depth are recovered with statistically insignificant isotropic components as determined by the F-test. Shallow explosions are biased by the theoretical ISO-CLVD tradeoff but the tectonic release component remains low, and the tradeoff can be eliminated with constraints from P wave first motion. Path-calibration to the 1D model can reduce non-double-couple components in earthquakes, non-isotropic components in explosions and composite sources and improve
Consistent quantum prediction in spin-foam quantum cosmology
NASA Astrophysics Data System (ADS)
Craig, David
2015-04-01
A complete ``consistent histories'' framework is given for a covariant ``spin-foam'' quantum cosmological model, a highly symmetry-reduced (FLRW) model of covariant loop quantum gravity. A decoherence functional is constructed through which probabilities may be consistently extracted from quantum amplitudes. Branch wave functions corresponding to different possible quantum histories of the universe are described, such as whether the universe ``bounces'' at small volume or becomes singular. We discuss the construction and calculation of such branch wave functions, with an emphasis on the crucial role played by the decoherence of histories in arriving at self-consistent quantum predictions for these closed quantum systems. [Based on joint work with Parampreet Singh].
NASA Astrophysics Data System (ADS)
Aryasova, Natalie; Reznikov, Yuri
2016-09-01
We study the effect of an isotropic-nematic (I -N ) phase transition on the liquid crystal alignment at untreated polymer surfaces. We demonstrate that the pattern at the untreated substrate in the planar cell where the other substrate is uniformly rubbed strongly depends on the temperature gradient across the cell during the I -N phase transition, being macroscopically isotropic if the untreated substrate is cooled faster, but becoming almost homogeneous along the rubbing direction in the opposite temperature gradient. We interpret the observed effect using complementary models of heat transfer and nematic elasticity. Based on the heat transfer model we show that the asymmetric temperature conditions in our experiments provide unidirectional propagation of the I -N interface during the phase transition and determine the initial director orientation pattern at the test's untreated surface. Using the Frank-Oseen model of nematic elasticity, we represent the three-dimensional director field in the nematic cell as a two-dimensional (2D) pattern at the untreated surface and perform 2D numeric simulations. The simulations explain the experimental results: Different initial director orientations at the untreated surface evolve into different stationary patterns.
NASA Astrophysics Data System (ADS)
Diehl, H. W.; Shpot, M.
2002-08-01
A two-loop renormalization group analysis of the critical behaviour at an isotropic Lifshitz point is presented. Using dimensional regularization and minimal subtraction of poles, we obtain the expansions of the critical exponents ν and η, the crossover exponent ϕ, as well as the (related) wave vector exponent βq and the correction-to-scaling exponent ω to second order in ɛ8 = 8 - d. They are compared with the authors' recent ɛ-expansion results (2000 Phys. Rev. B 62 12338, 2001 Nucl. Phys. B 612 340) for the general case of an m-axial Lifshitz point. It is shown that the expansions obtained here by a direct calculation for the isotropic (m = d) Lifshitz point all follow from the latter upon setting m = 8 - ɛ8. This is so despite recent claims to the contrary by de Albuquerque and Leite (2002 J. Phys. A: Math. Gen. 35 1807).
Constitutive modeling for isotropic materials (HOST)
NASA Technical Reports Server (NTRS)
Chan, Kwai S.; Lindholm, Ulric S.; Bodner, S. R.; Hill, Jeff T.; Weber, R. M.; Meyer, T. G.
1986-01-01
The results of the third year of work on a program which is part of the NASA Hot Section Technology program (HOST) are presented. The goals of this program are: (1) the development of unified constitutive models for rate dependent isotropic materials; and (2) the demonstration of the use of unified models in structural analyses of hot section components of gas turbine engines. The unified models selected for development and evaluation are those of Bodner-Partom and of Walker. A test procedure was developed for assisting the generation of a data base for the Bodner-Partom model using a relatively small number of specimens. This test procedure involved performing a tensile test at a temperature of interest that involves a succession of strain-rate changes. The results for B1900+Hf indicate that material constants related to hardening and thermal recovery can be obtained on the basis of such a procedure. Strain aging, thermal recovery, and unexpected material variations, however, preluded an accurate determination of the strain-rate sensitivity parameter is this exercise. The effects of casting grain size on the constitutive behavior of B1900+Hf were studied and no particular grain size effect was observed. A systematic procedure was also developed for determining the material constants in the Bodner-Partom model. Both the new test procedure and the method for determining material constants were applied to the alternate material, Mar-M247 . Test data including tensile, creep, cyclic and nonproportional biaxial (tension/torsion) loading were collected. Good correlations were obtained between the Bodner-Partom model and experiments. A literature survey was conducted to assess the effects of thermal history on the constitutive behavior of metals. Thermal history effects are expected to be present at temperature regimes where strain aging and change of microstructure are important. Possible modifications to the Bodner-Partom model to account for these effects are outlined
Topological insulating phases from two-dimensional nodal loop semimetals
NASA Astrophysics Data System (ADS)
Li, Linhu; Araújo, Miguel A. N.
2016-10-01
Starting from a minimal model for a two-dimensional nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase-winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases, and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak- and strong-field regimes, as well as the edge states in a ribbon geometry.
3D Loop Models and the CPn-1 Sigma Model
NASA Astrophysics Data System (ADS)
Nahum, Adam; Chalker, J. T.; Serna, P.; Ortuño, M.; Somoza, A. M.
2011-09-01
Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to CPn-1 sigma models, where n is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for n=1, 2, 3, and first order transitions for n≥5. The results are relevant to line defects in random media, as well as to Anderson localization and (2+1)-dimensional quantum magnets.
Loops in inflationary correlation functions
NASA Astrophysics Data System (ADS)
Tanaka, Takahiro; Urakawa, Yuko
2013-12-01
We review the recent progress regarding the loop corrections to the correlation functions in the inflationary universe. A naive perturbation theory predicts that the loop corrections generated during inflation suffer from various infrared (IR) pathologies. Introducing an IR cutoff by hand is neither satisfactory nor enough to fix the problem of a secular growth, which may ruin the predictive power of inflation models if the inflation lasts sufficiently long. We discuss the origin of the IR divergences and explore the regularity conditions of the loop corrections for the adiabatic perturbation, the iso-curvature perturbation, and the tensor perturbation, in turn. These three kinds of perturbations have qualitative differences, but in discussing the IR regularity there is a feature common to all cases, which is the importance of the proper identification of observable quantities. Genuinely, observable quantities should respect the gauge invariance from the view point of a local observer. Interestingly, we find that the requirement of the IR regularity restricts the allowed quantum states.
Re-entrant isotropic-nematic phase behavior in polymer-depleted amyloid fibrils
NASA Astrophysics Data System (ADS)
Zhao, Jianguo; Li, Chaoxu; Mezzenga, Raffaele
2014-11-01
Amyloid fibrils dispersed in water exhibit both isotropic (I) and nematic (N) phases, depending on concentration, but their coexistence, expected from the first order nature of the I - N thermodynamic transition is seldom observed. By adding a non-absorbing polymer to an amyloid fibrils suspension, we report, for the first time, an unusual closed-loop phase behavior. The phase diagrams reveal that the I + N coexistence does emerge, but only when the depleting polymer is present at intermediate concentrations. We combine depletion potentials in the dilute and semi-dilute polymer regime with the DLVO theory and the principle of equivalent law of corresponding states to calculate variations of the second virial coefficient with increasing polymer concentrations. We conclude that the decrease of the depletion potential range in the semi-dilute regime plays a pivotal role in the observed re-stabilization, leading to a closure of the I + N coexistence region.
Pseudonoise code tracking loop
NASA Technical Reports Server (NTRS)
Laflame, D. T. (Inventor)
1980-01-01
A delay-locked loop is presented for tracking a pseudonoise (PN) reference code in an incoming communication signal. The loop is less sensitive to gain imbalances, which can otherwise introduce timing errors in the PN reference code formed by the loop.
... breeding ground for bacteria. The bacteria may produce toxins as well as block the absorption of nutrients. The greater the length of small bowel involved in the blind loop, the greater the chance of bacterial overgrowth. What triggers blind loop syndrome? Blind loop ...
Toward loop quantization of plane gravitational waves
NASA Astrophysics Data System (ADS)
Hinterleitner, Franz; Major, Seth
2012-03-01
The polarized Gowdy model in terms of Ashtekar-Barbero variables is reduced with an additional constraint derived from the Killing equations for plane gravitational waves with parallel rays. The new constraint is formulated in a diffeomorphism invariant manner and, when it is included in the model, the resulting constraint algebra is first class, in contrast to the prior work done in special coordinates. Using an earlier work by Banerjee and Date, the constraints are expressed in terms of classical quantities that have an operator equivalent in loop quantum gravity, making these plane gravitational wave spacetimes accessible to loop quantization techniques.
Das, Animesh; Gieb, Klaus; Krupskaya, Yulia; Demeshko, Serhiy; Dechert, Sebastian; Klingeler, Rüdiger; Kataev, Vladislav; Büchner, Bernd; Müller, Paul; Meyer, Franc
2011-03-16
First members of a new family of heterometallic Mn/Ni complexes [Mn(2)Ni(3)X(2)L(4)(LH)(2)(H(2)O)(2)] (X = Cl: 1; X = Br: 2) with the new ligand 2-{3-(2-hydroxyphenyl)-1H-pyrazol-1-yl}ethanol (H(2)L) have been synthesized, and single crystals obtained from CH(2)Cl(2) solutions have been characterized crystallographically. The molecular structures feature a quasi-linear Mn(III)-Ni(II)-Ni(II)-Ni(II)-Mn(III) core with six-coordinate metal ions, where elongated axes of all the distorted octahedral coordination polyhedra are aligned parallel and are fixed with respect to each other by intramolecular hydrogen bonds. 1 and 2 exhibit quite strong ferromagnetic exchange interactions throughout (J(Mn-Ni) ≈ 40 K (1) or 42 K (2); J(Ni-Ni) ≈ 22 K (1) or 18 K (2)) that lead to an S(tot) = 7 ground state, and a sizable uniaxial magnetoanisotropy with D(mol) values -0.55 K (1) and -0.45 K (2). These values are directly derived also from frequency- and temperature-dependent high-field EPR spectra. Slow relaxation of the magnetization at low temperatures and single-molecule magnet (SMM) behavior are evident from frequency-dependent peaks in the out-of-phase ac susceptibilities and magnetization versus dc field measurements, with significant energy barriers to spin reversal U(eff) = 27 K (1) and 22 K (2). Pronounced quantum tunnelling steps are observed in the hysteresis loops of the temperature- and scan rate-dependent magnetization data, but with the first relaxation step shifted above (1) or below (2) the zero crossing of the magnetic field, despite the very similar molecular structures. The different behavior of 1 and 2 is interpreted in terms of antiferromagnetic (1) or ferromagnetic (2) intermolecular interactions, which are discussed in view of the subtle differences of intermolecular contacts within the crystal lattice.
USDA-ARS?s Scientific Manuscript database
An empirical correlation of volumetric mass transfer coefficient was developed for a pilot scale internal-loop rectangular airlift bioreactor that was designed for biotechnology. The empirical correlation combines classic turbulence theory, Kolmogorov’s isotropic turbulence theory with Higbie’s pen...
Azimuthally isotropic irradiance of GaN-based light-emitting diodes with GaN microlens arrays.
Wu, Mount-Learn; Lee, Yun-Chih; Yang, Shih-Pu; Lee, Po-Shen; Chang, Jenq-Yang
2009-04-13
In this paper, the irradiance-modifying concept is proposed by introducing a microlens array on the p-GaN layer of GaN-based light-emitting diode (LED). Every microlens can locally modulate photons emitting from a micro-scaled active region of multiple quantum wells (MQWs) just beneath the microlens. The azimuthally isotropic irradiance from the GaN-based LED with microlens arrays is demonstrated numerically and experimentally. To realize such a novel LED, one-dimensional GaN microlens array with a period of 1.6 microm and a filling factor of 0.64 are fabricated by using dry etching. According to experimental results, the azimuthally isotropic light emission of proposed LED is observed. By using the angular-resolved photoluminescence, its intensity variation corresponding to the azimuth angles is as low as 10% within the angle region of +/-50 degrees.
The energy decay in self-preserving isotropic turbulence revisited
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Bernard, Peter S.
1991-01-01
The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup - alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state towards which a complete self-preseving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.
The energy decay in self-preserving isotropic turbulence revisited
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Bernard, Peter S.
1992-01-01
The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup -alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state toward which a complete self-preserving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.
The energy decay in self-preserving isotropic turbulence revisited
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Bernard, Peter S.
1992-01-01
The assumption of self-preservation allows for an analytical determination of the energy decay in isotropic turbulence. Here, the self-preserving isotropic decay problem is analyzed, yielding a more complete picture of self-serving isotropic turbulence. It is proven rigorously that complete self-serving isotropic turbulence admits two general types of asymptotic solutions: one where the turbulent kinetic energy K approximately t (exp -1) and one where K approximately t (sup alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) and where K approximately t (sup -alpha) with an exponent alpha greater than 1 that is determined explicitly by the initial conditions. By a fixed point analysis and numerical integration of the exact one-point equations, it is demonstrated that the K approximately t (exp -1) power law decay is the asymptotically consistent high Reynolds number solution; the K approximately 1 (sup -alpha) decay law is only achieved in the limit as t yields infinity and the turbulence Reynolds number vanishes. Arguments are provided which indicate that a K approximately t (exp -1) power law decay is the asymptotic state toward which a complete self-preserving isotropic turbulence is driven at high Reynolds numbers in order to resolve the imbalance between vortex stretching and viscous diffusion.
Dynamical Casimir effect and loop corrections
NASA Astrophysics Data System (ADS)
Akhmedov, E. T.; Alexeev, S. O.
2017-09-01
We calculate quantum loop corrections to the stress-energy flux caused by moving mirrors. We consider massless, self-interacting, ϕ4, real scalar theory. In these calculations we encounter new and quite unexpected subtleties due to the absence of global hyperbolicity in the presence of mirrors. We attempt to clearly phrase as many hidden assumptions and complications as possible that appear while solving the problem in question. On top of that, we find that quantum loop corrections to the stress-energy flux grow with time and are not suppressed in comparison with the semiclassical contributions. Thus, we observe the breakdown of the perturbation theory, and we discuss its physical origin and ways to deal with such a situation. As a byproduct, we observe a similarity of the problem in question with that for the minimally coupled, massless scalar field in de Sitter space.
Gaussian effective potential: Quantum mechanics
NASA Astrophysics Data System (ADS)
Stevenson, P. M.
1984-10-01
We advertise the virtues of the Gaussian effective potential (GEP) as a guide to the behavior of quantum field theories. Much superior to the usual one-loop effective potential, the GEP is a natural extension of intuitive notions familiar from quantum mechanics. A variety of quantum-mechanical examples are studied here, with an eye to field-theoretic analogies. Quantum restoration of symmetry, dynamical mass generation, and "quantum-mechanical resuscitation" are among the phenomena discussed. We suggest how the GEP could become the basis of a systematic approximation procedure. A companion paper will deal with scalar field theory.
Line mixing effects in isotropic Raman spectra of pure N2: a classical trajectory study.
Ivanov, Sergey V; Boulet, Christian; Buzykin, Oleg G; Thibault, Franck
2014-11-14
Line mixing effects in the Q branch of pure N2 isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N2 molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of the results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.
Line mixing effects in isotropic Raman spectra of pure N2: A classical trajectory study
NASA Astrophysics Data System (ADS)
Ivanov, Sergey V.; Boulet, Christian; Buzykin, Oleg G.; Thibault, Franck
2014-11-01
Line mixing effects in the Q branch of pure N2 isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N2 molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of the results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.
Isotropic and anisotropic bouncing cosmologies in Palatini gravity
Barragan, Carlos; Olmo, Gonzalo J.
2010-10-15
We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini f(R) and f(R,R{sub {mu}{nu}R}{sup {mu}{nu}}) theories of gravity with a perfect fluid and consider the existence of nonsingular bouncing solutions in the early universe. We find that all f(R) models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model R+aR{sup 2}/R{sub P}+R{sub {mu}{nu}R}{sup {mu}{nu}/}R{sub P} exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for a<0) and radiation (for arbitrary a). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic (w>1) sources of matter/energy or extra degrees of freedom.
Stress waves in transversely isotropic media: The homogeneous problem
NASA Technical Reports Server (NTRS)
Marques, E. R. C.; Williams, J. H., Jr.
1986-01-01
The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.
Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators
NASA Astrophysics Data System (ADS)
Salazar, María Amelia; Sepe, Daniele
2017-05-01
Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-free actions in contact geometry, as shown in this paper. The main results concern a classification of these realisations up to a suitable notion of isomorphism, as well as establishing a relation between the existence of symplectic and contact isotropic realisations for Poisson manifolds. The main tool is the classical Spencer operator which is related to Jacobi structures via their associated Lie algebroid, which allows to generalise previous results as well as providing more conceptual proofs for existing ones.
Scaling of Lyapunov Exponents in Homogeneous, Isotropic DNS
NASA Astrophysics Data System (ADS)
Fitzsimmons, Nicholas; Malaya, Nicholas; Moser, Robert
2013-11-01
Lyapunov exponents measure the rate of separation of initially infinitesimally close trajectories in a chaotic system. Using the exponents, we are able to probe the chaotic nature of homogeneous isotropic turbulence and study the instabilities of the chaotic field. The exponents are measured by calculating the instantaneous growth rate of a linear disturbance, evolved with the linearized Navier-Stokes equation, at each time step. In this talk, we examine these exponents in the context of homogeneous isotropic turbulence with two goals: 1) to investigate the scaling of the exponents with respect to the parameters of forced homogeneous isotropic turbulence, and 2) to characterize the instabilities that lead to chaos in turbulence. Specifically, we explore the scaling of the Lyapunov exponents with respect to the Reynolds number and with respect to the ratio of the integral length scale and the computational domain size.
Sudden relaminarisation and lifetimes in forced isotropic turbulence
NASA Astrophysics Data System (ADS)
Linkmann, Moritz; Morozov, Alexander
2015-11-01
We demonstrate an unexpected connection between isotropic turbulence and wall-bounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from chaotic dynamics to a spatially simple flow, analogous to the laminar state in wall bounded shear flows. We find that the survival probabilities of turbulence are exponential and the typical lifetimes increase super-exponentially with the Reynolds number, similar to results on relaminarisation of localised turbulence in pipe and plane Couette flow. Results from simulations subjecting the observed large-scale flow to random perturbations of variable amplitude demonstrate that it is a linearly stable simple exact solution that can be destabilised by a finite-amplitude perturbation, like the Hagen-Poiseuille profile in pipe flow. Our results suggest that both isotropic turbulence and wall-bounded shear flows qualitatively share the same phase-space dynamics.
Comparative analysis of isotropic diffusion weighted imaging sequences
NASA Astrophysics Data System (ADS)
Vellmer, Sebastian; Stirnberg, Rüdiger; Edelhoff, Daniel; Suter, Dieter; Stöcker, Tony; Maximov, Ivan I.
2017-02-01
Visualisation of living tissue structure and function is a challenging problem of modern imaging techniques. Diffusion MRI allows one to probe in vivo structures on a micrometer scale. However, conventional diffusion measurements are time-consuming procedures, because they require several measurements with different gradient directions. Considerable time savings are therefore possible by measurement schemes that generate an isotropic diffusion weighting in a single shot. Multiple approaches for generating isotropic diffusion weighting are known and have become very popular as useful tools in clinical research. Thus, there is a strong need for a comprehensive comparison of different isotropic weighting approaches. In the present work we introduce two new sequences based on simple (co)sine modulations and compare their performance to established q-space magic-angle spinning sequences and conventional DTI, using a diffusion phantom assembled from microcapillaries and in vivo experiments at 7 T. The advantages and disadvantages of all compared schemes are demonstrated and discussed.
Visualization and computer graphics on isotropically emissive volumetric displays.
Mora, Benjamin; Maciejewski, Ross; Chen, Min; Ebert, David S
2009-01-01
The availability of commodity volumetric displays provides ordinary users with a new means of visualizing 3D data. Many of these displays are in the class of isotropically emissive light devices, which are designed to directly illuminate voxels in a 3D frame buffer, producing X-ray-like visualizations. While this technology can offer intuitive insight into a 3D object, the visualizations are perceptually different from what a computer graphics or visualization system would render on a 2D screen. This paper formalizes rendering on isotropically emissive displays and introduces a novel technique that emulates traditional rendering effects on isotropically emissive volumetric displays, delivering results that are much closer to what is traditionally rendered on regular 2D screens. Such a technique can significantly broaden the capability and usage of isotropically emissive volumetric displays. Our method takes a 3D dataset or object as the input, creates an intermediate light field, and outputs a special 3D volume dataset called a lumi-volume. This lumi-volume encodes approximated rendering effects in a form suitable for display with accumulative integrals along unobtrusive rays. When a lumi-volume is fed directly into an isotropically emissive volumetric display, it creates a 3D visualization with surface shading effects that are familiar to the users. The key to this technique is an algorithm for creating a 3D lumi-volume from a 4D light field. In this paper, we discuss a number of technical issues, including transparency effects due to the dimension reduction and sampling rates for light fields and lumi-volumes. We show the effectiveness and usability of this technique with a selection of experimental results captured from an isotropically emissive volumetric display, and we demonstrate its potential capability and scalability with computer-simulated high-resolution results.
Nuclear relaxation in an electric field enables the determination of isotropic magnetic shielding
NASA Astrophysics Data System (ADS)
Garbacz, Piotr
2016-08-01
It is shown that in contrast to the case of nuclear relaxation in a magnetic field B, simultaneous application of the magnetic field B and an additional electric field E causes transverse relaxation of a spin-1/2 nucleus with the rate proportional to the square of the isotropic part of the magnetic shielding tensor. This effect can contribute noticeably to the transverse relaxation rate of heavy nuclei in molecules that possess permanent electric dipole moments. Relativistic quantum mechanical computations indicate that for 205Tl nucleus in a Pt-Tl bonded complex, Pt(CN)5Tl, the transverse relaxation rate induced by the electric field is of the order of 1 s-1 at E = 5 kV/mm and B = 10 T.
Driven isotropic Heisenberg spin chain with arbitrary boundary twisting angle: Exact results
NASA Astrophysics Data System (ADS)
Popkov, V.; Karevski, D.; Schütz, G. M.
2013-12-01
We consider an open isotropic Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. Using a matrix product ansatz, we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady state of a chain with N sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle θ. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady-state currents scale as 1/N2 for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to 2θ/N.
A note on antenna models in a warm isotropic plasma
NASA Technical Reports Server (NTRS)
Singh, N.
1980-01-01
The electron-transparent and electron-reflecting models of antennas in a warm isotropic plasma are reexamined. It is shown that a purely electrical treatment of both the models without an explicit use of the boundary condition on electron velocity yields the same results as those previously obtained through an electromechanical treatment. The essential difference between the two models is that for the electron-reflecting model, fields are nonzero only in the exterior region, while for the electron-transparent model, they are nonzero both in the exterior and interior regions of the antenna. This distinction helps in clarifying some misconceptions about these models of antennas in warm isotropic plasma.
On the preferential sampling of helicity by isotropic helicoids
NASA Astrophysics Data System (ADS)
Biferale, Luca; Gustavsson, Kristian; Scatamacchia, Riccardo
2016-11-01
We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet unexplored, extension of the much studied case of small spherical particles. We show that heavy isotropic helicoids, due to the coupling between translational and rotational degrees of freedom, preferentially sample different helical regions in laminar or chaotic advecting flows. This opens the way to control and engineer particles able to track complex flow structures with potential applications to microfluidics and turbulence. ERC AdG Grant NewTURB no. 339032.
A note on antenna models in a warm isotropic plasma
NASA Technical Reports Server (NTRS)
Singh, N.
1980-01-01
The electron-transparent and electron-reflecting models of antennas in a warm isotropic plasma are reexamined. It is shown that a purely electrical treatment of both the models without an explicit use of the boundary condition on electron velocity yields the same results as those previously obtained through an electromechanical treatment. The essential difference between the two models is that for the electron-reflecting model, fields are nonzero only in the exterior region, while for the electron-transparent model, they are nonzero both in the exterior and interior regions of the antenna. This distinction helps in clarifying some misconceptions about these models of antennas in warm isotropic plasma.
Designing isotropic interactions for self-assembly of complex lattices.
Edlund, E; Lindgren, O; Jacobi, M Nilsson
2011-08-19
We present a direct method for solving the inverse problem of designing isotropic potentials that cause self-assembly into target lattices. Each potential is constructed by matching its energy spectrum to the reciprocal representation of the lattice to guarantee that the desired structure is a ground state. We use the method to self-assemble complex lattices not previously achieved with isotropic potentials, such as a snub square tiling and the kagome lattice. The latter is especially interesting because it provides the crucial geometric frustration in several proposed spin liquids. © 2011 American Physical Society
Unexpected collapses during isotropic consolidation of model granular materials
NASA Astrophysics Data System (ADS)
Doanh, Thiep; Le Bot, Alain; Abdelmoula, Nouha; Gribaa, Lassad; Hans, Stéphane; Boutin, Claude
2016-02-01
This paper reports the unexpected instantaneous instabilities of idealized granular materials under simple isotropic drained compression. Specimens of monosized glass beads submitted to isotropic compression exhibit a series of local collapses under undetermined external stress with partial liquefaction, experience sudden volumetric compaction and axial contraction of various amplitude. Short-lived excess pore water pressure vibrates like an oscillating underdamped system in the first dynamic transient phase and rapidly disperses in the subsequent longer dissipation phase. However, very dense samples maintain a collapse-free behaviour below a threshold void ratio e0col at 30 kPa of stress. The potential mechanisms that could explain these spontaneous collapses are discussed.
Flow birefringence in lyotropic mixtures in the isotropic phase
Fernandes, P.R.G.; Figueiredo Neto, A.M. )
1995-01-01
The flow-induced birefringence ([delta][ital n]) in lyotropic mixtures in the isotropic phase (ISO) was measured by means of optical techniques. As a function of temperature, the ISO is surrounded by two lamellar (LAM) phases. The shear flow produced by a perturbation in ISO induces a birefringent phase, which relaxes back to ISO with a typical relaxation time [tau]. [tau] increases near the transition to the more ordered LAM phases, and the behavior of [tau] versus temperature indicates the existence of a virtual nematic phase in the isotropic domain.
Quantum field theory on a cosmological, quantum space-time
Ashtekar, Abhay; Kaminski, Wojciech; Lewandowski, Jerzy
2009-03-15
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker space-times arise as well-defined approximations to specific quantum geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical space-time backgrounds to quantum space-times. These include a ''relational time''a la Leibniz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical Friedmann-LeMaitre-Robertson-Walker models arises as a well-defined reduction of this more fundamental theory.
Thiemann complexifier in classical and quantum FLRW cosmology
NASA Astrophysics Data System (ADS)
Ben Achour, Jibril; Livine, Etera R.
2017-09-01
In the context of loop quantum gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic Friedmann-Lemaitre-Roberston-Walker (FLRW) cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates the canonical transformations shifting the Barbero-Immirzi parameter. We focus on the closed algebra consisting in the complexifier, the 3d volume and the Hamiltonian constraint, which we call the CVH algebra (for Complexier-Volume-Hamiltonian constraint algebra). In standard cosmology, for gravity coupled to a scalar field, the CVH algebra is identified as a su (1 ,1 ) Lie algebra, with the Hamiltonian as a null generator, the complexifier as a boost and the su (1 ,1 ) Casimir given by the matter density. The loop gravity cosmology approach introduces a regularization length scale λ and regularizes the gravitational Hamiltonian in terms of SU(2) holonomies. We show that this regularization is compatible with the CVH algebra, if we suitably regularize the complexifier and inverse volume factor. The regularized complexifier generates a generalized version of the Barbero's canonical transformation which reduces to the classical one when λ →0 . This structure allows for the exact integration of the actions of the Hamiltonian constraints and the complexifier. This straightforwardly extends to the quantum level: the cosmological evolution is described in terms of SU(1, 1) coherent states and the regularized complexifier generates unitary transformations. The Barbero-Immirzi parameter is to be distinguished from the regularization scale λ , it can be rescaled unitarily and the Immirzi ambiguity ultimately disappears from the physical predictions of the theory. Finally, we show that the complexifier becomes the effective Hamiltonian when deparametrizing the dynamics using the scalar field as a clock, thus underlining the deep relation between cosmological evolution and scale transformations.
Quantum entanglement in the multiverse
NASA Astrophysics Data System (ADS)
Robles-Pérez, S.; González-Díaz, P. F.
2014-01-01
We show that the quantum state of a multiverse made up of classically disconnected regions of the space-time, whose dynamical evolution is dominated by a homogeneous and isotropic fluid, is given by a squeezed state. These are typical quantum states that have no classical counterpart and therefore allow analyzing the violation of classical inequalities as well as the EPR argument in the context of the quantum multiverse. The thermodynamical properties of entanglement are calculated for a composite quantum state of two universes whose states are quantum-mechanically correlated. The energy of entanglement between the positive and negative modes of a scalar field, which correspond to the expanding and contracting branches of a phantom universe, are also computed.
QED representation for the net of causal loops
NASA Astrophysics Data System (ADS)
Ciolli, Fabio; Ruzzi, Giuseppe; Vasselli, Ezio
2015-06-01
The present work tackles the existence of local gauge symmetries in the setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops, previously introduced by the authors, is a model independent construction of a covariant net of local C*-algebras on any 4-dimensional globally hyperbolic space-time, aimed to capture structural properties of any reasonable quantum gauge theory. Representations of this net can be described by causal and covariant connection systems, and local gauge transformations arise as maps between equivalent connection systems. The present paper completes these abstract results, realizing QED as a representation of the net of causal loops in Minkowski space-time. More precisely, we map the quantum electromagnetic field Fμν, not free in general, into a representation of the net of causal loops and show that the corresponding connection system and the local gauge transformations find a counterpart in terms of Fμν.
NASA Astrophysics Data System (ADS)
El-Kader, M. S. A.; Maroulis, G.
2017-09-01
Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures for the collisional complex of a hydrogen molecule and a helium atom are computed using the numerical results of the induced dipole moment and isotropic intermolecular potential as input. Comparison with measured spectra and first three spectral moments shows good agreement over the rototranslational band in the far infrared. The quality of the present potentials have been checked by comparing between calculated and experimental thermo-physical and transport properties, which are found to be in good agreement.
Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain
NASA Astrophysics Data System (ADS)
Žunkovič, Bojan; Prosen, Tomaž
2010-08-01
Explicit solution for the two-point correlation function in a non-equilibrium steady state of a nearly isotropic boundary driven open XY spin 1/2 chain in the Lindblad formulation is provided. A non-equilibrium quantum phase transition from exponentially decaying correlations to long range order is discussed analytically. In the regime of long range order a new phenomenon of correlation resonances is reported, where the correlation response of the system is unusually high for certain discrete values of the external bulk parameter, e.g. the magnetic field.
Switch isotropic/anisotropic wettability via dual-scale rods
NASA Astrophysics Data System (ADS)
He, Yang; Jiang, Chengyu; Wang, Shengkun; Ma, Zhibo; Yuan, Weizheng
2014-10-01
It is the first time to demonstrate the comparison of isotropic/anisotropic wettability between dual-scale micro-nano-rods and single-scale micro-rods. Inspired by the natural structures of rice leaf, a series of micro-nano-rods and micro-rods with different geometric parameters were fabricated using micro-fabrication technology. Experimental measured apparent contact angles and advancing and receding contact angles from orthogonal orientations were characterized. The difference of contact angles from orthogonal orientation on dual-scale rods was much smaller than those on single-scale rods in both static and dynamic situation. It indicated that the dual-scale micro-nano-rods showed isotropic wettability, while single-scale micro-rods showed anisotropic wettability. The switch of isotropic/anisotropic wettability could be illustrated by different wetting state and contact line moving. It offers a facial way to switch isotropic/anisotropic wettability of the surface via dual-scale or single-scale structure.
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
ERIC Educational Resources Information Center
Nita, Gelu M.
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
Equation of State and Sound Velocities from Isotropic Continuum Mechanics.
1986-10-01
of state and the shear and longitudinal velocity to fifth order elastic constants. The resulting expressions are implicit in terms of the pressure...The methods of finite elasticity in continuum mechanics of homogeneous isotropic materials are used to obtain the pressure dependence of the equation
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
ERIC Educational Resources Information Center
Nita, Gelu M.
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
Transformation to zero offset in transversely isotropic media
Alkhalifah, T.
1995-02-01
Nearly all dip moveout correction (DMO) implementations to date assume isotropic homogeneous media. Usually, this has been acceptable considering the tremendous cost savings of homogeneous isotropic DMO and considering the difficulty of obtaining the anisotropy parameters required for effective implementation. In the presence of typical anisotropy, however, ignoring the anisotropy can yield inadequate results. Since anisotropy may introduce large deviations from hyperbolic moveout, accurate transformation to zero-offset in anisotropic media should address such nonhyperbolic moveout behavior of reflections. Artley and Hale`s (1994) v(z) ray tracing-based DMO, developed for isotropic media, provides an attractive approach to treating such problems. By using a ray-tracing procedure crafted for anisotropic media, the author modifies some aspects of Artley and Hale`s DMO so that it can work for v(z) anisotropic media. Application of this anisotropic DMO to data from offshore Africa resulted in a considerably better alignment of reflections from horizontal and dipping reflectors in common-midpoint gather than that obtained using an isotropic DMO. Even the presence of vertical inhomogeneity in this medium could not eliminate the importance of considering the shale induced anisotropy.
Loop quantization of the Schwarzschild interior revisited
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Singh, Parampreet
2016-03-01
The loop quantization of the Schwarzschild interior region, as described by a homogeneous anisotropic Kantowski-Sachs model, is re-examined. As several studies of different—inequivalent—loop quantizations have shown, to date there exists no fully satisfactory quantum theory for this model. This fact poses challenges to the validity of some scenarios to address the black hole information problem. Here we put forward a novel viewpoint to construct the quantum theory that builds from some of the models available in the literature. The final picture is a quantum theory that is both independent of any auxiliary structure and possesses a correct low curvature limit. It represents a subtle but non-trivial modification of the original prescription given by Ashtekar and Bojowald. It is shown that the quantum gravitational constraint is well defined past the singularity and that its effective dynamics possesses a bounce into an expanding regime. The classical singularity is avoided, and a semiclassical spacetime satisfying vacuum Einstein’s equations is recovered on the ‘other side’ of the bounce. We argue that such a metric represents the interior region of a white-hole spacetime, but for which the corresponding ‘white hole mass’ differs from the original black hole mass. Furthermore, we find that the value of the white hole mass is proportional to the third power of the starting black hole mass.
Noncontractible loops in the dense O (n ) loop model on the cylinder
NASA Astrophysics Data System (ADS)
Alcaraz, F. C.; Brankov, J. G.; Priezzhev, V. B.; Rittenberg, V.; Rogozhnikov, A. M.
2014-11-01
A lattice model of critical dense polymers O (n ) is considered for finite cylinder geometry. Due to the presence of noncontractible loops with a fixed fugacity ξ , the model at n =0 is a generalization of the critical dense polymers solved by Pearce, Rasmussen, and Villani. We found the free energy for any height N and circumference L of the cylinder. The density ρ of noncontractible loops is obtained for N →∞ and large L . The results are compared with those found for the anisotropic quantum chain with twisted boundary conditions. Using the latter method, we derived ρ for any O (n ) model and an arbitrary fugacity.
Loop quantization of Schwarzschild interior revisited
NASA Astrophysics Data System (ADS)
Singh, Parampreet; Corichi, Alejandro
2016-03-01
Several studies of different inequivalent loop quantizations have shown, that there exists no fully satisfactory quantum theory for the Schwarzschild interior. Existing quantizations fail either on dependence on the fiducial structure or on the lack of the classical limit. Here we put forward a novel viewpoint to construct the quantum theory that overcomes all of the known problems of the existing quantizations. It is shown that the quantum gravitational constraint is well defined past the singularity and that its effective dynamics possesses a bounce into an expanding regime. The classical singularity is avoided, and a semiclassical spacetime satisfying vacuum Einstein's equations is recovered on the ``other side'' of the bounce. We argue that such metric represents the interior region of a white-hole spacetime, but for which the corresponding ``white-hole mass'' differs from the original black hole mass. We compare the differences in physical implications with other quantizations.
Fischer, Stefan; Swabeck, Joseph K; Alivisatos, A Paul
2017-09-06
Precise morphology and composition control is vital for designing multifunctional lanthanide-doped core/shell nanocrystals. Herein, we report controlled isotropic and anisotropic shell growth techniques in hexagonal sodium rare-earth tetrafluoride (β-NaLnF4) nanocrystals by exploiting the kinetics of the shell growth. A drastic change of the shell morphology was observed by changing the injection rate of the shell precursors while keeping all other reaction conditions constant. We obtained isotropic shell growth for fast sequential injection and a preferred growth of the shell layers along the crystal's c-axis [001] for slow dropwise injection. Using this slow shell growth technique, we have grown rod-like shells around different almost spherical core nanocrystals. Bright and efficient upconversion was measured for both isotropic and rod-like shells around β-NaYF4 nanocrystals doped with Yb(3+)/Er(3+) and Yb(3+)/Tm(3+). Photoluminescence upconversion quantum yield and lifetime measurements reveal the high quality of the core/shell nanocrystal. Furthermore, multishell rod-like nanostructures have been prepared with optically active cores and tips separated by an inert intermediate shell layer. The controlled anisotropic shell growth allows the design of new core/multishell nanostructures and enables independent investigations of the chemistry and physics of different nanocrystal facets.
Maurice, Rémi; Verma, Pragya; Zadrozny, Joseph M; Luo, Sijie; Borycz, Joshua; Long, Jeffrey R; Truhlar, Donald G; Gagliardi, Laura
2013-08-19
The metal-organic framework Fe2(dobdc) (dobdc(4-) = 2,5-dioxido-1,4-benzenedicarboxylate), often referred to as Fe-MOF-74, possesses many interesting properties such as a high selectivity in olefin/paraffin separations. This compound contains open-shell Fe(II) ions with open coordination sites which may have large single-ion magnetic anisotropies, as well as isotropic couplings between the nearest and next nearest neighbor magnetic sites. To complement a previous analysis of experimental data made by considering only isotropic couplings [Bloch et al. Science 2012, 335, 1606], the magnitude of the main magnetic interactions are here assessed with quantum chemical calculations performed on a finite size cluster. It is shown that the single-ion anisotropy is governed by same-spin spin-orbit interactions (i.e., weak crystal-field regime), and that this effect is not negligible compared to the nearest neighbor isotropic couplings. Additional magnetic data reveal a metamagnetic behavior at low temperature. This effect can be attributed to various microscopic interactions, and the most probable scenarios are discussed.
Control of quantum correlations in solid state systems
NASA Astrophysics Data System (ADS)
Berrada, K.
2015-11-01
The quantum correlations between two independent qubits immersed in an anisotropic and isotropic photonic band-gab (PBG) crystal have been studied without Born or Markovian approximation. We show that the amount of the entanglement and quantum discord between the qubits in the photonic crystal is greatly different from that of qubits in vacuum or that subjected to the usual non-Markovian reservoir. The results also show that, for PBG materials as environment, high values of quantum correlation trapping can be achieved and thus prevention of correlation sudden drop occurs, which seriously enhances the coherence and increase the amount of the correlations. Moreover, we show that the quantum correlations in the isotropic PBG are more easily preserved than that in the anisotropic PBG under the same condition. These features make the quantum systems in PBG materials as a good candidate for implementation of different schemes of quantum optics and information with high performance.
Effects of Coulomb collisions on cyclotron maser and plasma wave growth in magnetic loops
NASA Technical Reports Server (NTRS)
Hamilton, Russell J.; Petrosian, Vahe
1990-01-01
The evolution of nonthermal electrons accelerated in magnetic loops is determined by solving the kinetic equation, including magnetic field convergence and Coulomb collisions in order to determine the effects of these interactions on the induced cyclotron maser and plasma wave growth. It is found that the growth rates are larger and the possibility of cyclotron maser action is stronger for smaller loop column density, for larger magnetic field convergence, for a more isotropic injected electron pitch angle distribution, and for more impulsive acceleration. For modest values of the column density in the coronal portion of a flaring loop, the growth rates of instabilities are significantly reduced, and the reduction is much larger for the cyclotron modes than for the plasma wave modes. The rapid decrease in the growth rates with increasing loop column density suggests that, in flare loops when such phenomena occur, the densities are lower than commonly accepted.
Perturbative quantum field theory in the framework of the fermionic projector
Finster, Felix
2014-04-15
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
Multiproperty empirical isotropic interatomic potentials for CH4-inert gas mixtures.
El-Kader, M S A
2013-11-01
An approximate empirical isotropic interatomic potentials for CH4-inert gas mixtures are developed by simultaneously fitting the Exponential-Spline-Morse-Spline-van der Waals (ESMSV) potential form to viscosity, thermal conductivity, thermal diffusion factors, diffusion coefficient, interaction second pressure virial coefficient and scattering cross-section data. Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures for CH4-He and at T = 87 K for CH4-Ar are computed using theoretical values for overlap, octopole and hexadecapole mechanisms and interaction potential as input. Also, the quantum mechanical lineshapes of collision-induced light scattering (CILS) for the mixtures CH4-Ar and CH4-Xe at room temperature are calculated. The spectra of scattering consist essentially of an intense, purely translational component which includes scattering due to free pairs and bound dimers, and the other is due to the induced rotational scattering. These spectra have been interpreted by means of pair-polarizability terms, which arise from a long-range dipole-induced-dipole (DID) with small dispersion corrections and a short-range interaction mechanism involving higher-order dipole-quadrupole A and dipole-octopole E multipole polarizabilities. Good agreement between computed and experimental lineshapes of both absorption and scattering is obtained when the models of potential, interaction-induced dipole and polarizability components are used.
NASA Astrophysics Data System (ADS)
Vilar, Jose M. G.; Saiz, Leonor
2006-06-01
DNA looping plays a fundamental role in a wide variety of biological processes, providing the backbone for long range interactions on DNA. Here we develop the first model for DNA looping by an arbitrarily large number of proteins and solve it analytically in the case of identical binding. We uncover a switchlike transition between looped and unlooped phases and identify the key parameters that control this transition. Our results establish the basis for the quantitative understanding of fundamental cellular processes like DNA recombination, gene silencing, and telomere maintenance.
NASA Technical Reports Server (NTRS)
Gottschlich, Joseph M.; Richter, Robert
1991-01-01
The concept of a thermal power loop (TPL) to transport thermal power over relatively large distances is presented as an alternative to heat pipes and their derivatives. The TPL is compared to heat pipes, and capillary pumped loops with respect to size, weight, conservation of thermal potential, start-up, and 1-g testing capability. Test results from a proof of feasibility demonstrator at the NASA JPL are discussed. This analysis demonstrates that the development of specific thermal power loops will result in substantial weight and cost savings for many spacecraft.