Global unitary fixing and matrix-valued correlations in matrix models
Adler, S L; Horwitz, Lawrence P.
2003-01-01
We consider the partition function for a matrix model with a global unitary invariant energy function. We show that the averages over the partition function of global unitary invariant trace polynomials of the matrix variables are the same when calculated with any choice of a global unitary fixing, while averages of such polynomials without a trace define matrix-valued correlation functions, that depend on the choice of unitary fixing. The unitary fixing is formulated within the standard Faddeev-Popov framework, in which the squared Vandermonde determinant emerges as a factor of the complete Faddeev-Popov determinant. We give the ghost representation for the FP determinant, and the corresponding BRST invariance of the unitary-fixed partition function. The formalism is relevant for deriving Ward identities obeyed by matrix-valued correlation functions.
Large Representation Recurrences in Large N Random Unitary Matrix Models
Karczmarek, Joanna L
2011-01-01
In a random unitary matrix model at large N, we study the properties of the expectation value of the character of the unitary matrix in the rank k symmetric tensor representation. We address the problem of whether the standard semiclassical technique for solving the model in the large N limit can be applied when the representation is very large, with k of order N. We find that the eigenvalues do indeed localize on an extremum of the effective potential; however, for finite but sufficiently large k/N, it is not possible to replace the discrete eigenvalue density with a continuous one. Nonetheless, the expectation value of the character has a well-defined large N limit, and when the discreteness of the eigenvalues is properly accounted for, it shows an intriguing approximate periodicity as a function of k/N.
Unitary-matrix models as exactly solvable string theories
Periwal, Vipul; Shevitz, Danny
1990-01-01
Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.
Unitary-matrix models as exactly solvable string theories
Periwal, Vipul; Shevitz, Danny
1990-01-01
Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.
Entanglement Entropy from Corner Transfer Matrix in Forrester Baxter non-unitary RSOS models
Bianchini, Davide
2015-01-01
Using a Corner Transfer Matrix approach, we compute the bipartite entanglement R\\'enyi entropy in the off-critical perturbations of non-unitary conformal minimal models realised by lattice spin chains Hamiltonians related to the Forrester Baxter RSOS models in regime III. This allows to show on a set of explicit examples that the R\\'enyi entropies for non-unitary theories rescale near criticality as the logarithm of the correlation length with a coefficient proportional to the effective central charge. This complements a similar result, recently established for the size rescaling at the critical point, showing the expected agreement of the two behaviours. We also compute the first subleading unusual correction to the scaling behaviour, showing that it is expressible in terms of expansions of various fractional powers of the correlation length, related to the differences $\\Delta-\\Delta_{\\min}$ between the conformal dimensions of fields in the theory and the minimal conformal dimension. Finally, a few observati...
Singular Value Decomposition for Unitary Symmetric Matrix
Institute of Scientific and Technical Information of China (English)
ZOUHongxing; WANGDianjun; DAIQionghai; LIYanda
2003-01-01
A special architecture called unitary sym-metric matrix which embodies orthogonal, Givens, House-holder, permutation, and row (or column) symmetric ma-trices as its special cases, is proposed, and a precise corre-spondence of singular values and singular vectors between the unitary symmetric matrix and its mother matrix is de-rived. As an illustration of potential, it is shown that, for a class of unitary symmetric matrices, the singular value decomposition (SVD) using the mother matrix rather than the unitary symmetric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision.
Why is the $3\\times 3$ neutrino mixing matrix almost unitary in realistic seesaw models?
Xing, Z; Xing, Zhi-zhong; Zhou, Shun
2006-01-01
A simple extension of the standard model is to introduce $n$ heavy right-handed Majorana neutrinos and preserve its $\\rm SU(2)^{}_L \\times U(1)^{}_Y$ gauge symmetry. Diagonalizing the $(3+n) \\times (3+n)$ neutrino mass matrix, we obtain an exact analytical expression for the effective mass matrix of $\
Phase Structure of the T-matrix and Multichannel Unitary Isobar Model
Razavi, S.; Nakayama, K.
2015-04-01
By exploiting the full phase structure of the meson-baryon coupled channels reaction amplitude-here including also the photon-baryon channel-an isobar model is constructed which fulfills automatically the unitarity and analyticity conditions of the S-matrix, in addition to gauge invariance in the case of photoproduction. In particular, it is shown that the unitarity of the (resonance) pole amplitude arises from the dressing mechanism inherent in the basic T-matrix equation, requiring no extra unitarity condition on the pole amplitude as is the case in earlier works on isobar models. As an example, the present model is applied in the description of the meson-nucleon reactions including the πN , ηN , σN , ρN and πΔ channels. The latter three account effectively for the ππN channel. FFE-COSY Grant No. 41788390.
Killip, Rowan; Kozhan, Rostyslav
2017-02-01
We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these ensembles. This allows us to compute the joint law of the eigenvalues, which have a natural interpretation as resonances for open quantum systems or as electrostatic charges located in a dielectric medium. Our methods allow us to consider all values of {β > 0}, not merely {β=1,2,4}.
Unitary Response Regression Models
Lipovetsky, S.
2007-01-01
The dependent variable in a regular linear regression is a numerical variable, and in a logistic regression it is a binary or categorical variable. In these models the dependent variable has varying values. However, there are problems yielding an identity output of a constant value which can also be modelled in a linear or logistic regression with…
Spectral stability of unitary network models
Asch, Joachim; Bourget, Olivier; Joye, Alain
2015-08-01
We review various unitary network models used in quantum computing, spectral analysis or condensed matter physics and establish relationships between them. We show that symmetric one-dimensional quantum walks are universal, as are CMV matrices. We prove spectral stability and propagation properties for general asymptotically uniform models by means of unitary Mourre theory.
Computing a logarithm of a unitary matrix with general spectrum
Loring, Terry A
2012-01-01
In theory, a unitary matrix U has a skew-hermitian logarithm H. In a computing environment one expects only to know U^*U \\approx I and might wish to compute H with e^H \\approx U and H^*= -H. This is relatively easy to accomplish using the Schur decomposition. Reasonable error bounds are derived. In cases where the norm of U^*U-I is somewhat large we discuss the utility of pre-processing with Newton's method of approximating the polar decomposition. In the case of U being J-skew-symmetric, one can insist that H be J-skew-symmetric and skew-Hermitian.
The Schur algorithm for generalized Schur functions III : J-unitary matrix polynomials on the circle
Alpay, Daniel; Azizov, Tomas; Dijksma, Aad; Langer, Heinz
2003-01-01
The main result is that for J = ((1)(0) (0)(-1)) every J-unitary 2 x 2-matrix polynomial on the unit circle is an essentially unique product of elementary J-unitary 2 x 2-matrix polynomials which are either of degree 1 or 2k. This is shown by means of the generalized Schur transformation introduced
Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (II) - Application
Institute of Scientific and Technical Information of China (English)
DAI Lian-Rong; PAN Feng
2001-01-01
Simple analytical expressions for one- and two-body matrix elements in the unitary group approach to the configuration interaction problems of many-electron systems are obtained based on the previous results for general Un irreps.
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
Energy Technology Data Exchange (ETDEWEB)
Werry, Jason L.; Gould, Mark D.; Isaac, Phillip S. [School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072 (Australia)
2015-12-15
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.
Alpay, D.; Dijksma, A.; Langer, H.
2004-01-01
We prove that a 2 × 2 matrix polynomial which is J-unitary on the real line can be written as a product of normalized elementary J-unitary factors and a J-unitary constant. In the second part we give an algorithm for this factorization using an analog of the Schur transformation.
Boundary Relations, Unitary Colligations, and Functional Models
Behrndt, Jussi; Hassi, Seppo; de Snoo, Henk
2009-01-01
Recently a new notion, the so-called boundary relation, has been introduced involving an analytic object, the so-called Weyl family. Weyl families and boundary relations establish a link between the class of Nevanlinna families and unitary relations acting from one Krein in space, a basic (state) sp
Institute of Scientific and Technical Information of China (English)
邢志忠; 周顺
2006-01-01
对标准模型的一种简单扩充就是引入n个重的右手中微子且保持其SU(2)L×U(1)Y规范对称性.通过对角化(3+n)×(3+n)阶中微子质量矩阵,得到关于νe,νμ和ντ的有效质量矩阵的精确的解析表达式.结果表明,在轻子带电弱流中出现的3×3中微子混合矩阵V必须不是严格幺正的.如果通过跷跷板机制产生正确的轻的中微子的质量标度,那么V的幺正性破坏的程度非常小,几乎可以忽略.类似的结论同样可以在第二类跷跷板模型中得到.%A simple extension of the standard model is to introduce n heavy right-handed Majorana neutrinos and preserve its SU(2)L×U(1)Y gauge symmetry. Diagonalizing the (3+n)×(3+n) neutrino mass matrix,we obtain an exact analytical expression for the effective mass matrix of νe, νμ and ντ. It turns out that the 3×3 neutrino mixing matrix V, which appears in the leptonic charged-current weak interactions, must not be exactly unitary. The unitarity violation of V is negligibly tiny, however, if the canonical seesaw mechanism works to reproduce the correct mass scale of light Majorana neutrinos. A similar conclusion can be drawn in the realistic Type-Ⅱ seesaw models.
Fujii, Kazuyuki
2008-01-01
In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper {\\bf Chaturvedi et al} (arXiv : 0706.0964 [quant-ph]).
String-theoretic unitary S-matrix at the threshold of black-hole production
Veneziano, Gabriele
2004-01-01
Previous results on trans-Planckian collisions in superstring theory are rewritten in terms of an explicitly unitary S-matrix whose validity covers a large region of the energy/impact-parameter plane. Amusingly, as part of this region's border is approached, properties of the final state start resembling those expected from the evaporation of a black-hole even well below its production threshold. More specifically, we conjecture that, in an energy window extending up such a threshold, inclusive cross sections satisfy a peculiar "anti-scaling" behaviour seemingly preparing for a smooth transition to black-hole physics.
Random unitary evolution model of quantum Darwinism with pure decoherence
Balanesković, Nenad
2015-10-01
We study the behavior of Quantum Darwinism [W.H. Zurek, Nat. Phys. 5, 181 (2009)] within the iterative, random unitary operations qubit-model of pure decoherence [J. Novotný, G. Alber, I. Jex, New J. Phys. 13, 053052 (2011)]. We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system S from the point of view of its environment E, is not a generic phenomenon, but depends on the specific form of input states and on the type of S- E-interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial input states of environment E that allow to store information about an open system S of interest with maximal efficiency.
Unitary transformation method for solving generalized Jaynes-Cummings models
Indian Academy of Sciences (India)
Sudha Singh
2006-03-01
Two fully quantized generalized Jaynes-Cummings models for the interaction of a two-level atom with radiation field are treated, one involving intensity dependent coupling and the other involving multiphoton interaction between the field and the atom. The unitary transformation method presented here not only solves the time dependent problem but also allows a determination of the eigensolutions of the interacting Hamiltonian at the same time.
Siminovitch, David; Untidt, Thomas; Nielsen, Niels Chr
2004-01-01
Our recent exact effective Hamiltonian theory (EEHT) for exact analysis of nuclear magnetic resonance (NMR) experiments relied on a novel entanglement of unitary exponential operators via finite expansion of the logarithmic mapping function. In the present study, we introduce simple alternant quotient expressions for the coefficients of the polynomial matrix expansion of these entangled operators. These expressions facilitate an extension of our previous closed solution to the Baker-Campbell-Hausdorff problem for SU(N) systems from Nfunction. The general applicability of these expressions is demonstrated by several examples with relevance for NMR spectroscopy. The specific form of the alternant quotients is also used to demonstrate the fundamentally important equivalence of Sylvester's theorem (also known as the spectral theorem) and the EEHT expansion.
Institute of Scientific and Technical Information of China (English)
CHEN Jing-Ling; XUE Kang; GE Mo-Lin
2009-01-01
We show that all pure entangled states of two d-dimensional quantum systems (i.e.,two qudits) can be generated from an initial separable state via a universal Yang-Baxter matrix if one is assisted by local unitary transformations.
Qubit Transport Model for Unitary Black Hole Evaporation without Firewalls
Osuga, Kento
2016-01-01
We give an explicit toy qubit transport model for transferring information from the gravitational field of a black hole to the Hawking radiation by a continuous unitary transformation of the outgoing radiation and the black hole gravitational field. The model has no firewalls or other drama at the event horizon and fits the set of six physical constraints that Giddings has proposed for models of black hole evaporation. It does utilize nonlocal qubits for the gravitational field but assumes that the radiation interacts locally with these nonlocal qubits, so in some sense the nonlocality is confined to the gravitational sector. Although the qubit model is too crude to be quantitively correct for the detailed spectrum of Hawking radiation, it fits qualitatively with what is expected.
Unitary theory of pion photoproduction in the chiral bag model
Energy Technology Data Exchange (ETDEWEB)
Araki, M.; Afnan, I.R.
1987-07-01
We present a multichannel unitary theory of single pion photoproduction from a baryon B. Here, B is the nucleon or ..delta..(1232), with possible extension to include the Roper resonance and strange baryons. We treat the baryon as a three-quark state within the framework of the gauge and chiral Lagrangian, derived from the Lagrangian for the chiral bag model. By first exposing two-body, and then three-body unitarity, taking into consideration the ..pi pi..B and ..gamma pi..B intermediate states, we derive a set of equations for the amplitudes both on and off the energy shell. The Born term in the expansion of the amplitude has the new feature that the vertices in the pole diagram are undressed, while those in the crossed, contact, and pion pole diagrams are dressed.
Unitary theory of pion photoproduction in the chiral bag model
Araki, M.; Afnan, I. R.
1987-07-01
We present a multichannel unitary theory of single pion photoproduction from a baryon B. Here, B is the nucleon or Δ(1232), with possible extension to include the Roper resonance and strange baryons. We treat the baryon as a three-quark state within the framework of the gauge and chiral Lagrangian, derived from the Lagrangian for the chiral bag model. By first exposing two-body, and then three-body unitarity, taking into consideration the ππB and γπB intermediate states, we derive a set of equations for the amplitudes both on and off the energy shell. The Born term in the expansion of the amplitude has the new feature that the vertices in the pole diagram are undressed, while those in the crossed, contact, and pion pole diagrams are dressed.
Modeling Sampling in Tensor Products of Unitary Invariant Subspaces
Directory of Open Access Journals (Sweden)
Antonio G. García
2016-01-01
Full Text Available The use of unitary invariant subspaces of a Hilbert space H is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of L2(R and also periodic extensions of finite signals are remarkable examples where this occurs. As a consequence, the availability of an abstract unitary sampling theory becomes a useful tool to handle these problems. In this paper we derive a sampling theory for tensor products of unitary invariant subspaces. This allows merging the cases of finitely/infinitely generated unitary invariant subspaces formerly studied in the mathematical literature; it also allows introducing the several variables case. As the involved samples are identified as frame coefficients in suitable tensor product spaces, the relevant mathematical technique is that of frame theory, involving both finite/infinite dimensional cases.
Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun
2002-01-01
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Dijkgraaf, Robbert; Vafa, Cumrun
2002-11-01
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large- N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large- N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert E-mail: rhd@science.uva.nl; Vafa, Cumrun
2002-11-11
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large-N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large-N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Comparing the Rξ gauge and the unitary gauge for the standard model: An example
Wu, Tai Tsun; Wu, Sau Lan
2017-01-01
For gauge theory, the matrix element for any physical process is independent of the gauge used. However, since this is a formal statement, it does not guarantee this gauge independence in every case. An example is given here where, for a physical process in the standard model, the matrix elements calculated with two different gauge - the Rξ gauge and the unitary gauge - are explicitly verified to be different. This is accomplished by subtracting one matrix element from the other. This non-zero difference turns out to have a subtle origin. Two simple operators are found not to commute with each other: in one gauge these two operations are carried out in one order, while in the other gauge these same two operations are carried out in the opposite order. Because of this result, a series of question are raised such that the answers to these question may lead to a deeper understanding of the Yang-Mills non-Abelian gauge theory in general and the standard model in particular.
Unitary evolution for anisotropic quantum cosmologies: models with variable spatial curvature
Pandey, Sachin
2016-01-01
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they involve varying spatial curvature unlike the most talked about homogeneous but anisotropic cosmological models like Bianchi I, V and IX. We exhibit either explicit example of the unitary solutions of the Wheeler-DeWitt equation, or at least show that a self-adjoint extension is possible.
Unitary evolution for anisotropic quantum cosmologies: models with variable spatial curvature
Pandey, Sachin; Banerjee, Narayan
2016-11-01
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they involve varying spatial curvature unlike the most talked about homogeneous but anisotropic cosmological models like Bianchi I, V and IX. We exhibit either an explicit example of the unitary solutions of the Wheeler-DeWitt equation, or at least show that a self-adjoint extension is possible.
Kota, V K B
2015-01-01
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states and interacting via $k$-body interactions, we have EGUE($k$) and the embedding algebra is $U(N)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (same initial and final systems), nuclear beta and double beta decay (different initial and final systems), particle addition to/removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities, we have derived formulas for lower order bivariate moments of the strength densities generated by a variety of transition operators. For a spinless fermion system, using EGUE($k$) representation for Hamiltonian and an independent EGUE($...
Recombination rates from potential models close to the unitary limit
Garrido, E; Kievsky, A
2013-01-01
We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schr\\"odinger equation above the dimer threshold for different potentials having large values of the two-body scattering length $a$. To this aim we use the hyperspherical adiabatic expansion and we extract the $S$-matrix through the integral relations recently derived. The results are compared to the universal form, $\\alpha\\approx 67.1\\sin^2[s_0\\ln(\\kappa_*a)+\\gamma]$, for different values of $a$ and selected values of the three-body parameter $\\kappa_*$. A good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections, which have been recently proposed by two of the authors in Ref.[1]. Furthermore, we analyze the validity of the above formula in the description of a very different system: neutron-neutron-proton recombination. Our analysis confirms the universal character of the process in systems o...
Anisotropic models are unitary: A rejuvenation of standard quantum cosmology
Pal, Sridip
2016-01-01
The present work proves that the folk-lore of the pathology of non-conservation of probability in quantum anisotropic models is wrong. It is shown in full generality that all operator ordering can lead to a Hamiltonian with a self-adjoint extension as long as it is constructed to be a symmetric operator, thereby making the problem of non-unitarity in context of anisotropic homogeneous model a ghost. Moreover, it is indicated that the self-adjoint extension is not unique and this non-uniqueness is suspected not to be a feature of Anisotropic model only, in the sense that there exists operator orderings such that Hamiltonian for an isotropic homogeneous cosmological model does not have unique self-adjoint extension, albeit for isotropic model, there is a special unique extension associated with quadratic form of Hamiltonian i.e {\\it Friedrichs extension}. Details of calculations are carried out for a Bianchi III model.
Tensor Network Models of Unitary Black Hole Evaporation
Leutheusser, Samuel
2016-01-01
We introduce a general class of toy models to study the quantum information-theoretic properties of black hole radiation. The models are governed by a set of isometries that specify how microstates of the black hole at a given energy evolve to entangled states of a tensor product black-hole/radiation Hilbert space. The final state of the black hole radiation is conveniently summarized by a tensor network built from these isometries. We introduce a set of quantities generalizing the Renyi entropies that provide a complete set of bipartite/multipartite entanglement measures, and give a general formula for the average of these over initial black hole states in terms of the isometries defining the model. For models where the dimension of the final tensor product radiation Hilbert space is the same as that of the space of initial black hole microstates, the entanglement structure is universal, independent of the choice of isometries. In the more general case, we find that models which best capture the "information...
Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks
Directory of Open Access Journals (Sweden)
Nelson Jorge G. Fonseca
2015-01-01
Full Text Available The Lorentz reciprocity theorem enables us to establish that the transmitting and receiving patterns of any antenna are identical, provided some hypotheses on this antenna and the surrounding medium are satisfied. But reciprocity does not mean that the antenna behaves the same in the transmitting and the receiving modes. In this paper, array antennas fed by multiple beam forming networks are discussed, highlighting the possibility to have different values of internal losses in the beam forming network depending on the operation mode. In particular, a mathematical condition is derived for the specific case of a multiple beam forming network with lossless transmitting mode and lossy receiving mode, such a behavior being fully consistent with the reciprocity theorem. A theoretical discussion is provided, starting from a simple 2-element array to a general M×N multiple beam forming network. A more practical example is then given, discussing a specific 4×8 Nolen matrix design and comparing theoretical aspects with simulation results.
Elegant Coercion and Iran: Beyond the Unitary Actor Model
2005-05-01
leader to manipulate state information and propaganda . The Supreme Leader’s authority to appoint the commander of the Artesh, the Chief of the...are parochial • Decisio rather r compro • State de collages outcom politica Figure 10 – Summary of Allison’s Decision-Making Models Data for this
Physical Aspects of Unitary evolution of Bianchi-I Quantum Cosmological Model
Pal, Sridip
2015-01-01
In this work, we study some physical aspects of unitary evolution of Bianchi-I model. In particular, we study the behavior of the volume and the scale factor as a function of time for the Bianchi-I universe with ultra-relativistic fluid ($\\alpha=1$). The expectation value of volume is shown not to hit any singularity. We elucidate on the anisotropic nature of the solution and physically interpret the wavefunction as a superposition of collapsing universe and expanding universe mimicking Hartle-Hawking type wavefunction. The same analysis has been done for $\\alpha\
Energy Technology Data Exchange (ETDEWEB)
Brown, T.W.
2010-11-15
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)
Aoki, H; Kawai, H; Kitazawa, Y; Tada, T; Tsuchiya, A
1999-01-01
We review our proposal for a constructive definition of superstring, type IIB matrix model. The IIB matrix model is a manifestly covariant model for space-time and matter which possesses N=2 supersymmetry in ten dimensions. We refine our arguments to reproduce string perturbation theory based on the loop equations. We emphasize that the space-time is dynamically determined from the eigenvalue distributions of the matrices. We also explain how matter, gauge fields and gravitation appear as fluctuations around dynamically determined space-time.
Kock, B. E.
2008-12-01
The increased availability and understanding of agent-based modeling technology and techniques provides a unique opportunity for water resources modelers, allowing them to go beyond traditional behavioral approaches from neoclassical economics, and add rich cognition to social-hydrological models. Agent-based models provide for an individual focus, and the easier and more realistic incorporation of learning, memory and other mechanisms for increased cognitive sophistication. We are in an age of global change impacting complex water resources systems, and social responses are increasingly recognized as fundamentally adaptive and emergent. In consideration of this, water resources models and modelers need to better address social dynamics in a manner beyond the capabilities of neoclassical economics theory and practice. However, going beyond the unitary curve requires unique levels of engagement with stakeholders, both to elicit the richer knowledge necessary for structuring and parameterizing agent-based models, but also to make sure such models are appropriately used. With the aim of encouraging epistemological and methodological convergence in the agent-based modeling of water resources, we have developed a water resources-specific cognitive model and an associated collaborative modeling process. Our cognitive model emphasizes efficiency in architecture and operation, and capacity to adapt to different application contexts. We describe a current application of this cognitive model and modeling process in the Arkansas Basin of Colorado. In particular, we highlight the potential benefits of, and challenges to, using more sophisticated cognitive models in agent-based water resources models.
Kitazawa, Y; Saito, O; Kitazawa, Yoshihisa; Mizoguchi, Shun'ya; Saito, Osamu
2006-01-01
We study the zero-dimensional reduced model of D=6 pure super Yang-Mills theory and argue that the large N limit describes the (2,0) Little String Theory. The one-loop effective action shows that the force exerted between two diagonal blocks of matrices behaves as 1/r^4, implying a six-dimensional spacetime. We also observe that it is due to non-gravitational interactions. We construct wave functions and vertex operators which realize the D=6, (2,0) tensor representation. We also comment on other "little" analogues of the IIB matrix model and Matrix Theory with less supercharges.
General linear matrix model, Minkowski spacetime and the Standard Model
Belyea, Chris
2010-01-01
The Hermitian matrix model with general linear symmetry is argued to decouple into a finite unitary matrix model that contains metastable multidimensional lattice configurations and a fermion determinant. The simplest metastable state is a Hermitian Weyl kinetic operator of either handedness on a 3+1 D lattice with general nonlocal interactions. The Hermiticity produces 16 effective Weyl fermions by species doubling, 8 left- and 8 right-handed. These are identified with a Standard Model generation. Only local non-anomalous gauge fields within the soup of general fluctuations can survive at long distances, and the degrees of freedom for gauge fields of an $SU(8)_L X SU(8)_R$ GUT are present. Standard Model gauge symmetries associate with particular species symmetries, for example change of QCD color associates with permutation of doubling status amongst space directions. Vierbein gravity is probably also generated. While fundamental Higgs fields are not possible, low fermion current masses can arise from chira...
Unitary input DEA model to identify beef cattle production systems typologies
Directory of Open Access Journals (Sweden)
Eliane Gonçalves Gomes
2012-08-01
Full Text Available The cow-calf beef production sector in Brazil has a wide variety of operating systems. This suggests the identification and the characterization of homogeneous regions of production, with consequent implementation of actions to achieve its sustainability. In this paper we attempted to measure the performance of 21 livestock modal production systems, in their cow-calf phase. We measured the performance of these systems, considering husbandry and production variables. The proposed approach is based on data envelopment analysis (DEA. We used unitary input DEA model, with apparent input orientation, together with the efficiency measurements generated by the inverted DEA frontier. We identified five modal production systems typologies, using the isoefficiency layers approach. The results showed that the knowledge and the processes management are the most important factors for improving the efficiency of beef cattle production systems.
Mideros, A.; O'Donoghue, C.
2014-01-01
We examine the effect of unconditional cash transfers by a unitary discrete labour supply model. We argue that there is no negative income effect of social transfers in the case of poor adults because leisure could not be assumed to be a normal good under such conditions. Using data from the nationa
Mideros, A.; O'Donoghue, C.
2014-01-01
We examine the effect of unconditional cash transfers by a unitary discrete labour supply model. We argue that there is no negative income effect of social transfers in the case of poor adults because leisure could not be assumed to be a normal good under such conditions. Using data from the
Mideros, A.; O'Donoghue, C.
2014-01-01
We examine the effect of unconditional cash transfers by a unitary discrete labour supply model. We argue that there is no negative income effect of social transfers in the case of poor adults because leisure could not be assumed to be a normal good under such conditions. Using data from the nationa
Veloz, Tomas; Desjardins, Sylvie
2015-01-01
Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations. PMID:26617556
Wall Crossing As Seen By Matrix Models
Ooguri, Hirosi; Yamazaki, Masahito
2010-01-01
The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold $X$, both are naturally related to the K\\"ahler moduli space ${\\cal M}(X)$. We construct unitary one-matrix models which count such BPS states for a class of toric Calabi-Yau manifolds at infinite 't Hooft coupling. The matrix model for the BPS counting on $X$ turns out to give the topological string partition function for another Calabi-Yau manifold $Y$, whose K\\"ahler moduli space ${\\cal M}(Y)$ contains two copies of ${\\cal M}(X)$, one related to the BPS charges and another to the stability conditions. The two sets of data are unified in ${\\cal M}(Y)$. The matrix models have a number of other interesting features. They compute spectral curves and mirror maps relevant to the remodeling conjecture. For finite 't Hooft coupling they give rise to yet more general geometry $\\widetilde{Y}$ contain...
Entanglement continuous unitary transformations
Sahin, Serkan; Schmidt, Kai Phillip; Orús, Román
2017-01-01
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second quantization. Yet, one of their main challenges is how to approximate the infinitely-many coupled differential equations that are produced throughout this flow. Here we show that tensor networks offer a natural and non-perturbative truncation scheme in terms of entanglement. The corresponding scheme is called “entanglement-CUT” or eCUT. It can be used to extract the low-energy physics of quantum many-body Hamiltonians, including quasiparticle energy gaps. We provide the general idea behind eCUT and explain its implementation for finite 1d systems using the formalism of matrix product operators. We also present proof-of-principle results for the spin-(1/2) 1d quantum Ising model and the 3-state quantum Potts model in a transverse field. Entanglement-CUTs can also be generalized to higher dimensions and to the thermodynamic limit.
A Tree-level Unitary Noncompact Weyl-Einstein-Yang-Mills Model
Dengiz, Suat
2016-01-01
We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus $SU(N)$ phase invariant Higgs-like field, conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable constant curvature vacuum. The model is unitary in de Si...
Entanglement Continuous Unitary Transformations
Sahin, S; Orus, R
2016-01-01
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second quantization. Yet, one of their main challenges is how to approximate the infinitely-many coupled differential equations that are produced throughout this flow. Here we show that tensor networks offer a natural and non-perturbative truncation scheme in terms of entanglement. The corresponding scheme is called "entanglement-CUT" or eCUT. It can be used to extract the low-energy physics of quantum many-body Hamiltonians, including quasiparticle energy gaps. We provide the general idea behind eCUT and explain its implementation for finite 1d systems using the formalism of matrix product operators, and we present proof-of-principle results for the spin-1/2 1d quantum Ising model in a transverse field. Entanglement-CUTs can also be generalized to higher dimensions and to the thermo...
Matrix models and stochastic growth in Donaldson-Thomas theory
Energy Technology Data Exchange (ETDEWEB)
Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, United Kingdom and Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); Tierz, Miguel [Grupo de Fisica Matematica, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa (Portugal); Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain)
2012-10-15
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Matrix models and stochastic growth in Donaldson-Thomas theory
Szabo, Richard J.; Tierz, Miguel
2012-10-01
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Matrix models and stochastic growth in Donaldson-Thomas theory
Szabo, Richard J
2010-01-01
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating ...
Direct dialling of Haar random unitary matrices
Russell, Nicholas J.; Chakhmakhchyan, Levon; O’Brien, Jeremy L.; Laing, Anthony
2017-03-01
Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly implement Haar random unitary matrices in optical circuits, with no requirement for prior or explicit matrix calculations. Our physically motivated and compact representation directly maps independent probability density functions for parameters in Haar random unitary matrices, to optical circuit components. We go on to extend the results to the case of random unitaries for qubits.
Random matrix model for disordered conductors
Indian Academy of Sciences (India)
Zafar Ahmed; Sudhir R Jain
2000-03-01
We present a random matrix ensemble where real, positive semi-deﬁnite matrix elements, , are log-normal distributed, $\\exp[-\\log^{2}(x)]$. We show that the level density varies with energy, , as 2/(1 + ) for large , in the unitary family, consistent with the expectation for disordered conductors. The two-level correlation function is studied for the unitary family and found to be largely of the universal form despite the fact that the level density has a non-compact support. The results are based on the method of orthogonal polynomials (the Stieltjes-Wigert polynomials here). An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson's Coulomb gas analogy breaks down whenever the conﬁning potential is given by a transcendental function for which there exist orthogonal polynomials.
Matrix Models and Gravitational Corrections
Dijkgraaf, R; Temurhan, M; Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2002-01-01
We provide evidence of the relation between supersymmetric gauge theories and matrix models beyond the planar limit. We compute gravitational R^2 couplings in gauge theories perturbatively, by summing genus one matrix model diagrams. These diagrams give the leading 1/N^2 corrections in the large N limit of the matrix model and can be related to twist field correlators in a collective conformal field theory. In the case of softly broken SU(N) N=2 super Yang-Mills theories, we find that these exact solutions of the matrix models agree with results obtained by topological field theory methods.
Energy Technology Data Exchange (ETDEWEB)
Dorey, Nick [Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Wilberforce Road, Cambridge, CB3 OWA (United Kingdom); Tong, David [Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Wilberforce Road, Cambridge, CB3 OWA (United Kingdom); Department of Theoretical Physics, TIFR,Homi Bhabha Road, Mumbai 400 005 (India); Stanford Institute for Theoretical Physics,Via Pueblo, Stanford, CA 94305 (United States); Turner, Carl [Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Wilberforce Road, Cambridge, CB3 OWA (United Kingdom)
2016-08-01
We study a U(N) gauged matrix quantum mechanics which, in the large N limit, is closely related to the chiral WZW conformal field theory. This manifests itself in two ways. First, we construct the left-moving Kac-Moody algebra from matrix degrees of freedom. Secondly, we compute the partition function of the matrix model in terms of Schur and Kostka polynomials and show that, in the large N limit, it coincides with the partition function of the WZW model. This same matrix model was recently shown to describe non-Abelian quantum Hall states and the relationship to the WZW model can be understood in this framework.
Dorey, Nick; Turner, Carl
2016-01-01
We study a U(N) gauged matrix quantum mechanics which, in the large N limit, is closely related to the chiral WZW conformal field theory. This manifests itself in two ways. First, we construct the left-moving Kac-Moody algebra from matrix degrees of freedom. Secondly, we compute the partition function of the matrix model in terms of Schur and Kostka polynomials and show that, in the large $N$ limit, it coincides with the partition function of the WZW model. This same matrix model was recently shown to describe non-Abelian quantum Hall states and the relationship to the WZW model can be understood in this framework.
Matrix algebra for linear models
Gruber, Marvin H J
2013-01-01
Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f
Universality of Correlation Functions in Random Matrix Models of QCD
Jackson, A D; Verbaarschot, J J M
1997-01-01
We demonstrate the universality of the spectral correlation functions of a QCD inspired random matrix model that consists of a random part having the chiral structure of the QCD Dirac operator and a deterministic part which describes a schematic temperature dependence. We calculate the correlation functions analytically using the technique of Itzykson-Zuber integrals for arbitrary complex super-matrices. An alternative exact calculation for arbitrary matrix size is given for the special case of zero temperature, and we reproduce the well-known Laguerre kernel. At finite temperature, the microscopic limit of the correlation functions are calculated in the saddle point approximation. The main result of this paper is that the microscopic universality of correlation functions is maintained even though unitary invariance is broken by the addition of a deterministic matrix to the ensemble.
Altafini, C
2004-01-01
For the 3-qubit UPB state, i.e., the bound entangled state constructed from an Unextendable Product Basis of Bennett et al. (Phys. Rev. Lett. 82:5385, 1999), we provide a set of violations of Local Hidden Variable (LHV) models based on the particular type of reflection symmetry encoded in this state. The explicit nonlocal unitary operation needed to prepare the state from its reflected separable mixture of pure states is given, as well as a nonlocal one-parameter orbit of states with Positive Partial Transpositions (PPT) which swaps the entanglement between a state and its reflection twice during a period.
Eigenvalue Separation in Some Random Matrix Models
Bassler, Kevin E; Frankel, Norman E
2008-01-01
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian u...
Large N classical dynamics of holographic matrix models
Asplund, Curtis T; Dzienkowski, Eric
2014-01-01
Using a numerical simulation of the classical dynamics of the plane-wave and flat space matrix models of M-theory, we study the thermalization, equilibrium thermodynamics and fluctuations of these models as we vary the temperature and the size of the matrices, N. We present our numerical implementation in detail and several checks of its precision and consistency. We show evidence for thermalization by matching the time-averaged distributions of the matrix eigenvalues to the distributions of the appropriate Traceless Gaussian Unitary Ensemble of random matrices. We study the autocorrelations and power spectra for various fluctuating observables and observe evidence of the expected chaotic dynamics as well as a hydrodynamic type limit at large N, including near-equilibrium dissipation processes. These configurations are holographically dual to black holes in the dual string theory or M-theory and we discuss how our results could be related to the corresponding supergravity black hole solutions.
Matrix Model Approach to Cosmology
Chaney, A; Stern, A
2015-01-01
We perform a systematic search for rotationally invariant cosmological solutions to matrix models, or more specifically the bosonic sector of Lorentzian IKKT-type matrix models, in dimensions $d$ less than ten, specifically $d=3$ and $d=5$. After taking a continuum (or commutative) limit they yield $d-1$ dimensional space-time surfaces, with an attached Poisson structure, which can be associated with closed, open or static cosmologies. For $d=3$, we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit. Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit. The solutions provide for a matrix resolution of cosmological singularities. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the $d=3$ soluti...
Model Reduction via Reducibility Matrix
Institute of Scientific and Technical Information of China (English)
Musa Abdalla; Othman Alsmadi
2006-01-01
In this work, a new model reduction technique is introduced. The proposed technique is derived using the matrix reducibility concept. The eigenvalues of the reduced model are preserved; that is, the reduced model eigenvalues are a subset of the full order model eigenvalues. This preservation of the eigenvalues makes the mathematical model closer to the physical model. Finally, the outcomes of this method are fully illustrated using simulations of two numeric examples.
Erickson, G. E.; Burner, A. W.; DeLoach, R.
1999-01-01
Pressure-sensitive paint (PSP) and video model deformation (VMD) systems have been installed in the Unitary Plan Wind Tunnel at the NASA Langley Research Center to support the supersonic wind tunnel testing requirements of the High Speed Research (HSR) program. The PSP and VMD systems have been operational since early 1996 and provide the capabilities of measuring global surface static pressures and wing local twist angles and deflections (bending). These techniques have been successfully applied to several HSR wind tunnel models for wide ranges of the Mach number, Reynolds number, and angle of attack. A review of the UPWT PSP and VMD systems is provided, and representative results obtained on selected HSR models are shown. A promising technique to streamline the wind tunnel testing process, Modern Experimental Design, is also discussed in conjunction with recently-completed wing deformation measurements at UPWT.
Unitary Approximations in Fault Detection Filter Design
Directory of Open Access Journals (Sweden)
Dušan Krokavec
2016-01-01
Full Text Available The paper is concerned with the fault detection filter design requirements that relax the existing conditions reported in the previous literature by adapting the unitary system principle in approximation of fault detection filter transfer function matrix for continuous-time linear MIMO systems. Conditions for the existence of a unitary construction are presented under which the fault detection filter with a unitary transfer function can be designed to provide high residual signals sensitivity with respect to faults. Otherwise, reflecting the emplacement of singular values in unitary construction principle, an associated structure of linear matrix inequalities with built-in constraints is outlined to design the fault detection filter only with a Hurwitz transfer function. All proposed design conditions are verified by the numerical illustrative examples.
Extremal spacings of random unitary matrices
Smaczynski, Marek; Kus, Marek; Zyczkowski, Karol
2012-01-01
Extremal spacings between unimodular eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Probability distributions for the minimal spacing for various ensembles are derived for N=4. We show that for large matrices the average minimal spacing s_min of a random unitary matrix behaves as N^(-1/(1+B)) for B equal to 0,1 and 2 for circular Poisson, orthogonal and unitary ensembles, respectively. For these ensembles also asymptotic probability distributions P(s_min) are obtained and the statistics of the largest spacing s_max are investigated.
Pseudo-random unitary operators for quantum information processing.
Emerson, Joseph; Weinstein, Yaakov S; Saraceno, Marcos; Lloyd, Seth; Cory, David G
2003-12-19
In close analogy to the fundamental role of random numbers in classical information theory, random operators are a basic component of quantum information theory. Unfortunately, the implementation of random unitary operators on a quantum processor is exponentially hard. Here we introduce a method for generating pseudo-random unitary operators that can reproduce those statistical properties of random unitary operators most relevant to quantum information tasks. This method requires exponentially fewer resources, and hence enables the practical application of random unitary operators in quantum communication and information processing protocols. Using a nuclear magnetic resonance quantum processor, we were able to realize pseudorandom unitary operators that reproduce the expected random distribution of matrix elements.
Bicudo, P.; Cardoso, M.
2016-11-01
We address q q Q ¯Q ¯ exotic tetraquark bound states and resonances with a fully unitarized and microscopic quark model. We propose a triple string flip-flop potential, inspired by lattice QCD tetraquark static potentials and flux tubes, combining meson-meson and double Y potentials. Our model includes the color excited potential, but neglects the spin-tensor potentials, as well as all the other relativistic effects. To search for bound states and resonances, we first solve the two-body mesonic problem. Then we develop fully unitary techniques to address the four-body tetraquark problem. We fold the four-body Schrödinger equation with the mesonic wave functions, transforming it into a two-body meson-meson problem with nonlocal potentials. We find bound states for some quark masses, including the one reported in lattice QCD. Moreover, we also find resonances and calculate their masses and widths, by computing the T matrix and finding its pole positions in the complex energy plane, for some quantum numbers. However, a detailed analysis of the quantum numbers where binding exists shows a discrepancy with recent lattice QCD results for the l l b ¯ b ¯ tetraquark bound states. We conclude that the string flip-flop models need further improvement.
Multivariate Modelling via Matrix Subordination
DEFF Research Database (Denmark)
Nicolato, Elisa
stochastic volatility via time-change is quite ineffective when applied to the multivariate setting. In this work we propose a new class of models, which is obtained by conditioning a multivariate Brownian Motion to a so-called matrix subordinator. The obtained model-class encompasses the vast majority...
Noncommutative spaces from matrix models
Lu, Lei
Noncommutative (NC) spaces commonly arise as solutions to matrix model equations of motion. They are natural generalizations of the ordinary commutative spacetime. Such spaces may provide insights into physics close to the Planck scale, where quantum gravity becomes relevant. Although there has been much research in the literature, aspects of these NC spaces need further investigation. In this dissertation, we focus on properties of NC spaces in several different contexts. In particular, we study exact NC spaces which result from solutions to matrix model equations of motion. These spaces are associated with finite-dimensional Lie-algebras. More specifically, they are two-dimensional fuzzy spaces that arise from a three-dimensional Yang-Mills type matrix model, four-dimensional tensor-product fuzzy spaces from a tensorial matrix model, and Snyder algebra from a five-dimensional tensorial matrix model. In the first part of this dissertation, we study two-dimensional NC solutions to matrix equations of motion of extended IKKT-type matrix models in three-space-time dimensions. Perturbations around the NC solutions lead to NC field theories living on a two-dimensional space-time. The commutative limit of the solutions are smooth manifolds which can be associated with closed, open and static two-dimensional cosmologies. One particular solution is a Lorentzian fuzzy sphere, which leads to essentially a fuzzy sphere in the Minkowski space-time. In the commutative limit, this solution leads to an induced metric that does not have a fixed signature, and have a non-constant negative scalar curvature, along with singularities at two fixed latitudes. The singularities are absent in the matrix solution which provides a toy model for resolving the singularities of General relativity. We also discussed the two-dimensional fuzzy de Sitter space-time, which has irreducible representations of su(1,1) Lie-algebra in terms of principal, complementary and discrete series. Field
Quantum unitary dynamics in cosmological spacetimes
Energy Technology Data Exchange (ETDEWEB)
Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Mena Marugán, Guillermo A., E-mail: mena@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: jvelhi@ubi.pt [Departamento de Física, Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã (Portugal)
2015-12-15
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.
Energy Transfer Using Unitary Transformations
Directory of Open Access Journals (Sweden)
Winny O'Kelly de Galway
2013-11-01
Full Text Available We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a cyclic manner by time-dependent external fields. The S-matrix (scattering matrix of the cycle is obtained in analytic form. The total number of quanta contained in the system is a conserved quantity. As a consequence, the spectrum of the S-matrix is purely discrete, and the evolution of the system is quasi-periodic. The explicit knowledge of the S-matrix makes it possible to do accurate numerical evaluations of the time-dependent wave function. They confirm the quasi-periodic behavior. In particular, the energy flows back and forth between the two oscillators in a quasi-periodic manner.
Parameterization for Neutrino Mixing Matrix with Deviated Unitarity
Institute of Scientific and Technical Information of China (English)
LU Lei; WANG Wen-Yu; XIONG Zhao-Hua
2009-01-01
Neutrino oscillation experiments provide the first evidence on non-zero neutrino masses and indicate new physics beyond the standard model.With Majorana neutrinos introduced to acquire tiny neutrino maases,it leads to the existence of more than three neutrino species,implying that the ordinary neutrino mixing matrix is only a part of the whole extended unitary mixing matrix and thus no longer unitary.We give a parameterization for a non-unitary neutrino mixing matrix under seesaw framework and further present a method to test the unitarity of the ordinary neutrino mixing matrix.
Chaos in matrix models and black hole evaporation
Berkowitz, Evan; Hanada, Masanori; Maltz, Jonathan
2016-12-01
Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole's negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. Finally, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.
Unitary lens semiconductor device
Lear, Kevin L.
1997-01-01
A unitary lens semiconductor device and method. The unitary lens semiconductor device is provided with at least one semiconductor layer having a composition varying in the growth direction for unitarily forming one or more lenses in the semiconductor layer. Unitary lens semiconductor devices may be formed as light-processing devices such as microlenses, and as light-active devices such as light-emitting diodes, photodetectors, resonant-cavity light-emitting diodes, vertical-cavity surface-emitting lasers, and resonant cavity photodetectors.
Hyland, Philip; Boduszek, Daniel
2012-01-01
This primary purpose of this paper is to consider the differential cognitive conceptualization of emotions postulated by the two main schools of cognitive behavioural therapy (CBT), namely Rational Emotive Behaviour Therapy (REBT) and Cognitive Therapy (CT).While CT theory favours a unitary model of emotional distress, REBT theory posits a binary model of emotional distress. This paper will address how the two approaches differ in their conceptualizations of emotional disturbance and the impl...
Cowling, W R
2001-06-01
Unitary appreciative inquiry is described as an orientation, process, and approach for illuminating the wholeness, uniqueness, and essence that are the pattern of human life. It was designed to bring the concepts, assumptions, and perspectives of the science of unitary human beings into reality as a mode of inquiry. Unitary appreciative inquiry provides a way of giving fullest attention to important facets of human life that often are not fully accounted for in current methods that have a heavier emphasis on diagnostic representations. The participatory, synoptic, and transformative qualities of the unitary appreciative process are explicated. The critical dimensions of nursing knowledge development expressed in dialectics of the general and the particular, action and theory, stories and numbers, sense and soul, aesthetics and empirics, and interpretation and emancipation are considered in the context of the unitary appreciative stance. Issues of legitimacy of knowledge and credibility of research are posed and examined in the context of four quality standards that are deemed important to evaluate the worthiness of unitary appreciative inquiry for the advancement of nursing science and practice.
Energy Technology Data Exchange (ETDEWEB)
Lee, Jun Myung; Ha, Man Yeong; Son, Chang Min; Doo, Jeong Hoon; Min, June Kee [Pusan National University, Busan (Korea, Republic of)
2016-03-15
Diverse cross-corrugated surface geometries were considered to estimate the sensitivity of four variants of k-ε turbulence models (Low Reynolds, standard, RNG and realizable models). The cross-corrugated surfaces considered in this study are a conventional sinusoidal shape and two different asymmetric shapes. The numerical simulations using the steady incompressible Reynolds-averaged Navier Stokes (RANS) equations were carried out to obtain the steady solutions of the flow and thermal fields in the unitary cell of the heat exchanger matrix. In addition, the experimental test for the measurement of local convective heat transfer coefficients on the heat transfer surfaces was performed by means of the Transient liquid crystal (TLC) technique in order to compare the numerical results with the measured data. The features on detailed flow structure and corresponding heat transfer in the unitary cell of the matrix type heat exchanger are compared and analyzed against four different turbulence models considered in this study.
Study of optical techniques for the Ames unitary wind tunnels. Part 4: Model deformation
Lee, George
1992-01-01
A survey of systems capable of model deformation measurements was conducted. The survey included stereo-cameras, scanners, and digitizers. Moire, holographic, and heterodyne interferometry techniques were also looked at. Stereo-cameras with passive or active targets are currently being deployed for model deformation measurements at NASA Ames and LaRC, Boeing, and ONERA. Scanners and digitizers are widely used in robotics, motion analysis, medicine, etc., and some of the scanner and digitizers can meet the model deformation requirements. Commercial stereo-cameras, scanners, and digitizers are being improved in accuracy, reliability, and ease of operation. A number of new systems are coming onto the market.
Direct Model Checking Matrix Algorithm
Institute of Scientific and Technical Information of China (English)
Zhi-Hong Tao; Hans Kleine Büning; Li-Fu Wang
2006-01-01
During the last decade, Model Checking has proven its efficacy and power in circuit design, network protocol analysis and bug hunting. Recent research on automatic verification has shown that no single model-checking technique has the edge over all others in all application areas. So, it is very difficult to determine which technique is the most suitable for a given model. It is thus sensible to apply different techniques to the same model. However, this is a very tedious and time-consuming task, for each algorithm uses its own description language. Applying Model Checking in software design and verification has been proved very difficult. Software architectures (SA) are engineering artifacts that provide high-level and abstract descriptions of complex software systems. In this paper a Direct Model Checking (DMC) method based on Kripke Structure and Matrix Algorithm is provided. Combined and integrated with domain specific software architecture description languages (ADLs), DMC can be used for computing consistency and other critical properties.
Nuclear numerical range and quantum error correction codes for non-unitary noise models
Lipka-Bartosik, Patryk; Życzkowski, Karol
2017-01-01
We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator A among normalized pure states, which belong to the nucleus of an auxiliary operator Z. This notion proves to be applicable to investigate models of quantum noise with block-diagonal structure of the corresponding Kraus operators. The problem of constructing a suitable quantum error correction code for this model can be restated as a geometric problem of finding intersection points of certain sets in the complex plane. This technique, worked out in the case of two-qubit systems, can be generalized for larger dimensions.
A study of Feshbach resonances and the unitary limit in a model of strongly correlated nucleons
Mekjian, Aram Z
2010-01-01
A model of strongly interacting and correlated hadrons is developed. The interaction used contains a long range attraction and short range repulsive hard core. Using this interaction and various limiting situations of it, a study of the effect of bound states and Feshbach resonances is given. The limiting situations are a pure square well interaction, a delta-shell potential and a pure hard core potential. The limit of a pure hard core potential are compared with results for a spinless Bose and Fermi gas. The limit of many partial waves for a pure hard core interaction is also considered and result in expressions involving the hard core volume. This feature arises from a scaling relation similar to that for hard sphere scattering with diffractive corrections. The role of underlying isospin symmetries associated with the strong interaction of protons and neutrons in this two component model is investigated. Properties are studied with varying proton fraction. An analytic expression for the Beth Uhlenbeck conti...
Reggeon cuts in a multiparticle unitary model II Four-particle case
Drummond, I T
1976-01-01
For pt.I see ibid., vol.B105, p.293, 1976. The reggeon cuts in a model with four-particle unitarity in the t-channel are investigated. The model, which was previously discussed by McCoy and Wu (1974) is derived from phi /sup 3/ theory. The analysis of asymptotic behaviour uses momentum-space techniques. The integral equation for the partial- wave amplitude is carefully investigated and used to exhibit the origin of the various reggeon cuts, which turn out to satisfy discontinuity formulae consistent with Gribov's reggeon calculus. It is suggested that there is a four-particle Regge pole to the right of all the cuts. (12 refs).
Reggeon cuts in a multiparticle unitary model I Three-particle case
Drummond, I T
1976-01-01
The authors investigate the reggeon cuts in a model derived from phi /sup 3/ theory, which exhibits three-particle unitarity in the non- asymptotic channel. They use momentum-space techniques to derive the asymptotic behaviour of the Feynman diagrams and discuss the anomalous structure of certain low-order contributions. Finally they show how the integral equation for the partial-wave amplitude can be used to derive the discontinuity formula across the reggeon cut which turns out to have the same structure and sign as that of the original Mandelstam contribution. (16 refs).
d- $\\overline{B}$ mixing and rare D decays in the Littlest Higgs model with non-unitarity matrix
Chen, Chuan-Hung; Yuan, Tzu-Chiang
2007-01-01
We study the $D-\\bar D$ mixing and rare D decays in the Littlest Higgs model. As the new weak singlet quark with the electric charge of 2/3 is introduced to cancel the quadratic divergence induced by the top-quark, the standard unitary $3\\times 3$ Cabibbo-Kobayashi-Maskawa matrix is extended to a non-unitary $4\\times 3$ matrix in the quark charged currents and Z-mediated flavor changing neutral currents are generated at tree level. In this model, we show that the $D-\\bar D$ mixing parameter can be as large as the current experimental value and the decay branching ratio (BR) of $D\\to X_u \\ga$ is small but its direct CP asymmetry could be $O(10%)$. In addition, we find that the BRs of $D\\to X_u \\ell^{+} \\ell^{-}$, $D\\to X_u\
2D fuzzy Anti-de Sitter space from matrix models
Jurman, Danijel
2013-01-01
We study the fuzzy hyperboloids AdS^2 and dS^2 as brane solutions in matrix models. The unitary representations of SO(2,1) required for quantum field theory are identified, and explicit formulae for their realization in terms of fuzzy wavefunctions are given. In a second part, we study the (A)dS^2 brane geometry and its dynamics, as governed by a suitable matrix model. In particular, we show that trace of the energy-momentum tensor of matter induces transversal perturbations of the brane and of the Ricci scalar. This leads to a linearized form of Henneaux-Teitelboim-type gravity, illustrating the mechanism of emergent gravity in matrix models.
Imposing causality on a matrix model
Energy Technology Data Exchange (ETDEWEB)
Benedetti, Dario [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON (Canada)], E-mail: dbenedetti@perimeterinstitute.ca; Henson, Joe [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON (Canada)
2009-07-13
We introduce a new matrix model that describes Causal Dynamical Triangulations (CDT) in two dimensions. In order to do so, we introduce a new, simpler definition of 2D CDT and show it to be equivalent to the old one. The model makes use of ideas from dually weighted matrix models, combined with multi-matrix models, and can be studied by the method of character expansion.
Govil, Karan
2012-01-01
Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of superconformal groups SU(2,2|N) and OSp(8*|2n) in four and six dimensions were constructed as minreps and their U(1) and SU(2) deformations, respectively. In this paper we extend these results to SU(2) deformations of the minrep of N=4 superconformal algebra D(2,1;\\lambda) in one dimension. We find that SU(2) deformations can be achieved using n pairs of bosons and m pairs of fermions simultaneously. The generators of deformed minimal representations of D(2,1;\\lambda) commute with the generators of a dual superalgebra OSp(2n*|2m) realized in terms of these bosons and fermions. We show that there exists a precise mapping between symmetry generators of N=4 superconformal models in harmonic superspace studied recently and minimal unitary supermultiplets of D(2,1;\\lambda) deformed by a pair...
Modeling and Simulation of Matrix Converter
DEFF Research Database (Denmark)
Liu, Fu-rong; Klumpner, Christian; Blaabjerg, Frede
2005-01-01
This paper discusses the modeling and simulation of matrix converter. Two models of matrix converter are presented: one is based on indirect space vector modulation and the other is based on power balance equation. The basis of these two models is• given and the process on modeling is introduced...
Chaos in Matrix Models and Black Hole Evaporation
Berkowitz, Evan; Maltz, Jonathan
2016-01-01
Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question ---especially aspects of this question such as a black hole's negative specific heat---we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large $N$ limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of...
Kolomiytsev, G. V.; Igashov, S. Yu.; Urin, M. H.
2017-07-01
A unitary version of the single-particle dispersive optical model was proposed with the aim of applying it to describing high-energy single-hole excitations in medium-heavy mass nuclei. By considering the example of experimentally studied single-hole excitations in the 90Zr and 208Pb parent nuclei, the contribution of the fragmentation effect to the real part of the optical-model potential was estimated quantitatively in the framework of this version. The results obtained in this way were used to predict the properties of such excitations in the 132Sn parent nucleus.
Intercept Capacity: Unknown Unitary Transformation
Directory of Open Access Journals (Sweden)
Bill Moran
2008-11-01
Full Text Available We consider the problem of intercepting communications signals between Multiple-Input Multiple-Output (MIMO communication systems. To correctly detect a transmitted message it is necessary to know the gain matrix that represents the channel between the transmitter and the receiver. However, even if the receiver has knowledge of the message symbol set, it may not be possible to estimate the channel matrix. Blind Source Separation (BSS techniques, such as Independent Component Analysis (ICA can go some way to extracting independent signals from individual transmission antennae but these may have been preprocessed in a manner unknown to the receiver. In this paper we consider the situation where a communications interception system has prior knowledge of the message symbol set, the channel matrix between the transmission system and the interception system and is able to resolve the transmissionss from independent antennae. The question then becomes: what is the mutual information available to the interceptor when an unknown unitary transformation matrix is employed by the transmitter.
String Interactions in c=1 Matrix Model
De Boer, J; Verlinde, E; Yee, J T; Boer, Jan de; Sinkovics, Annamaria; Verlinde, Erik; Yee, Jung-Tay
2004-01-01
We study string interactions in the fermionic formulation of the c=1 matrix model. We give a precise nonperturbative description of the rolling tachyon state in the matrix model, and discuss S-matrix elements of the c=1 string. As a first step to study string interactions, we compute the interaction of two decaying D0-branes in terms of free fermions. This computation is compared with the string theory cylinder diagram using the rolling tachyon ZZ boundary states.
Institute of Scientific and Technical Information of China (English)
徐常伟; 朱峰; 刘丽娜; 牛大鹏
2013-01-01
基于H波入射,根据二维介质散射的边界条件,利用二维格林函数的展开式和消光定理,求得T矩阵方法构造方程式；在此基础上,对T矩阵方法的极限问题进行了系统的分析,即当散射体的边界趋于理想圆柱边界时,T矩阵方法实现了由数值解到经典解析解的极限过渡。%The unitary problem between numerical solutions and the analytic solutions is an important issue to value whether or not the physical nature and structure of a numerical method are reasonable in computational electromagnetics. This paper presents the structure functions of T-matrix method based on H-wave incident, boundary conditions of 2D dielectric scattering, and 2D Green’s function and extinction theorem. The full analysis of T-matrix’s limitation problem shows that when the boundary of a dielectric is limited to the cylindrical one, the limitation transition from the T-matrix solutions to classical ones is obtained.
Black holes as random particles: entanglement dynamics in infinite range and matrix models
Magan, Javier M
2016-01-01
We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large-$\\mathcal{N}$ matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large-$\\mathcal{N}$ matrix models, where we provide a gauge invariant entanglement entropy for `generalized free fields', again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a ...
Matrix model description of baryonic deformations
Energy Technology Data Exchange (ETDEWEB)
Bena, Iosif; Murayama, Hitoshi; Roiban, Radu; Tatar, Radu
2003-03-13
We investigate supersymmetric QCD with N{sub c} + 1 flavors using an extension of the recently proposed relation between gauge theories and matrix models.The impressive agreement between the two sides provides a beautiful confirmation of the extension of the gauge theory-matrix model relation to this case.
Perturbative analysis of gauged matrix models
Dijkgraaf, Robbert; Gukov, Sergei; Kazakov, Vladimir A.; Vafa, Cumrun
2003-08-01
We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that nonperturbative aspects of N=1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for N=2 gauge theory, the Montonen-Olive modular invariance for N=1*, and the superpotential for the Leigh-Strassler deformation of N=4 can be systematically computed in perturbation theory of the matrix model or gauge theory (even though in some of these cases an exact answer can also be obtained by summing up planar diagrams of matrix models).
Perturbative Analysis of Gauged Matrix Models
Dijkgraaf, R; Kazakov, V A; Vafa, C; Dijkgraaf, Robbert; Gukov, Sergei; Kazakov, Vladimir A.; Vafa, Cumrun
2003-01-01
We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that non-perturbative aspects of N=1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for N=2 gauge theory, the Montonen-Olive modular invariance for N=1*, and the superpotential for the Leigh-Strassler deformation of N=4 can be systematically computed in perturbation theory of the matrix model/gauge theory (even though in some of these cases the exact answer can also be obtained by summing up planar diagrams of matrix models).
Orbifold matrix models and fuzzy extra dimensions
Chatzistavrakidis, Athanasios; Zoupanos, George
2011-01-01
We revisit an orbifold matrix model obtained as a restriction of the type IIB matrix model on a Z_3-invariant sector. An investigation of its moduli space of vacua is performed and issues related to chiral gauge theory and gravity are discussed. Modifications of the orbifolded model triggered by Chern-Simons or mass deformations are also analyzed. Certain vacua of the modified models exhibit higher-dimensional behaviour with internal geometries related to fuzzy spheres.
Entanglement quantification by local unitaries
Monras, A; Giampaolo, S M; Gualdi, G; Davies, G B; Illuminati, F
2011-01-01
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitaries play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as "shield entanglement". They are constructed by first considering the (squared) Hilbert- Schmidt distance of the state from the set of states obtained by applying to it a given local unitary. To the action of each different local unitary there corresponds a different distance. We then minimize these distances over the sets of local unitaries with different spectra, obtaining an entire family of different entanglement monotones. We show that these shield entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary f...
Sensitivity analysis of periodic matrix population models.
Caswell, Hal; Shyu, Esther
2012-12-01
Periodic matrix models are frequently used to describe cyclic temporal variation (seasonal or interannual) and to account for the operation of multiple processes (e.g., demography and dispersal) within a single projection interval. In either case, the models take the form of periodic matrix products. The perturbation analysis of periodic models must trace the effects of parameter changes, at each phase of the cycle, on output variables that are calculated over the entire cycle. Here, we apply matrix calculus to obtain the sensitivity and elasticity of scalar-, vector-, or matrix-valued output variables. We apply the method to linear models for periodic environments (including seasonal harvest models), to vec-permutation models in which individuals are classified by multiple criteria, and to nonlinear models including both immediate and delayed density dependence. The results can be used to evaluate management strategies and to study selection gradients in periodic environments.
Decomposition of Unitary Matrices for Finding Quantum Circuits
Daskin, Anmer
2010-01-01
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Here, we use the group leaders optimization algorithm, which is an effective and simple global optimization algorithm, to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. Using this procedure, we present new circuit designs for the simulation of the Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, the sender part of the quantum teleportation and the Hamiltonian for the Hydrogen molecule. In addition, we give two algorithmic methods for the construction of unitary matrices with respect to the different types of the quantum control gates. Our results indicate that the procedure is effective, general, and easy to implement.
Multiscale Modeling of Ceramic Matrix Composites
Bednarcyk, Brett A.; Mital, Subodh K.; Pineda, Evan J.; Arnold, Steven M.
2015-01-01
Results of multiscale modeling simulations of the nonlinear response of SiC/SiC ceramic matrix composites are reported, wherein the microstructure of the ceramic matrix is captured. This micro scale architecture, which contains free Si material as well as the SiC ceramic, is responsible for residual stresses that play an important role in the subsequent thermo-mechanical behavior of the SiC/SiC composite. Using the novel Multiscale Generalized Method of Cells recursive micromechanics theory, the microstructure of the matrix, as well as the microstructure of the composite (fiber and matrix) can be captured.
Risk matrix model for rotating equipment
Directory of Open Access Journals (Sweden)
Wassan Rano Khan
2014-07-01
Full Text Available Different industries have various residual risk levels for their rotating equipment. Accordingly the occurrence rate of the failures and associated failure consequences categories are different. Thus, a generalized risk matrix model is developed in this study which can fit various available risk matrix standards. This generalized risk matrix will be helpful to develop new risk matrix, to fit the required risk assessment scenario for rotating equipment. Power generation system was taken as case study. It was observed that eight subsystems were under risk. Only vibration monitor system was under high risk category, while remaining seven subsystems were under serious and medium risk categories.
Makowitz, Dr Henry
2009-01-01
Arguments are presented based on particle phenomenology and the requirement for Unitarity for a complex valued postulated four generation CKM Matrix (VCKM ) based on a Sequential Fourth Generation Model (sometimes named SM4). A modified four generation QCD Standard Model Lagrangian is utilized per SM4. A four generation neutrino mass mixing MNS Matrix, (VMNS) is estimated utilizing a Unitary (to Order (Lambda**k), k = 1, 2, 3, 4, etc) 4 x 4 Bimaximal Matrix, VBIMAX. The Unitary VBIMAX is based on a weighted 3 x 3 VBIMAX scheme and is studied in conjunction with the postulated four generation VCKM complex Unitary Matrix. A single parameter has been utilized in our analysis along with three complex DELTA(i,j) phases. A four generation Wolfenstein Parameterization of VCKM is deduced which is valid for order Lambda**3. Experimental implications of the model are discussed. The issues of Baryogenesis in the context of Leptogenesis associated with MNS Matrix neutrino mixing and Baryogenesis associated with CKM Matri...
Partial chord diagrams and matrix models
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Fuji, Hiroyuki; Manabe, Masahide
spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations......In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length...... – obtained independently by cut-and-join arguments in an earlier work – for the corresponding generating functions....
Slevin, Keith; Ohtsuki, Tomi
2016-10-01
Disordered non-interacting systems are classified into ten symmetry classes, with the unitary class being the most fundamental. The three and four-dimensional unitary universality classes are attracting renewed interest because of their relation to three-dimensional Weyl semi-metals and four-dimensional topological insulators. Determining the critical exponent of the correlation/localisation length for the Anderson transition in these classes is important both theoretically and experimentally. Using the transfer matrix technique, we report numerical estimations of the critical exponent in a U(1) model in three and four dimensions.
Energy Technology Data Exchange (ETDEWEB)
Ginsparg, P.
1991-01-01
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Energy Technology Data Exchange (ETDEWEB)
Ginsparg, P.
1991-12-31
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date.
Matrix Models, Monopoles and Modified Moduli
Erlich, J; Unsal, M; Erlich, Joshua; Hong, Sungho; Unsal, Mithat
2004-01-01
Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model duals of N=1 supersymmetric SU(Nc) gauge theories with Nf flavors. We demonstrate via the matrix model solutions a relation between vacua of theories with different numbers of colors and flavors. This relation is due to an N=2 nonrenormalization theorem which is inherited by these N=1 theories. Specializing to the case Nf=Nc, the simplest theory containing baryons, we demonstrate that the explicit matrix model predictions for the locations on the Coulomb branch at which monopoles condense are consistent with the quantum modified constraints on the moduli in the theory. The matrix model solutions include the case that baryons obtain vacuum expectation values. In specific cases we check explicitly that these results are also consistent with the factorization of corresponding Seiberg-Witten curves. Certain results are easily understood in terms of M5-brane constructions of these gauge theories.
Matrix Models, Monopoles and Modified Moduli
Erlich, Joshua; Hong, Sungho; Unsal, Mithat
2004-09-01
Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model duals of Script N = 1 supersymmetric SU(Nc) gauge theories with Nf flavors. We demonstrate via the matrix model solutions a relation between vacua of theories with different numbers of colors and flavors. This relation is due to an Script N = 2 nonrenormalization theorem which is inherited by these Script N = 1 theories. Specializing to the case Nf = Nc, the simplest theory containing baryons, we demonstrate that the explicit matrix model predictions for the locations on the Coulomb branch at which monopoles condense are consistent with the quantum modified constraints on the moduli in the theory. The matrix model solutions include the case that baryons obtain vacuum expectation values. In specific cases we check explicitly that these results are also consistent with the factorization of corresponding Seiberg-Witten curves. Certain results are easily understood in terms of M5-brane constructions of these gauge theories.
Modeling and Simulation of Matrix Converter
DEFF Research Database (Denmark)
Liu, Fu-rong; Klumpner, Christian; Blaabjerg, Frede
2005-01-01
This paper discusses the modeling and simulation of matrix converter. Two models of matrix converter are presented: one is based on indirect space vector modulation and the other is based on power balance equation. The basis of these two models is• given and the process on modeling is introduced...... in details. The results of simulations developed for different researches reveal that different mdel may be suitable for different purpose, thus the model should be chosen different carefully. Some details and tricks in modeling are also introduced which give a reference for further research....
A matrix model from string field theory
Directory of Open Access Journals (Sweden)
Syoji Zeze
2016-09-01
Full Text Available We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large $N$ matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
A matrix model from string field theory
Zeze, Syoji
2016-09-01
We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N) vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large N matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
Transition from Poisson to circular unitary ensemble
Indian Academy of Sciences (India)
Vinayak; Akhilesh Pandey
2009-09-01
Transitions to universality classes of random matrix ensembles have been useful in the study of weakly-broken symmetries in quantum chaotic systems. Transitions involving Poisson as the initial ensemble have been particularly interesting. The exact two-point correlation function was derived by one of the present authors for the Poisson to circular unitary ensemble (CUE) transition with uniform initial density. This is given in terms of a rescaled symmetry breaking parameter Λ. The same result was obtained for Poisson to Gaussian unitary ensemble (GUE) transition by Kunz and Shapiro, using the contour-integral method of Brezin and Hikami. We show that their method is applicable to Poisson to CUE transition with arbitrary initial density. Their method is also applicable to the more general ℓ CUE to CUE transition where CUE refers to the superposition of ℓ independent CUE spectra in arbitrary ratio.
Multivariate Modelling via Matrix Subordination
DEFF Research Database (Denmark)
Nicolato, Elisa
Extending the vast library of univariate models to price multi-asset derivatives is still a challenge in the field of Quantitative Finance. Within the literature on multivariate modelling, a dichotomy may be noticed. On one hand, the focus has been on the construction of models displaying...... stochastic correlation within the framework of discussion processes (see e.g. Pigorsh and Stelzer (2008), Hubalek and Nicolato (2008) and Zhu (2000)). On the other hand a number of authors have proposed multivariate Levy models, which allow for flexible modelling of returns, but at the expenses of a constant...... correlation structure (see e.g. Leoni and Schoutens (2007) and Leoni and Schoutens (2007) among others). Tractable multivariate models displaying flexible and stochastic correlation structures combined with jumps is proving to be rather problematic. In particular, the classical technique of introducing...
Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons
Moriyama, Sanefumi
2016-01-01
We study the partition function of the orientifold ABJM theory, which is a superconformal Chern-Simons theory associated with the orthosymplectic supergroup. We find that the partition function associated with any orthosymplectic supergroup can be realized as that of a Fermi gas system whose density matrix is identical to that associated with the corresponding unitary supergroup with a projection to the even or odd chirality. Furthermore we propose an identity and use it to identify all of the Gopakumar-Vafa invariants for the worldsheet instanton effects systematically.
Random matrix model approach to chiral symmetry
Verbaarschot, J J M
1996-01-01
We review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for universal properties of the Dirac spectrum: i) finite volume corrections to valence quark mass dependence of the chiral condensate, and ii) microscopic fluctuations of Dirac spectra. Comparisons with lattice QCD simulations are made. Most notably, the variance of the number of levels in an interval containing $n$ levels on average is suppressed by a factor $(\\log n)/\\pi^2 n$. An extension of the random matrix model model to nonzero temperatures and chemical potential provides us with a schematic model of the chiral phase transition. In particular, this elucidates the nature of the quenched approximation at nonzero chemical potential.
Miyagi, Takayuki; Okamoto, Ryoji; Otsuka, Takaharu
2015-01-01
We study the nuclear ground-state properties by using the unitary-model-operator approach (UMOA). Recently, the particle-basis formalism has been introduced in the UMOA and enables us to employ the charge-dependent nucleon-nucleon interaction. We evaluate the ground-state energies and charge radii of $^{4}$He, $^{16}$O, $^{40}$Ca, and $^{56}$Ni with the charge-dependent Bonn potential. The ground-state energy is dominated by the contributions from the one- and two-body cluster terms, while, for the radius, the one-particle-one-hole excitations are more important than the two-particle-two-hole excitations. The calculated results reproduce the trend of experimental data of the saturation property for finite nuclei.
Energy Technology Data Exchange (ETDEWEB)
Asano, Yuhma; Kawai, Daisuke; Yoshida, Kentaroh [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan)
2015-06-29
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Matrix Tricks for Linear Statistical Models
Puntanen, Simo; Styan, George PH
2011-01-01
In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and
Asano, Yuhma; Kawai, Daisuke; Yoshida, Kentaroh
2015-06-01
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Asano, Yuhma; Yoshida, Kentaroh
2015-01-01
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ans\\"atze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincar\\'e sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Supersymmetric Matrix model on Z-orbifold
Miyake, A
2003-01-01
We find that the IIA Matrix models defined on the non-compact $C^3/Z_6$, $C^2/Z_2$ and $C^2/Z_4$ orbifolds preserve supersymmetry where the fermions are on-mass-shell Majorana-Weyl fermions. In these examples supersymmetry is preserved both in the orbifolded space and in the non-orbifolded space at the same time. The Matrix model on $C^3/Z_6$ orbifold has the same ${\\cal N}=2$ supersymmetry as the case of $C^3/Z_3$ orbifold, whose particular case was previously pointed out. On the other hand the Matrix models on $C^2/Z_2$ and $C^2/Z_4$ orbifold have a half of the ${\\cal N}=2$ supersymmetry. We further find that the Matrix model on $C^2/Z_2$ orbifold with parity-like identification preserves ${\\cal N}=2$ supersymmetry both in the orbifolded space and non-orbifolded space, and furthermore has ${\\cal N}=4$ supersymmetry parameters in the total space.
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...
Bloch-Messiah reduction of Gaussian unitaries by Takagi factorization
Cariolaro, Gianfranco; Pierobon, Gianfranco
2016-12-01
The Bloch-Messiah (BM) reduction allows the decomposition of an arbitrarily complicated Gaussian unitary into a very simple scheme in which linear optical components are separated from nonlinear ones. The nonlinear part is due to the squeezing possibly present in the Gaussian unitary. The reduction is usually obtained by exploiting the singular value decomposition (SVD) of the matrices appearing in the Bogoliubov transformation of the given Gaussian unitary. This paper discusses a different approach, where the BM reduction is obtained in a straightforward way. It is based on the Takagi factorization of the (complex and symmetric) squeeze matrix and has the advantage of avoiding several matrix operations of the previous approach (polar decomposition, eigendecomposition, SVD, and Takagi factorization). The theory is illustrated with an application example in which the previous and present approaches are compared.
Defect of a Kronecker product of unitary matrices
Tadej, Wojciech
2010-01-01
The defect d(U) of an NxN unitary matrix U with no zero entries is the dimension (called the generalized defect D(U)) of the real space of directions, moving into which from U we do not disturb the moduli |U_ij| as well as the Gram matrix U'*U in the first order, diminished by 2N-1. Calculation of d(U) involves calculating the dimension of the space in R^(N^2) spanned by a certain set of vectors associated with U. We split this space into a direct sum, assuming that U is a Kronecker product of unitary matrices, thus making it easier to perform calculations numerically. Basing on this, we give a lower bound on D(U) (equivalently d(U)), supposing it is achieved for most unitaries with a fixed Kronecker product structure. Also supermultiplicativity of D(U) with respect to Kronecker subproducts of U is shown.
Generalized multicritical one-matrix models
Ambjorn, J; Makeenko, Y
2016-01-01
We show that there exists a simple generalization of Kazakov's multicritical one-matrix model, which interpolates between the various multicritical points of the model. The associated multicritical potential takes the form of a power series with a heavy tail, leading to a cut of the potential and its derivative at the real axis, and reduces to a polynomial at Kazakov's multicritical points. From the combinatorial point of view the generalized model allows polygons of arbitrary large degrees (or vertices of arbitrary large degree, when considering the dual graphs), and it is the weight assigned to these large order polygons which brings about the interpolation between the multicritical points in the one-matrix model.
Generalized multicritical one-matrix models
Ambjørn, J.; Budd, T.; Makeenko, Y.
2016-12-01
We show that there exists a simple generalization of Kazakov's multicritical one-matrix model, which interpolates between the various multicritical points of the model. The associated multicritical potential takes the form of a power series with a heavy tail, leading to a cut of the potential and its derivative at the real axis, and reduces to a polynomial at Kazakov's multicritical points. From the combinatorial point of view the generalized model allows polygons of arbitrary large degrees (or vertices of arbitrary large degree, when considering the dual graphs), and it is the weight assigned to these large order polygons which brings about the interpolation between the multicritical points in the one-matrix model.
Deformations of polyhedra and polygons by the unitary group
Livine, Etera R.
2013-12-01
We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient {{C}}^{2N}//SU(2). A framed polyhedron is then parametrized by N spinors living in {{C}}2 satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N-2)). We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in a
Notes on Mayer expansions and matrix models
Energy Technology Data Exchange (ETDEWEB)
Bourgine, Jean-Emile, E-mail: jebourgine@apctp.org
2014-03-15
Mayer cluster expansion is an important tool in statistical physics to evaluate grand canonical partition functions. It has recently been applied to the Nekrasov instanton partition function of N=2 4d gauge theories. The associated canonical model involves coupled integrations that take the form of a generalized matrix model. It can be studied with the standard techniques of matrix models, in particular collective field theory and loop equations. In the first part of these notes, we explain how the results of collective field theory can be derived from the cluster expansion. The equalities between free energies at first orders is explained by the discrete Laplace transform relating canonical and grand canonical models. In a second part, we study the canonical loop equations and associate them with similar relations on the grand canonical side. It leads to relate the multi-point densities, fundamental objects of the matrix model, to the generating functions of multi-rooted clusters. Finally, a method is proposed to derive loop equations directly on the grand canonical model.
Tensor Models: extending the matrix models structures and methods
Dartois, Stephane
2016-01-01
In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor models. Despite the generic title of this review, we, in particular, invoke the Topological Recursion. We explain its appearance in matrix models. Then we state that a family of tensor models provides a natural example which satisfies a version of the most general form of the topological recursion, named the blobbed topological recursion. We discuss the difficulties of extending the technical solutions existing for matrix models to tensor models. Some proofs are not published yet but will be given in a coming paper, the rest of the results are well known in the literature.
Unitary Transformation in Quantum Teleportation
Institute of Scientific and Technical Information of China (English)
WANG Zheng-Chuan
2006-01-01
In the well-known treatment of quantum teleportation, the receiver should convert the state of his EPR particle into the replica of the unknown quantum state by one of four possible unitary transformations. However, the importance of these unitary transformations must be emphasized. We will show in this paper that the receiver cannot transform the state of his particle into an exact replica of the unknown state which the sender wants to transfer if he has not a proper implementation of these unitary transformations. In the procedure of converting state, the inevitable coupling between EPR particle and environment which is needed by the implementation of unitary transformations will reduce the accuracy of the replica.
Bradley, P. F.; Siemers, P. M., III; Flanagan, P. F.; Henry, M. W.
1983-01-01
Pressure distribution tests on a 0.04-scale model of the forward fuselage of the Space Shuttle Orbiter are presented without analysis. The tests were completed in the Langley Unitary Plan Wind Tunnel (UPWT). The UPWT has two different test sections operating in the continuous mode. Each test section has its own Mach number range. The model was tested at angles of attack from -2.5 deg to 30 deg and angles of sideslip from -5 deg to 5 deg in both test sections. The test Reynolds number was 6.6 x 10 to the 6th power per meter. The tests were conducted in support of the development of the Shuttle Entry Air Data System (SEADS). In addition to modeling the 20 SEADS pressure orifices, the wind-tunnel model was also instrumented with orifices to match Development Flight Instrumentation (DFI) port locations currently existing on the Space Shuttle Orbiter Columbia (OV-102). This DFI simulation has provided a means for comparisons between reentry flight pressure data and wind-tunnel data.
All maximally entangling unitary operators
Energy Technology Data Exchange (ETDEWEB)
Cohen, Scott M. [Department of Physics, Duquesne University, Pittsburgh, Pennsylvania 15282 (United States); Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 (United States)
2011-11-15
We characterize all maximally entangling bipartite unitary operators, acting on systems A and B of arbitrary finite dimensions d{sub A}{<=}d{sub B}, when ancillary systems are available to both parties. Several useful and interesting consequences of this characterization are discussed, including an understanding of why the entangling and disentangling capacities of a given (maximally entangling) unitary can differ and a proof that these capacities must be equal when d{sub A}=d{sub B}.
Matrix model calculations beyond the spherical limit
Energy Technology Data Exchange (ETDEWEB)
Ambjoern, J. (Niels Bohr Institute, Copenhagen (Denmark)); Chekhov, L. (L.P.T.H.E., Universite Pierre et Marie Curie, 75 - Paris (France)); Kristjansen, C.F. (Niels Bohr Institute, Copenhagen (Denmark)); Makeenko, Yu. (Institute of Theoretical and Experimental Physics, Moscow (Russian Federation))
1993-08-30
We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We develop a version which gives directly the result in the double scaling limit and present explicit results up to genus four. Using the latter version we prove that the hermitian and the complex matrix model are equivalent in the double scaling limit and that in this limit they are both equivalent to the Kontsevich model. We discuss how our results away from the double scaling limit are related to the structure of moduli space. (orig.)
Siemers, P. M., III; Henry, M. W.
1986-01-01
Pressure distribution test data obtained on a 0.10-scale model of the forward fuselage of the Space Shuttle Orbiter are presented without analysis. The tests were completed in the Ames Unitary Wind Tunnel (UPWT). The UPWT tests were conducted in two different test sections operating in the continuous mode, the 8 x 7 feet and 9 x 7 feet test sections. Each test section has its own Mach number range, 1.6 to 2.5 and 2.5 to 3.5 for the 9 x 7 feet and 8 x 7 feet test section, respectively. The test Reynolds number ranged from 1.6 to 2.5 x 10 to the 6th power ft and 0.6 to 2.0 x 10 to the 6th power ft, respectively. The tests were conducted in support of the development of the Shuttle Entry Air Data System (SEADS). In addition to modeling the 20 SEADS orifices, the wind-tunnel model was also instrumented with orifices to match Development Flight Instrumentation (DFI) port locations that existed on the Space Shuttle Columbia (OV-102) during the Orbiter Flight test program. This DFI simulation has provided a means for comparisons between reentry flight pressure data and wind-tunnel and computational data.
Two-Matrix model with ABAB interaction
Kazakov, V A
1999-01-01
Using recently developed methods of character expansions we solve exactly in the large N limit a new two-matrix model of hermitean matrices A and B with the action S={1øver 2}(\\tr A^2+\\tr B^2)-{\\alphaøver 4}(\\tr A^4+\\tr B^4)-{\\betaøver 2} \\tr(AB)^2. This model can be mapped onto a special case of the 8-vertex model on dynamical planar graphs. The solution is parametrized in terms of elliptic functions. A phase transition is found: the critical point is a conformal field theory with central charge c=1 coupled to 2D quantum gravity.
A Matrix Model for Type 0 Strings
Peñalba, J P
1999-01-01
A matrix model for type 0 strings is proposed. It consists in making a non-supersymmetric orbifold projection in the Yang-Mills theory and identifying the infrared configurations of the system at infinite coupling with strings. The correct partition function is calculated. Also, the usual spectrum of branes is found. Both type A and B models are constructed. The model in a torus contains all the degrees of freedom and interpolates between the four string theories (IIA, IIB, 0A, 0B) and the M theory as different limits are taken.
Perturbation analysis of nonlinear matrix population models
Directory of Open Access Journals (Sweden)
Hal Caswell
2008-03-01
Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.
Complete Pick Positivity and Unitary Invariance
Bhattacharya, Angshuman
2009-01-01
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 - z\\ow)^{-1}$ for $|z|, |w| < 1$, by means of $(1/k_S)(T,T^*) \\ge 0$, we consider an arbitrary open connected domain $\\Omega$ in $\\BC^n$, a complete Nevanilinna-Pick kernel $k$ on $\\Omega$ and a tuple $T = (T_1, ..., T_n)$ of commuting bounded operators on a complex separable Hilbert space $\\clh$ such that $(1/k)(T,T^*) \\ge 0$. For a complete Pick kernel the $1/k$ functional calculus makes sense in a beautiful way. It turns out that the model theory works very well and a characteristic function can be associated with $T$. Moreover, the characteristic function then is a complete unitary invariant for a suitable class of tuples $T$.
Quantum Mutual Information Along Unitary Orbits
Jevtic, Sania; Rudolph, Terry
2011-01-01
Motivated by thermodynamic considerations, we analyse the variation of the quantum mutual information on a unitary orbit of a bipartite system state, with and without global constraints such as energy conservation. We solve the full optimisation problem for the smallest system of two qubits, and explore thoroughly the effect of unitary operations on the space of reduced-state spectra. We then provide applications of these ideas to physical processes within closed quantum systems, such as a generalized collision model approach to thermal equilibrium and a global Maxwell demon playing tricks on local observers. For higher dimensions, the maximization of correlations is relatively straightforward, however the minimisation of correlations displays non-trivial structures. We characterise a set of separable states in which the minimally correlated state resides, and find a collection of classically correlated states admitting a particular "Young tableau" form. Furthermore, a partial order exists on this set with re...
Pattern, participation, praxis, and power in unitary appreciative inquiry.
Cowling, W Richard
2004-01-01
This article is an explication and clarification of unitary appreciative inquiry based on several recent projects. Four central dimensions of the inquiry process are presented: pattern, participation, praxis, and power. Examples of inquiry projects demonstrate and illuminate the possibilities of unitary appreciative inquiry. The relationship of these central dimensions to experiential, presentational, propositional, and practical knowledge outcomes is articulated. A matrix framework integrating pattern, participation, praxis, and power demonstrates the potential for generating knowledge relevant to the lives of participants and creating an inquiry process worthy of human aspiration.
Mirror of the refined topological vertex from a matrix model
Eynard, B
2011-01-01
We find an explicit matrix model computing the refined topological vertex, starting from its representation in terms of plane partitions. We then find the spectral curve of that matrix model, and thus the mirror symmetry of the refined vertex. With the same method we also find a matrix model for the strip geometry, and we find its mirror curve. The fact that there is a matrix model shows that the refined topological string amplitudes also satisfy the remodeling the B-model construction.
Characteristic Polynomials of Complex Random Matrix Models
Akemann, G
2003-01-01
We calculate the expectation value of an arbitrary product of characteristic polynomials of complex random matrices and their hermitian conjugates. Using the technique of orthogonal polynomials in the complex plane our result can be written in terms of a determinant containing these polynomials and their kernel. It generalizes the known expression for hermitian matrices and it also provides a generalization of the Christoffel formula to the complex plane. The derivation we present holds for complex matrix models with a general weight function at finite-N, where N is the size of the matrix. We give some explicit examples at finite-N for specific weight functions. The characteristic polynomials in the large-N limit at weak and strong non-hermiticity follow easily and they are universal in the weak limit. We also comment on the issue of the BMN large-N limit.
ROTATION CONSTELLATION FOR DIFFERENTIAL UNITARY SPACE-TIME MODULATION
Institute of Scientific and Technical Information of China (English)
Li Jun; Cao Haiyan; Wei Gang
2006-01-01
A new constellation which is the multiplication of the rotation matrix and the diagonal matrix according to the number of transmitters is proposed to increase the diversity product, the key property to the performance of the differential unitary space-time modulation. Analyses and the simulation results show that the proposed constellation performs better and 2dB or more coding gain can be achieved over the traditional cyclic constellation.
Black holes as random particles: entanglement dynamics in infinite range and matrix models
Energy Technology Data Exchange (ETDEWEB)
Magán, Javier M. [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena,Utrecht University, Princetonplein 5, Utrecht, 3508 TD The (Netherlands)
2016-08-11
We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large-N matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large-N matrix models, where we provide a gauge invariant entanglement entropy for ‘generalized free fields’, again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.
Black holes as random particles: entanglement dynamics in infinite range and matrix models
Magán, Javier M.
2016-08-01
We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large- {N} matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large- {N} matrix models, where we provide a gauge invariant entanglement entropy for `generalized free fields', again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.
A matrix model for the topological string I: Deriving the matrix model
Eynard, Bertrand; Marchal, Olivier
2010-01-01
We construct a matrix model that reproduces the topological string partition function on arbitrary toric Calabi-Yau 3-folds. This demonstrates, in accord with the BKMP "remodeling the B-model" conjecture, that Gromov-Witten invariants of any toric Calabi-Yau 3-fold can be computed in terms of the spectral invariants of a spectral curve. Moreover, it proves that the generating function of Gromov-Witten invariants is a tau-function for an integrable hierarchy. In a follow-up paper, we will explicitly construct the spectral curve of our matrix model and argue that it equals the mirror curve of the toric Calabi-Yau manifold.
Spectral density of the correlation matrix of factor models: a random matrix theory approach.
Lillo, F; Mantegna, R N
2005-07-01
We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.
Corlett, W. A.
1979-01-01
A metric half-span model is considered as a means of mechanical support for a wind-tunnel model which allows measurement of aerodynamic forces and moments without support interference or model distortion. This technique can be applied to interference-free propulsion models. The vapor screen method of flow visualization at supersonic Mach numbers is discussed. The use of smoke instead of water vapor as a medium to produce the screen is outlined. Vapor screen data are being used in the development of analytical vortex tracking programs. Test results for a remote control model system are evaluated. Detailed control effectiveness and cross-coupling data were obtained with a single run. For the afterbody tail configuration, tested control boundaries at several roll orientations were established utilizing the facility's on-line capability to 'fly' the model in the wind tunnel.
Can a non-unitary effect be prominent In neutrino oscillation measurements?
Institute of Scientific and Technical Information of China (English)
L(U) Lei; WANG Wen-Yu; XIONG zhao-Hua
2010-01-01
Subject to neutrino experiments, the mixing matrix of ordinary neutrinos can still have small vi-olation from unitarity. We introduce a quasi-unitary matrix to interpret this violation and propose a natural scheme to parameterize it. A quasi-unitary factor △QF is defined to be measured in neutrino oscillation exper-iments and the numerical results show that the improvement in experimental precision may help us figure out the secret of neutrino mixing.
Matrix-model dualities in the collective field formulation
Andric, I
2005-01-01
We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field formulation, the duality is displayed in terms of the generators of the conformal group. The conformally invariant master Hamiltonian is constructed and we conjecture that the master Hamiltonian corresponds to the hermitian matrix model.
Unitary pattern: a review of theoretical literature.
Musker, Kathleen M
2012-07-01
It is the purpose of this article to illuminate the phenomenon of unitary pattern through a review of theoretical literature. Unitary pattern is a phenomenon of significance to the discipline of nursing because it is manifested in and informs all person-environment health experiences. Unitary pattern was illuminated by: addressing the barriers to understanding the phenomenon, presenting a definition of unitary pattern, and exploring Eastern and Western theoretical literature which address unitary pattern in a way that is congruent with the definition presented. This illumination of unitary pattern will expand nursing knowledge and contribute to the discipline of nursing.
Despair: a unitary appreciative inquiry.
Cowling, W Richard
2004-01-01
A unitary appreciative case study method was used to explicate unitary understandings of despair embedded in the unique personal life contexts of the participants. Fourteen women engaged in dialogical, appreciative interviews that led to the creation of profiles of the life pattern or course associated with despair for each woman. Three exemplar cases are detailed including the profiles that incorporate story, metaphor, music, and imagery. The voices of the women provide morphogenic knowledge of the contexts, nature, consequences, and contributions of despair as well as practical guidance for healthcare providers.
Spectral properties in supersymmetric matrix models
Energy Technology Data Exchange (ETDEWEB)
Boulton, Lyonell, E-mail: L.Boulton@hw.ac.uk [Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Garcia del Moral, Maria Pilar, E-mail: garciamormaria@uniovi.es [Departamento de Fisica, Universidad de Oviedo, Avda Calvo Sotelo 18, 33007 Oviedo (Spain); Restuccia, Alvaro, E-mail: arestu@usb.ve [Departamento de Fisica, Universidad Simon Bolivar, Apartado 89000, Caracas (Venezuela, Bolivarian Republic of); Departamento de Fisica, Universidad de Oviedo, Avda Calvo Sotelo 18, 33007 Oviedo (Spain)
2012-03-21
We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.
Classical states and decoherence by unitary evolution in the thermodynamic limit
Frasca, M
2002-01-01
It is shown how classical states, meant as states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics. Besides, using a simple model of a single spin interacting with a spin-bath, it is seen how decoherence, with the off-diagonal terms in the density matrix going to zero, can be obtained when the number of the spins in the bath is taken to go formally to infinity. In this case, indeed, the system appears to flop at a frequency being formally infinity that, from a physical standpoint, can be proved equivalent to a time average.
String coupling and interactions in type IIB matrix model
Kitazawa, Yoshihisa
2008-01-01
We investigate the interactions of closed strings in IIB matrix model. The basic interaction of the closed superstring is realized by the recombination of two intersecting strings. Such interaction is investigated in IIB matrix model via two dimensional noncommutative gauge theory in the IR limit. By estimating the probability of the recombination, we identify the string coupling g_s in IIB matrix model. We confirm that our identification is consistent with matrix string theory.
Project-matrix models of marketing organization
Directory of Open Access Journals (Sweden)
Gutić Dragutin
2009-01-01
Full Text Available Unlike theory and practice of corporation organization, in marketing organization numerous forms and contents at its disposal are not reached until this day. It can be well estimated that marketing organization today in most of our companies and in almost all its parts, noticeably gets behind corporation organization. Marketing managers have always been occupied by basic, narrow marketing activities as: sales growth, market analysis, market growth and market share, marketing research, introduction of new products, modification of products, promotion, distribution etc. They rarely found it necessary to focus a bit more to different aspects of marketing management, for example: marketing planning and marketing control, marketing organization and leading. This paper deals with aspects of project - matrix marketing organization management. Two-dimensional and more-dimensional models are presented. Among two-dimensional, these models are analyzed: Market management/products management model; Products management/management of product lifecycle phases on market model; Customers management/marketing functions management model; Demand management/marketing functions management model; Market positions management/marketing functions management model. .
Teleportation of M-Qubit Unitary Operations
Institute of Scientific and Technical Information of China (English)
郑亦庄; 顾永建; 郭光灿
2002-01-01
We discuss teleportation of unitary operations on a two-qubit in detail, then generalize the bidirectional state teleportation scheme from one-qubit to M-qubit unitary operations. The resources required for the optimal implementation of teleportation of an M-qubit unitary operation using a bidirectional state teleportation scheme are given.
Correlators of Matrix Models on Homogeneous Spaces
Kitazawa, Y; Tomino, D; Kitazawa, Yoshihisa; Takayama, Yastoshi; Tomino, Dan
2004-01-01
We investigate the correlators of TrA_{mu}A_{nu} in matrix models on homogeneous spaces: S^2 and S^2 x S^2. Their expectation value is a good order parameter to measure the geometry of the space on which non-commutative gauge theory is realized. They also serve as the Wilson lines which carry the minimum momentum. We develop an efficient procedure to calculate them through 1PI diagrams. We determine the large N scaling behavior of the correlators. The order parameter shows that fuzzy S^2 x S^2 acquires a 4 dimensional fractal structure in contrast to fuzzy S^2. We also find that the two point functions exhibit logarithmic scaling violations.
Matrix model and dimensions at hypercube vertices
Morozov, A; Popolitov, A
2015-01-01
In hypercube approach to correlation functions in Chern-Simons theory (knot polynomials) the central role is played by the numbers of cycles, in which the link diagram is decomposed under different resolutions. Certain functions of these numbers are further interpreted as dimensions of graded spaces, associated with hypercube vertices. Finding these functions is, however, a somewhat non-trivial problem. In arXiv:1506.07516 it was suggested to solve it with the help of the matrix model technique, in the spirit of AMM/EO topological recursion. In this paper we further elaborate on this idea and provide a vast collection of non-trivial examples, related both to ordinary and virtual links and knots. Remarkably, most powerful versions of the formalism freely convert ordinary knots/links to virtual and back -- moreover, go beyond the knot-related set of the (2,2)-valent graphs.
An ancilla-based quantum simulation framework for non-unitary matrices
Daskin, Ammar; Kais, Sabre
2017-01-01
The success probability in an ancilla-based circuit generally decreases exponentially in the number of qubits consisted in the ancilla. Although the probability can be amplified through the amplitude amplification process, the input dependence of the amplitude amplification makes difficult to sequentially combine two or more ancilla-based circuits. A new version of the amplitude amplification known as the oblivious amplitude amplification runs independently of the input to the system register. This allows us to sequentially combine two or more ancilla-based circuits. However, this type of the amplification only works when the considered system is unitary or non-unitary but somehow close to a unitary. In this paper, we present a general framework to simulate non-unitary processes on ancilla-based quantum circuits in which the success probability is maximized by using the oblivious amplitude amplification. In particular, we show how to extend a non-unitary matrix to an almost unitary matrix. We then employ the extended matrix by using an ancilla-based circuit design along with the oblivious amplitude amplification. Measuring the distance of the produced matrix to the closest unitary matrix, a lower bound for the fidelity of the final state obtained from the oblivious amplitude amplification process is presented. Numerical simulations for random matrices of different sizes show that independent of the system size, the final amplified probabilities are generally around 0.75 and the fidelity of the final state is mostly high and around 0.95. Furthermore, we discuss the complexity analysis and show that combining two such ancilla-based circuits, a matrix product can be implemented. This may lead us to efficiently implement matrix functions represented as infinite matrix products on quantum computers.
Unitary equivalence of quantum walks
Energy Technology Data Exchange (ETDEWEB)
Goyal, Sandeep K., E-mail: sandeep.goyal@ucalgary.ca [School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, 4000 Durban (South Africa); Konrad, Thomas [School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, 4000 Durban (South Africa); National Institute for Theoretical Physics (NITheP), KwaZulu-Natal (South Africa); Diósi, Lajos [Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, H-1525 Budapest 114, P.O.B. 49 (Hungary)
2015-01-23
Highlights: • We have found unitary equivalent classes in coined quantum walks. • A single parameter family of coin operators is sufficient to realize all simple one-dimensional quantum walks. • Electric quantum walks are unitarily equivalent to time dependent quantum walks. - Abstract: A simple coined quantum walk in one dimension can be characterized by a SU(2) operator with three parameters which represents the coin toss. However, different such coin toss operators lead to equivalent dynamics of the quantum walker. In this manuscript we present the unitary equivalence classes of quantum walks and show that all the nonequivalent quantum walks can be distinguished by a single parameter. Moreover, we argue that the electric quantum walks are equivalent to quantum walks with time dependent coin toss operator.
Elements of matrix modeling and computing with Matlab
White, Robert E
2006-01-01
As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables. Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applicat
Matrix diffusion model. In situ tests using natural analogues
Energy Technology Data Exchange (ETDEWEB)
Rasilainen, K. [VTT Energy, Espoo (Finland)
1997-11-01
Matrix diffusion is an important retarding and dispersing mechanism for substances carried by groundwater in fractured bedrock. Natural analogues provide, unlike laboratory or field experiments, a possibility to test the model of matrix diffusion in situ over long periods of time. This thesis documents quantitative model tests against in situ observations, done to support modelling of matrix diffusion in performance assessments of nuclear waste repositories. 98 refs. The thesis includes also eight previous publications by author.
Kondratyuk, S
2000-01-01
Pion-loop corrections for Compton scattering are calculated in a novel approach based on the use of dispersion relations in a formalism obeying unitarity. The basic framework is presented, including an application to Compton scattering. In the approach the effects of the non-pole contribution arising from pion dressing are expressed in terms of (half-off-shell) form factors and the nucleon self-energy. These quantities are constructed through the application of dispersion integrals to the pole contribution of loop diagrams, the same as those included in the calculation of the amplitudes through a K-matrix formalism. The prescription of minimal substitution is used to restore gauge invariance. The resulting relativistic-covariant model combines constraints from unitarity, causality, and crossing symmetry.
On exact superpotentials, free energies and matrix models
Energy Technology Data Exchange (ETDEWEB)
Hailu, Girma; Georgi, Howard [Jefferson Laboratory of Physics, Harvard University, Cambridge, MA (United States)]. E-mail addresses: hailu@feynman.harvard.edu; georgi@physics.harvard.edu
2004-02-01
We discuss exact results for the full nonperturbative effective superpotentials of four dimensional N=1 supersymmetric U(N) gauge theories with additional chiral superfield in the adjoint representation and the free energies of the related zero dimensional bosonic matrix models with polynomial potentials in the planar limit using the Dijkgraaf-Vafa matrix model prescription and integrating in and out. The exact effective superpotentials are produced including the leading Veneziano-Yankielowicz term directly from the matrix models. We also discuss how to use integrating in and out as a tool to do random matrix integrals in the large-N limit. (author)
Amending entanglement-breaking channels via intermediate unitary operations
Cuevas, Á.; De Pasquale, A.; Mari, A.; Orieux, A.; Duranti, S.; Massaro, M.; Di Carli, A.; Roccia, E.; Ferraz, J.; Sciarrino, F.; Mataloni, P.; Giovannetti, V.
2017-08-01
We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase-damping or rotated amplitude-damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve entanglement transmission. This proof-of-principle demonstration could be generalized to many other physical scenarios where entanglement-breaking communication lines may be amended by unitary filters.
Non-unitary fusion categories and their doubles via endomorphisms
Evans, David E
2015-01-01
We realise non-unitary fusion categories using subfactor-like methods, and compute their quantum doubles and modular data. For concreteness we focus on generalising the Haagerup-Izumi family of Q-systems. For example, we construct endomorphism realisations of the (non-unitary) Yang-Lee model, and non-unitary analogues of one of the even subsystems of the Haagerup subfactor and of the Grossman-Snyder system. We supplement Izumi's equations for identifying the half-braidings, which were incomplete even in his Q-system setting. We conjecture a remarkably simple form for the modular S and T matrices of the doubles of these fusion categories. We would expect all of these doubles to be realised as the category of modules of a rational VOA and conformal net of factors. We expect our approach will also suffice to realise the non-semisimple tensor categories arising in logarithmic conformal field theories.
Right-unitary transformation theory and applications
Tang, Z
1996-01-01
We develop a new transformation theory in quantum physics, where the transformation operators, defined in the infinite dimensional Hilbert space, have right-unitary inverses only. Through several theorems, we discuss the properties of state space of such operators. As one application of the right-unitary transformation (RUT), we show that using the RUT method, we can solve exactly various interactions of many-level atoms with quantized radiation fields, where the energy of atoms can be two levels, three levels in Lambda, V and equiv configurations, and up to higher (>3) levels. These interactions have wide applications in atomic physics, quantum optics and quantum electronics. In this paper, we focus on two typical systems: one is a two-level generalized Jaynes-Cummings model, where the cavity field varies with the external source; the other one is the interaction of three-level atom with quantized radiation fields, where the atoms have Lambda-configuration energy levels, and the radiation fields are one-mode...
Matrix models for β-ensembles from Nekrasov partition functions
Sułkowski, P.
2010-01-01
We relate Nekrasov partition functions, with arbitrary values of ∊ 1, ∊ 2 parameters, to matrix models for β-ensembles. We find matrix models encoding the instanton part of Nekrasov partition functions, whose measure, to the leading order in ∊ 2 expansion, is given by the Vandermonde determinant to
Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
Palao, J P; Palao, Jose P.; Kosloff, Ronnie
2002-01-01
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The approach is illustrated in the implementation of one and two qubits gates in model molecular systems.
Truncations of random unitary matrices
Zyczkowski, K; Zyczkowski, Karol; Sommers, Hans-Juergen
1999-01-01
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ratio M/N. For the truncated CUE we derive analytically the joint density of eigenvalues from which easily all correlation functions are obtained. For N-M fixed and N--> infinity the universal resonance-width distribution with N-M open channels is recovered.
Hydrodynamics of a unitary Bose gas
Man, Jay; Fletcher, Richard; Lopes, Raphael; Navon, Nir; Smith, Rob; Hadzibabic, Zoran
2016-05-01
In general, normal-phase Bose gases are well described by modelling them as ideal gases. In particular, hydrodynamic flow is usually not observed in the expansion dynamics of normal gases, and is more readily observable in Bose-condensed gases. However, by preparing strongly-interacting clouds, we observe hydrodynamic behaviour in normal-phase Bose gases, including the `maximally' hydrodynamic unitary regime. We avoid the atom losses that often hamper experimental access of this regime by using radio-frequency injection, which switches on interactions much faster than trap or loss timescales. At low phase-space densities, we find excellent agreement with a collisional model based on the Boltzmann equation. At higher phase-space densities our results show a deviation from this model in the vicinity of an Efimov resonance, which cannot be accounted for by measured losses.
Goldberg, Robert K.; Stouffer, Donald C.
1998-01-01
Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.
Matrix models, topological strings, and supersymmetric gauge theories
Dijkgraaf, Robbert; Vafa, Cumrun
2002-11-01
We show that B-model topological strings on local Calabi-Yau threefolds are large- N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover ( p, q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.
Mandal, Gautam
2013-01-01
Quantum quench dynamics is considered in a one dimensional unitary matrix model with a single trace potential. This model is integrable and has been studied in the context of non-critical string theory. We find dynamical phase transitions, and study the role of the quantum critical point. In course of the time evolutions, we find evidence of selective equilibration for a certain class of observables. The equilibrium is governed by the Generalized Gibbs Ensemble (GGE) and differs from the standard Gibbs ensemble. We compute the production of entropy which is O(N) for large N matrices. An important feature of the equilibration is the appearance of an energy cascade, reminiscent of the Richardson cascade in turbulence, where we find flow of energy from initial long wavelength modes to progressively shorter wavelength excitations. We discuss possible implication of the equilibration and of GGE in string theories and higher spin theories. In another related study, we compute time evolutions in a double trace unita...
Singular-potential random-matrix model arising in mean-field glassy systems.
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
2014-06-01
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
Singular-potential random-matrix model arising in mean-field glassy systems
Akemann, Gernot; Villamaina, Dario; Vivo, Pierpaolo
2014-06-01
We consider an invariant random matrix ensemble where the standard Gaussian potential is distorted by an additional single pole of arbitrary fixed order. Potentials with first- and second-order poles have been considered previously and found applications in quantum chaos and number theory. Here we present an application to mean-field glassy systems. We derive and solve the loop equation in the planar limit for the corresponding class of potentials. We find that the resulting mean or macroscopic spectral density is generally supported on two disconnected intervals lying on the two sides of the repulsive pole, whose edge points can be completely determined imposing the additional constraint of traceless matrices on average. For an unbounded potential with an attractive pole, we also find a possible one-cut solution for certain values of the couplings, which is ruled out when the traceless condition is imposed. Motivated by the calculation of the distribution of the spin-glass susceptibility in the Sherrington-Kirkpatrick spin-glass model, we consider in detail a second-order pole for a zero-trace model and provide the most explicit solution in this case. In the limit of a vanishing pole, we recover the standard semicircle. Working in the planar limit, our results apply to matrices with orthogonal, unitary, and symplectic invariance. Numerical simulations and an independent analytical Coulomb fluid calculation for symmetric potentials provide an excellent confirmation of our results.
A diode matrix is an extremely low-density form of read-only memory. It's one of the earliest forms of ROMs (dating back to the 1950s). Each bit in the ROM is represented by the presence or absence of one diode. The ROM is easily user-writable using a soldering iron and pair of wire cutters.This diode matrix board is a floppy disk boot ROM for a PDP-11, and consists of 32 16-bit words. When you access an address on the ROM, the circuit returns the represented data from that address.
Free particles from Brauer algebras in complex matrix models
Kimura, Yusuke; Turton, David
2009-01-01
The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition. The Brauer algebra basis for complex matrix models developed earlier is useful in projecting to a sector which matches the state counting of N free fermions on a circle. The Brauer algebra projection is characterized by the vanishing of a scale invariant laplacian constructed from the complex matrix. The special case of N=2 is studied in detail: the ring of gauge invariant functions as well as a ring of scale and gauge invariant differential operators are characterized completely. The orthonormal basis of wavefunctions in this special case is completely characterized by a set of five commuting Hamiltonians, which display free particle structures. Applications to the reduced matrix quantum mechanics coming from radial quantization in N=4 SYM are described. We propose that th...
Unitary Root Music and Unitary Music with Real-Valued Rank Revealing Triangular Factorization
2010-06-01
AFRL-RY-WP-TP-2010-1213 UNITARY ROOT MUSIC AND UNITARY MUSIC WITH REAL-VALUED RANK REVEALING TRIANGULAR FACTORIZATION (Postprint) Nizar...DATES COVERED (From - To) June 2010 Journal Article Postprint 08 September 2006 – 31 August 2009 4. TITLE AND SUBTITLE UNITARY ROOT MUSIC AND...UNITARY MUSIC WITH REAL-VALUED RANK REVEALING TRIANGULAR FACTORIZATION (Postprint) 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA8650-05-D-1912-0007 5c
An algebraic study of unitary one dimensional quantum cellular automata
Arrighi, P
2005-01-01
We provide algebraic characterizations of unitary one dimensional quantum cellular automata. We do so both by algebraizing existing decision procedures, and by adding constraints into the model which do not change the quantum cellular automata's computational power. The configurations we consider have finite but unbounded size.
Establishing the Unitary Classroom: Organizational Change and School Culture.
Eddy, Elizabeth M.; True, Joan H.
1980-01-01
This paper examines the organizational changes introduced in two elementary schools to create unitary (desegregated) classrooms. The different models adopted by the two schools--departmentalization and team teaching--are considered as expressions of their patterns of interaction, behavior, and values. (Part of a theme issue on educational…
Deformations of Polyhedra and Polygons by the Unitary Group
Livine, Etera R
2013-01-01
We introduce the set of framed convex polyhedra with N faces as the symplectic quotient C^2N//SU(2). A framed polyhedron is then parametrized by N spinors living in C^2 satisfying suitable closure constraints and defines a usual convex polyhedron plus a phase for each face. We show that there is an action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any polyhedron onto any other with the same total area. This realizes the isomorphism of the space of framed polyhedra with the Grassmannian space U(N)/SU(2)*U(N-2). We show how to write averages and correlations of geometrical observables over the ensemble of polyhedra as polynomial integrals over U(N) and we use the Itzykson-Zuber formula from matrix models as the generating function for them. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners. The individual face areas are quantized as half-integers (spins) and the Hilbert spaces...
On an average over the Gaussian Unitary Ensemble
Mezzadri, F
2009-01-01
We study the asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We compute the leading order term of the partition function and of the coefficients of its Taylor expansion. Our results are valid in the range N^(-1/2) < z < N^(1/4). Such partition function contains all the information on a new statistics of the eigenvalues of matrices in the Gaussian Unitary Ensemble (GUE) that was introduced by Berry and Shukla (J. Phys. A: Math. Theor., Vol. 41 (2008), 385202, arXiv:0807.3474). It can also be interpreted as the moment generating function of a singular linear statistics.
Noncommutative Yang-Mills in IIB Matrix Model
Aoki, H; Iso, S; Kawai, H; Kitazawa, Y; Tada, T
2000-01-01
We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.
DOA estimation for monostatic MIMO radar based on unitary root-MUSIC
Wang, Wei; Wang, Xianpeng; Li, Xin; Song, Hongru
2013-11-01
Direction of arrival (DOA) estimation is an important issue for monostatic MIMO radar. A DOA estimation method for monostatic MIMO radar based on unitary root-MUSIC is presented in this article. In the presented method, a reduced-dimension matrix is first utilised to transform the high dimension of received signal data into low dimension one. Then, a low-dimension real-value covariance matrix is obtained by forward-backward (FB) averaging and unitary transformation. The DOA of targets can be achieved by unitary root-MUSIC. Due to the FB averaging of received signal data and the eigendecomposition of the real-valued matrix covariance, the proposed method owns better angle estimation performance and lower computational complexity. The simulation results of the proposed method are presented and the performances are investigated and discussed.
Efficient Matrix Models for Relational Learning
2009-10-01
contains no information about Z. Aldous ex- changeability is an extension of de Finetti exchangeability to matrices of random variables, and like de... Finetti exchangeability, it leads to a representation theorem: Theorem 1 (Aldous’ Theorem [1]). If Z is row-column exchangeable, then there exists a...objectives for matrix factorization. It should be noted that Theorem 1 is descriptive, not prescriptive (just like de Finetti exchangeability): no
Unitary symmetry, combinatorics, and special functions
Energy Technology Data Exchange (ETDEWEB)
Louck, J.D.
1996-12-31
From 1967 to 1994, Larry Biedenham and I collaborated on 35 papers on various aspects of the general unitary group, especially its unitary irreducible representations and Wigner-Clebsch-Gordan coefficients. In our studies to unveil comprehensible structures in this subject, we discovered several nice results in special functions and combinatorics. The more important of these will be presented and their present status reviewed.
Complex positive maps and quaternionic unitary evolution
Energy Technology Data Exchange (ETDEWEB)
Asorey, M [Departamento de Fisica Teorica, Universidad de Zaragoza, 50009 Zaragoza (Spain); Scolarici, G [Dipartimento di Fisica dell' Universita di Lecce and INFN, Sezione di Lecce, I-73100 Lecce (Italy)
2006-08-04
The complex projection of any n-dimensional quaternionic unitary dynamics defines a one-parameter positive semigroup dynamics. We show that the converse is also true, i.e. that any one-parameter positive semigroup dynamics of complex density matrices with maximal rank can be obtained as the complex projection of suitable quaternionic unitary dynamics.
Composed ensembles of random unitary ensembles
Pozniak, M; Kus, M; Pozniak, Marcin; Zyczkowski, Karol; Kus, Marek
1997-01-01
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate their physical relevance. We discuss also the methods of generating random matrices distributed according to invariant Haar measure on the orthogonal and unitary group.
Tensor Products of Random Unitary Matrices
Tkocz, Tomasz; Kus, Marek; Zeitouni, Ofer; Zyczkowski, Karol
2012-01-01
Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random matrices becomes Poissonian if M=2, N become large or M become large and N=2.
Space-Time Structures from IIB Matrix Model
Aoki, H; Kawai, H; Kitazawa, Y; Tada, T
1998-01-01
We derive a long distance effective action for space-time coordinates from a IIB matrix model. It provides us an effective tool to study the structures of space-time. We prove the finiteness of the theory for finite $N$ to all orders of the perturbation theory. Space-time is shown to be inseparable and its dimensionality is dynamically determined. The IIB matrix model contains a mechanism to ensure the vanishing cosmological constant which does not rely on the manifest supersymmetry. We discuss possible mechanisms to obtain realistic dimensionality and gauge groups from the IIB matrix model.
On a Random Matrix Models of Quantum Relaxation
Lebowitz, J L; Pastur, L
2007-01-01
Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a $n\\times n$ reservoir and assuming that the interaction is modelled by a random matrix. We presented there a formula for the reduced density matrix in the limit $n\\to \\infty $ as well as several its properties and asymptotic forms in various regimes. In this paper we give the proofs of the assertions, and present also a new fact about the model.
Statistical Analysis of Q-matrix Based Diagnostic Classification Models
Chen, Yunxiao; Liu, Jingchen; Xu, Gongjun; Ying, Zhiliang
2014-01-01
Diagnostic classification models have recently gained prominence in educational assessment, psychiatric evaluation, and many other disciplines. Central to the model specification is the so-called Q-matrix that provides a qualitative specification of the item-attribute relationship. In this paper, we develop theories on the identifiability for the Q-matrix under the DINA and the DINO models. We further propose an estimation procedure for the Q-matrix through the regularized maximum likelihood. The applicability of this procedure is not limited to the DINA or the DINO model and it can be applied to essentially all Q-matrix based diagnostic classification models. Simulation studies are conducted to illustrate its performance. Furthermore, two case studies are presented. The first case is a data set on fraction subtraction (educational application) and the second case is a subsample of the National Epidemiological Survey on Alcohol and Related Conditions concerning the social anxiety disorder (psychiatric application). PMID:26294801
An improved transfer-matrix model for optical superlenses.
Moore, Ciaran P; Blaikie, Richard J; Arnold, Matthew D
2009-08-01
The use of transfer-matrix analyses for characterizing planar optical superlensing systems is studied here, and the simple model of the planar superlens as an isolated imaging element is shown to be defective in certain situations. These defects arise due to neglected interactions between the superlens and the spatially varying shadow masks that are normally used as scattering objects for imaging, and which are held in near-field proximity to the superlenses. An extended model is proposed that improves the accuracy of the transfer-matrix analysis, without adding significant complexity, by approximating the reflections from the shadow mask by those from a uniform metal layer. Results obtained using both forms of the transfer matrix model are compared to finite element models and two example superlenses, one with a silver monolayer and the other with three silver sublayers, are characterized. The modified transfer matrix model gives much better agreement in both cases.
Energy Technology Data Exchange (ETDEWEB)
Christian, J.E.
1977-07-01
This technology evaluation covers commercially available unitary heat pumps ranging from nominal capacities of 1/sup 1///sub 2/ to 45 tons. The nominal COP of the heat pump models, selected as representative, vary from 2.4 to 2.9. Seasonal COPs for heat pump installations and single-family dwellings are reported to vary from 2.5 to 1.1, depending on climate. For cooling performance, the nominal EER's vary from 6.5 to 8.7. Representative part-load performance curves along with cost estimating and reliability data are provided to aid: (1) the systems design engineer to select suitably sized heat pumps based on life-cycle cost analyses, and (2) the computer programmer to develop a simulation code for heat pumps operating in an Integrated Community Energy System.
Unitary Quantum Relativity - (Work in Progress)
Finkelstein, David Ritz
2016-12-01
A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.
Unitary Quantum Relativity. (Work in Progress)
Finkelstein, David Ritz
2017-01-01
A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.
Universal Loss Dynamics in a Unitary Bose Gas
Eismann, Ulrich; Khaykovich, Lev; Laurent, Sébastien; Ferrier-Barbut, Igor; Rem, Benno S.; Grier, Andrew T.; Delehaye, Marion; Chevy, Frédéric; Salomon, Christophe; Ha, Li-Chung; Chin, Cheng
2016-04-01
The low-temperature unitary Bose gas is a fundamental paradigm in few-body and many-body physics, attracting wide theoretical and experimental interest. Here, we present experiments performed with unitary 133Cs and 7Li atoms in two different setups, which enable quantitative comparison of the three-body recombination rate in the low-temperature domain. We develop a theoretical model that describes the dynamic competition between two-body evaporation and three-body recombination in a harmonically trapped unitary atomic gas above the condensation temperature. We identify a universal "magic" trap depth where, within some parameter range, evaporative cooling is balanced by recombination heating and the gas temperature stays constant. Our model is developed for the usual three-dimensional evaporation regime as well as the two-dimensional evaporation case, and it fully supports our experimental findings. Combined 133Cs and 7Li experimental data allow investigations of loss dynamics over 2 orders of magnitude in temperature and 4 orders of magnitude in three-body loss rate. We confirm the 1 /T2 temperature universality law. In particular, we measure, for the first time, the Efimov inelasticity parameter η*=0.098 (7 ) for the 47.8-G d -wave Feshbach resonance in 133Cs. Our result supports the universal loss dynamics of trapped unitary Bose gases up to a single parameter η*.
Matrix-analytic methods in stochastic models
Chakravarthy, S
1996-01-01
The Marcovian arrival process: some future directions; an algorithm for the P(n,t) matrices of a continuous BMAP; a pre-emptive priority Queue with non-renewal inputs; analysis of a multiserver delay-loss system with a general Markovian arrival process; analysis of a finite capacity multi-server Queue with non-preemptive priorities and non-renewal input; matrix-multiplicative approach to quasi-birth-and-death processes; a level crossing analysis in the MAP/G/1 Queue; performance analysis and optimal threshold policies for Queueing systems with several heterogeneous servers and Markov modulated
Elementary Proof for Asymptotics of Large Haar-Distributed Unitary Matrices
Mastrodonato, Christian; Tumulka, Roderich
2007-01-01
We provide an elementary proof for a theorem due to Petz and R\\'effy which states that for a random $n\\times n$ unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) $k\\times k$ submatrix converges in distribution, after multiplying by a normalization factor $\\sqrt{n}$ and as $n\\to\\infty$, to a matrix of independent complex Gaussian random variables with mean 0 and variance 1.
Entanglement entropy of Wilson loops: Holography and matrix models
Gentle, Simon A
2014-01-01
A half-BPS circular Wilson loop in $\\mathcal{N}=4$ $SU(N)$ supersymmetric Yang-Mills theory in an arbitrary representation is described by a Gaussian matrix model with a particular insertion. The additional entanglement entropy of a spherical region in the presence of such a loop was recently computed by Lewkowycz and Maldacena using exact matrix model results. In this note we utilize the supergravity solutions that are dual to such Wilson loops in a representation with order $N^2$ boxes to calculate this entropy holographically. Employing the matrix model results of Gomis, Matsuura, Okuda and Trancanelli we express this holographic entanglement entropy in a form that can be compared with the calculation of Lewkowycz and Maldacena. We find complete agreement between the matrix model and holographic calculations.
Thermodynamics of the BMN matrix model at strong coupling
Costa, Miguel S.; Greenspan, Lauren; Penedones, João; Santos, Jorge E.
2015-03-01
We construct the black hole geometry dual to the deconfined phase of the BMN matrix model at strong 't Hooft coupling. We approach this solution from the limit of large temperature where it is approximately that of the non-extremal D0-brane geometry with a spherical S 8 horizon. This geometry preserves the SO(9) symmetry of the matrix model trivial vacuum. As the temperature decreases the horizon becomes deformed and breaks the SO(9) to the SO(6) × SO(3) symmetry of the matrix model. When the black hole free energy crosses zero the system undergoes a phase transition to the confined phase described by a Lin-Maldacena geometry. We determine this critical temperature, whose computation is also within reach of Monte Carlo simulations of the matrix model.
Entanglement entropy of Wilson loops: Holography and matrix models
Gentle, Simon A.; Gutperle, Michael
2014-09-01
A half-Bogomol'nyi-Prasad-Sommerfeld circular Wilson loop in N=4 SU(N) supersymmetric Yang-Mills theory in an arbitrary representation is described by a Gaussian matrix model with a particular insertion. The additional entanglement entropy of a spherical region in the presence of such a loop was recently computed by Lewkowycz and Maldacena using exact matrix model results. In this paper we utilize the supergravity solutions that are dual to such Wilson loops in a representation with order N2 boxes to calculate this entropy holographically. Employing the matrix model results of Gomis, Matsuura, Okuda and Trancanelli we express this holographic entanglement entropy in a form that can be compared with the calculation of Lewkowycz and Maldacena. We find complete agreement between the matrix model and holographic calculations.
Thermodynamics of the BMN matrix model at strong coupling
Costa, Miguel S; Penedones, Joao; Santos, Jorge
2014-01-01
We construct the black hole geometry dual to the deconfined phase of the BMN matrix model at strong 't Hooft coupling. We approach this solution from the limit of large temperature where it is approximately that of the non-extremal D0-brane geometry with a spherical $S^8$ horizon. This geometry preserves the $SO(9)$ symmetry of the matrix model trivial vacuum. As the temperature decreases the horizon becomes deformed and breaks the $SO(9)$ to the $SO(6)\\times SO(3)$ symmetry of the matrix model. When the black hole free energy crosses zero the system undergoes a phase transition to the confined phase described by a Lin-Maldacena geometry. We determine this critical temperature, whose computation is also within reach of Monte Carlo simulations of the matrix model.
Special Geometries Emerging from Yang-Mills Type Matrix Models
Blaschke, Daniel N
2011-01-01
I review some recent results which demonstrate how various geometries, such as Schwarzschild and Reissner-Nordstroem, can emerge from Yang-Mills type matrix models with branes. Furthermore, explicit embeddings of these branes as well as appropriate Poisson structures and star-products which determine the non-commutativity of space-time are provided. These structures are motivated by higher order terms in the effective matrix model action which semi-classically lead to an Einstein-Hilbert type action.
Matrix models vs. Seiberg-Witten/Whitham theories
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L.; Mironov, A
2003-01-23
We discuss the relation between matrix models and the Seiberg-Witten type (SW) theories, recently proposed by Dijkgraaf and Vafa. In particular, we prove that the partition function of the Hermitian one-matrix model in the planar (large N) limit coincides with the prepotential of the corresponding SW theory. This partition function is the logarithm of a Whitham {tau}-function. The corresponding Whitham hierarchy is explicitly constructed. The double-point problem is solved.
Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
Sperling, Marcus; Steinacker, Harold C.
2017-09-01
We study in detail generalized 4-dimensional fuzzy spheres with twisted extra dimensions. These spheres can be viewed as SO(5) -equivariant projections of quantized coadjoint orbits of SO(6) . We show that they arise as solutions in Yang-Mills matrix models, which naturally leads to higher-spin gauge theories on S 4. Several types of embeddings in matrix models are found, including one with self-intersecting fuzzy extra dimensions \
Quantum Entanglement Growth under Random Unitary Dynamics
Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haah, Jeongwan
2017-07-01
Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time )1/3 and are spatially correlated over a distance ∝(time )2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.
Quantum Entanglement Growth under Random Unitary Dynamics
Directory of Open Access Journals (Sweden)
Adam Nahum
2017-07-01
Full Text Available Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ equation. The mean entanglement grows linearly in time, while fluctuations grow like (time^{1/3} and are spatially correlated over a distance ∝(time^{2/3}. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i a stochastic model of a growing surface, (ii a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.
Density matrix of black hole radiation
Alberte, Lasma; Khmelnitsky, Andrei; Medved, A J M
2015-01-01
Hawking's model of black hole evaporation is not unitary and leads to a mixed density matrix for the emitted radiation, while the Page model describes a unitary evaporation process in which the density matrix evolves from an almost thermal state to a pure state. We compare a recently proposed model of semiclassical black hole evaporation to the two established models. In particular, we study the density matrix of the outgoing radiation and determine how the magnitude of the off-diagonal corrections differs for the three frameworks. For Hawking's model, we find power-law corrections to the two-point functions that induce exponentially suppressed corrections to the off-diagonal elements of the full density matrix. This verifies that the Hawking result is correct to all orders in perturbation theory and also allows one to express the full density matrix in terms of the single-particle density matrix. We then consider the semiclassical theory for which the corrections, being non-perturbative from an effective fie...
Modeling of the flexural behavior of ceramic-matrix composites
Kuo, Wen-Shyong; Chou, Tsu-Wei
1990-01-01
This paper examines the effects of matrix cracking and fiber breakage on the flexural behavior of ceramic composite beams. A model has been proposed to represent the damage evolution of the beam, of which the matrix fracture strain is smaller than that of the fibers. Close form solutions of the critical loads for the initiation of matrix cracking and fiber breakage in the tension side of the beam have been found. The effects of thermal residual stresses and fiber/matrix debonding have been taken into account. The initial deviation of the load-deflection curve from linearity is due to matrix cracking, while fiber breakages are responsible for the drop in the load carrying capacity of the beam. The proportional limit as well as the nonlinear behavior of the beam deflection have been identified. The growth of the damaged zone has also been predicted. A three-point bending case is given as a numerical example.
Strain Rate Dependent Modeling of Polymer Matrix Composites
Goldberg, Robert K.; Stouffer, Donald C.
1999-01-01
A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to high strain rate impact loads. Strain rate dependent inelastic constitutive equations have been developed to model the polymer matrix, and have been incorporated into a micromechanics approach to analyze polymer matrix composites. The Hashin failure criterion has been implemented within the micromechanics results to predict ply failure strengths. The deformation model has been implemented within LS-DYNA, a commercially available transient dynamic finite element code. The deformation response and ply failure stresses for the representative polymer matrix composite AS4/PEEK have been predicted for a variety of fiber orientations and strain rates. The predicted results compare favorably to experimentally obtained values.
Modeling the Stress Strain Behavior of Woven Ceramic Matrix Composites
Morscher, Gregory N.
2006-01-01
Woven SiC fiber reinforced SiC matrix composites represent one of the most mature composite systems to date. Future components fabricated out of these woven ceramic matrix composites are expected to vary in shape, curvature, architecture, and thickness. The design of future components using woven ceramic matrix composites necessitates a modeling approach that can account for these variations which are physically controlled by local constituent contents and architecture. Research over the years supported primarily by NASA Glenn Research Center has led to the development of simple mechanistic-based models that can describe the entire stress-strain curve for composite systems fabricated with chemical vapor infiltrated matrices and melt-infiltrated matrices for a wide range of constituent content and architecture. Several examples will be presented that demonstrate the approach to modeling which incorporates a thorough understanding of the stress-dependent matrix cracking properties of the composite system.
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
Diagnosing declining grassland wader populations using simple matrix models
Klok, Chris; Roodbergen, Maja; Hemerik, Lia
2009-01-01
Many populations of wader species have shown a strong decline in number in Western-Europe in recent years. The use of simple population models such as matrix models can contribute to conserve these populations by identifying the most profitable management measures. Parameterization of such models is
Matrix models of RNA folding with external interactions: A review
Indian Academy of Sciences (India)
I Garg; N Deo
2011-11-01
The matrix model of (simpliﬁed) RNA folding with an external linear interaction in the action of the partition function is reviewed. The important results for structure combinatorics of the model are discussed and analysed in terms of the already existing models.
Truncating an exact matrix product state for the XY model: Transfer matrix and its renormalization
Rams, Marek M.; Zauner, Valentin; Bal, Matthias; Haegeman, Jutho; Verstraete, Frank
2015-12-01
We discuss how to analytically obtain an essentially infinite matrix product state (MPS) representation of the ground state of the XY model. On one hand this allows us to illustrate how the Ornstein-Zernike form of the correlation function emerges in the exact case using standard MPS language. On the other hand we study the consequences of truncating the bond dimension of the exact MPS, which is also part of many tensor network algorithms, and analyze how the truncated MPS transfer matrix is representing the dominant part of the exact quantum transfer matrix. In the gapped phase we observe that the correlation length obtained from a truncated MPS approaches the exact value following a power law in effective bond dimension. In the gapless phase we find a good match between a state obtained numerically from standard MPS techniques with finite bond dimension and a state obtained by effective finite imaginary time evolution in our framework. This provides a direct hint for a geometric interpretation of finite entanglement scaling at the critical point in this case. Finally, by analyzing the spectra of transfer matrices, we support the interpretation put forward by V. Zauner et al. [New J. Phys. 17, 053002 (2015), 10.1088/1367-2630/17/5/053002] that the MPS transfer matrix emerges from the quantum transfer matrix though the application of Wilson's numerical renormalization group along the imaginary-time direction.
Automatic generation of matrix element derivatives for tight binding models
Elena, Alin M.; Meister, Matthias
2005-10-01
Tight binding (TB) models are one approach to the quantum mechanical many-particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a tight binding computer program, like, for instance, DINAMO, they obviate the need to type all the required derivatives of all occurring matrix elements by hand.
Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun
2002-01-01
We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.
Matrix models, topological strings, and supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert E-mail: rhd@science.uva.nl; Vafa, Cumrun
2002-11-11
We show that B-model topological strings on local Calabi-Yau threefolds are large-N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.
Charge and Current in the Quantum Hall Matrix Model
2003-01-01
We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even at the classical level. We calculate the linear response at low momenta -- this is unambigously defined. In particular, we obtain the correct fractional quantum Hall conductivity, and the expected density modulations in response to a weak and slowly varying magnetic field. These results show that the classical quantum Hall ...
Radiative fermion mass matrix generation in supersymmetric models
Energy Technology Data Exchange (ETDEWEB)
Papantonopoulos, E.; Zoupanos, G.
1984-01-01
Supersymmetric SU(2)sub(L)xU(1) horizontal models are studied. The non-renormalisation theorems of sypersymmetry are used to make the mass generation and flavour mixing natural. For three families, the fermion mass matrix generation mechanism is studied as a radiative effect due to horizontal interactions, using various representations of the gauge horizontal groups SU(2)sub(H) and SU(3)sub(H). An attractive possibility leading to a realistic mass matrix is found.
Asymptotic Evolution of Random Unitary Operations
Novotny, J; Jex, I
2009-01-01
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
Non-unitary probabilistic quantum computing
Gingrich, Robert M.; Williams, Colin P.
2004-01-01
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.
Entanglement entropy of non-unitary integrable quantum field theory
Directory of Open Access Journals (Sweden)
Davide Bianchini
2015-07-01
Full Text Available In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee–Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by ceff3logℓ where ceff is the effective central charge of the theory (a positive number related to the central charge and ℓ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum, it appears to be much more model-dependent for non-unitary models.
Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
Cordova, Clay; Popolitov, Alexandr; Shakirov, Shamil
2016-01-01
We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarthmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.
Entanglement quantification by local unitary operations
Energy Technology Data Exchange (ETDEWEB)
Monras, A.; Giampaolo, S. M.; Gualdi, G.; Illuminati, F. [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, CNISM, Unita di Salerno, and INFN, Sezione di Napoli-Gruppo Collegato di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); Adesso, G.; Davies, G. B. [School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2011-07-15
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as ''mirror entanglement.'' They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the ''stellar mirror entanglement'' associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Right-unitary transformation theory and applications
Tang, Zhong
1996-01-01
We develop a new transformation theory in quantum physics, where the transformation operators, defined in the infinite dimensional Hilbert space, have right-unitary inverses only. Through several theorems, we discuss the properties of state space of such operators. As one application of the right-unitary transformation (RUT), we show that using the RUT method, we can solve exactly various interactions of many-level atoms with quantized radiation fields, where the energy of atoms can be two le...
Entanglement quantification by local unitary operations
Monras, A.; Adesso, G.; Giampaolo, S. M.; Gualdi, G.; Davies, G. B.; Illuminati, F.
2011-07-01
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as “mirror entanglement.” They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the “stellar mirror entanglement” associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.76.042301 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Participatory dreaming: a conceptual exploration from a unitary appreciative inquiry perspective.
Repede, Elizabeth J
2009-10-01
Dreaming is a universal phenomenon in human experience and one that carries multiple meanings in the narrative discourse across disciplines. Dreams can be collective, communal, and emancipatory, as well as individual. While individual dreaming has been extensively studied in the literature, the participatory nature of dreaming as a unitary phenomenon is limited. The concept of participatory dreaming within a unitary appreciative framework for healing is explored from perspectives in anthropology, psychology, and nursing. A participatory model of dreaming is proposed from a synthesis of the literature for use in future research using unitary appreciative inquiry.
Participatory dreaming: a unitary appreciative inquiry into healing with women abused as children.
Repede, Elizabeth
2011-01-01
Unitary appreciative inquiry was used to explore healing in the lives of 11 women abused as children using a model of participatory dreaming. Aesthetics, imagery, and journaling were used in a participatory design aimed at the appreciation of healing in the lives of the participants as it related to the abuse. Using Cowling's theory of unitary healing, research and practice were combined within a unitary-transformative framework. Participatory dreaming was useful in illuminating the life patterning in the lives of the women and promoted the development of new knowledge and skills that led to change and transformation, both individually and collectively.
Modeling food matrix effects on chemical reactivity: Challenges and perspectives.
Capuano, Edoardo; Oliviero, Teresa; van Boekel, Martinus A J S
2017-06-29
The same chemical reaction may be different in terms of its position of the equilibrium (i.e., thermodynamics) and its kinetics when studied in different foods. The diversity in the chemical composition of food and in its structural organization at macro-, meso-, and microscopic levels, that is, the food matrix, is responsible for this difference. In this viewpoint paper, the multiple, and interconnected ways the food matrix can affect chemical reactivity are summarized. Moreover, mechanistic and empirical approaches to explain and predict the effect of food matrix on chemical reactivity are described. Mechanistic models aim to quantify the effect of food matrix based on a detailed understanding of the chemical and physical phenomena occurring in food. Their applicability is limited at the moment to very simple food systems. Empirical modeling based on machine learning combined with data-mining techniques may represent an alternative, useful option to predict the effect of the food matrix on chemical reactivity and to identify chemical and physical properties to be further tested. In such a way the mechanistic understanding of the effect of the food matrix on chemical reactions can be improved.
Hyperstate matrix models : extending demographic state spaces to higher dimensions
Roth, G.; Caswell, H.
2016-01-01
1. Demographic models describe population dynamics in terms of the movement of individuals among states (e.g. size, age, developmental stage, parity, frailty, physiological condition). Matrix population models originally classified individuals by a single characteristic. This was enlarged to two cha
Matrix eigenvalue model: Feynman graph technique for all genera
Energy Technology Data Exchange (ETDEWEB)
Chekhov, Leonid [Steklov Mathematical Institute, ITEP and Laboratoire Poncelet, Moscow (Russian Federation); Eynard, Bertrand [SPhT, CEA, Saclay (France)
2006-12-15
We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power {beta} by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves)
Hierarchical spatiotemporal matrix models for characterizing invasions.
Hooten, Mevin B; Wikle, Christopher K; Dorazio, Robert M; Royle, J Andrew
2007-06-01
The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.
A hierarchical model for ordinal matrix factorization
DEFF Research Database (Denmark)
Paquet, Ulrich; Thomson, Blaise; Winther, Ole
2012-01-01
their ratings for other movies. The Netflix data set is used for evaluation, which consists of around 100 million ratings. Using root mean-squared error (RMSE) as an evaluation metric, results show that the suggested model outperforms alternative factorization techniques. Results also show how Gibbs sampling...
All unitary cubic curvature gravities in D dimensions
Energy Technology Data Exchange (ETDEWEB)
Sisman, Tahsin Cagri; Guellue, Ibrahim; Tekin, Bayram, E-mail: sisman@metu.edu.tr, E-mail: e075555@metu.edu.tr, E-mail: btekin@metu.edu.tr [Department of Physics, Middle East Technical University, 06531 Ankara (Turkey)
2011-10-07
We construct all the unitary cubic curvature gravity theories built on the contractions of the Riemann tensor in D-dimensional (anti)-de Sitter spacetimes. Our construction is based on finding the equivalent quadratic action for the general cubic curvature theory and imposing ghost and tachyon freedom, which greatly simplifies the highly complicated problem of finding the propagator of cubic curvature theories in constant curvature backgrounds. To carry out the procedure we have also classified all the unitary quadratic models. We use our general results to study the recently found cubic curvature theories using different techniques and the string generated cubic curvature gravity model. We also study the scattering in critical gravity and give its cubic curvature extensions.
J(l)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting
Alpay, D.; Dijksma, A.; Langer, H.
2006-01-01
We introduce a Schur transformation for generalized Nevanlinna functions and show that it can be used in obtaining the unique minimal factorization of a class of rational J(l)-unitary 2 x 2 matrix functions into elementary factors from the same class. (c) 2006 Elsevier Inc. All rights reserved.
Effective Actions of IIB Matrix Model on S^3
Kaneko, Hiromichi; Matsumoto, Koichiro
2007-01-01
S^3 is a simple principle bundle which is locally S^2 \\times S^1. It has been shown that such a space can be constructed in terms of matrix models. It has been also shown that such a space can be realized by a generalized compactification procedure in the S^1 direction. We investigate the effective action of supersymmetric gauge theory on S^3 with an angular momentum cutoff and that of a matrix model compactification. The both cases can be realized in a deformed IIB matrix model with a Myers Term. We find that the highly divergent contributions at the tree and one loop level are sensitive to the uv cutoff. However the two loop level contributions are universal since they are only logarithmically divergent. We expect that the higher loop contributions are insensitive to the uv cutoff since 3d gauge theory is super renormalizable.
pp-wave matrix models from point-like gravitons
Energy Technology Data Exchange (ETDEWEB)
Lozano, Y. [Departamento de Fisica, Universidad de Oviedo, Av. Calvo Sotelo 18, 33007 Oviedo (Spain); Rodriguez-Gomez, D. [Department of Physics, Princeton University, Princeton, NJ 08540 (United States)
2007-05-15
The BFSS Matrix model can be regarded as a theory of coincident M-theory gravitons. In this spirit, we summarize how using the action for coincident gravitons proposed in hep-th/0207199 it is possible to go beyond the linear order approximation of Kabat and Taylor, and to provide a satisfactory microscopical description of giant gravitons in AdS{sub m} x S{sup n} backgrounds. We then show that in the M-theory maximally supersymmetric pp-wave background, the action for coincident gravitons, besides reproducing the BMN Matrix model, predicts a new quadrupolar coupling to the M-theory 6-form potential, which supports the so far elusive fuzzy 5-sphere giant graviton solution. Finally, we discuss similar Matrix models that can be derived in Type II string theories using dualities. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Pp-wave Matrix Models from Point-like Gravitons
Lozano, Y; Lozano, Yolanda; Rodriguez-Gomez, Diego
2007-01-01
The BFSS Matrix model can be regarded as a theory of coincident M-theory gravitons. In this spirit, we summarize how using the action for coincident gravitons proposed in hep-th/0207199 it is possible to go beyond the linear order approximation of Kabat and Taylor, and to provide a satisfactory microscopical description of giant gravitons in $AdS_m\\times S^n$ backgrounds. We then show that in the M-theory maximally supersymmetric pp-wave background, the action for coincident gravitons, besides reproducing the BMN Matrix model, predicts a new quadrupolar coupling to the M-theory 6-form potential, which supports the so far elusive fuzzy 5-sphere giant graviton solution. Finally, we discuss similar Matrix models that can be derived in Type II string theories using dualities.
Matrix models with hard walls: geometry and solutions
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L [Steklov Mathematical Institute, Moscow (Russian Federation); Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); Poncelet Laboratoire International Franco-Russe, Moscow (Russian Federation); Department of Mathematics and Statistics, Concordia University, Montreal (Canada)
2006-07-14
We discuss various aspects of most general multisupport solutions to matrix models in the presence of hard walls, i.e., in the case where the eigenvalue support is confined to subdomains of the real axis. The structure of the solution at the leading order is described by semiclassical or generalized Whitham-Krichever hierarchies as in the unrestricted case. Derivatives of tau-functions for these solutions are associated with families of Riemann surfaces (with possible double points) and satisfy the Witten-Dijkgraaf-Verlinde-Verlinde equations. We then develop the diagrammatic technique for finding free energy of this model in all orders of the 't Hooft expansion in the reciprocal matrix size generalizing the Feynman diagrammatic technique for the Hermitian one-matrix model due to Eynard.
A New Model for Quark Mass Matrix
Institute of Scientific and Technical Information of China (English)
JIANG Zhi-Wei
2011-01-01
We study the status of S3, I.e. A slightly broken symmetry of quarks and propose a new model in which the S3 symmetry among the three generation up-quarks is slightly broken into the C2 symmetry while the S3 symmetry of the down-quarks is completely broken in a different way.%@@ We study the status of Sa, i.e.a slightly broken symmetry of quarks and propose a new model in which the Sa symmetry among the three generation up-quarks is slightly broken into the C symmetry while the S symmetry of the down-quarks is completely broken in a different way.
The CKM matrix from anti-SU(7) unification of GUT families
Kim, Jihn E; Seo, Min-Seok
2015-01-01
We estimate the CKM matrix elements in the recently proposed minimal model, anti-SU(7) GUT for the family unification, $[\\,3\\,]+2\\,[\\,2\\,]+8\\,[\\,\\bar{1}\\,]$+\\,(singlets). It is shown that the real angles of the right-handed unitary matrix diagonalizing the mass matrix can be determined to fit the Particle Data Group data. However, the phase in the right-handed unitary matrix is not constrained very much. We also includes an argument about allocating the Jarlskog phase in the CKM matrix. Phenomenologically, there are three classes of possible parametrizations, $\\delq=\\alpha,\\beta,$ or $\\gamma$ of the unitarity triangle. For the choice of $\\delq=\\alpha$, the phase is close to a maximal one.
Effective Actions of Matrix Models on Homogeneous Spaces
Imai, T; Takayama, Y; Tomino, D
2002-01-01
We evaluate the effective actions of supersymmetric matrix models on fuzzy S^2times S^2 up to the two loop level. Remarkably it turns out to be a consistent solution of IIB matrix model. Based on the power counting and SUSY cancellation arguments, we can identify the 't Hooft coupling and large N scaling behavior of the effective actions to all orders. In the large N limit, the quantum corrections survive except in 2 dimensional limits. They are O(N) and O(N^{4over 3}) for 4 and 6 dimensional spaces respectively. We argue that quantum effects single out 4 dimensionality of space-time.
Irregular conformal states and spectral curve: Irregular matrix model approach
Rim, Chaiho
2016-01-01
We present recent developments of irregular conformal conformal states. Irregular vertex operators and their adjoint are used to define the irregular conformal states and their Inner product. Free field formalism can be augmented by screening operators which provide more degrees of freedom. The inner product is conveniently given as partition function of a irregular matrix model. (Deformed) spectral curve is the loop equation of the matrix model at Nekrasov-Shatashivili limit. We present the details of analytic structure of the spectral curve for Virasoso symmetry and its extensions, W-symmetry and super-symmetry.
On the complete perturbative solution of one-matrix models
Directory of Open Access Journals (Sweden)
A. Mironov
2017-08-01
Full Text Available We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear group GL(N, and arbitrary correlators in the Gaussian phase are given by finite sums over Young diagrams of a given size, which involve also the well known characters of symmetric group. The previously known integrability and Virasoro constraints are simple corollaries, but no vice versa: complete solvability is a peculiar property of the matrix model (hypergeometric τ-functions, which is actually a combination of these two complementary requirements.
Five-Brane Thermodynamics from the Matrix Model
Furuuchi, K; Semenoff, G W
2003-01-01
A certain sector of the matrix model for M-theory on a plane wave background has recently been shown to produce the transverse five-brane. We consider this theory at finite temperature. We find that, at a critical temperature it has a Gross-Witten phase transition which corresponds to deconfinement of the matrix model gauge theory. We interpret the phase transition as the Hagedorn transition of M-theory and of type II string theory in the five-brane background. We also show that there is no Hagedorn behaviour in the transverse membrane background case.
Explicit examples of DIM constraints for network matrix models
Awata, Hidetoshi; Matsumoto, Takuya; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor
2016-01-01
Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the hidden Ding-Iohara-Miki (DIM) symmetry. This lifting is especially simple for what we call balanced networks. Then, the Ward identities (known under the names of Virasoro/W-constraints or loop equations or regularity condition for qq-characters) are also promoted to the DIM level, where they all become corollaries of a single identity.
Transmission line matrix modelling of thermal injuries to skin.
Aliouat Bellia, S; Saidane, A; Hamou, A; Benzohra, M; Saiter, J M
2008-08-01
A numerical model based on the transmission line matrix method is presented for the quantitative prediction of skin burn resulting from exposure of a specific region of human skin surface to a high temperature heat source. Transient temperatures were numerically estimated by Pennes' bioheat equation, and the damage function denoting the extent of burn was calculated using the Arrhenius assumptions for protein damage rate. A two-dimensional transmission line matrix model was used to predict the effects of exposure time and structure thicknesses on the transient temperature distribution and damage extent. Compared with other numerical sources the transmission line matrix results revealed good agreement, suggesting that this method may be an effective tool for the thermal diagnostic of burns.
HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.
Fan, Jianqing; Liao, Yuan; Mincheva, Martina
2011-01-01
The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.
High-dimensional covariance matrix estimation in approximate factor models
Fan, Jianqing; Mincheva, Martina; 10.1214/11-AOS944
2012-01-01
The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu [J. Amer. Statist. Assoc. 106 (2011) 672--684], taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studi...
Unitary Noise and the Mermin-GHZ Game
Fialík, Ivan
2010-01-01
Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems. We speak of pseudo-telepathy when it is able to completely eliminate the need for communication. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of erroneously performed unitary transformations on the quantum winning strategy for the Mermin-GHZ game. The question of how strong the unitary noise can be so that quantum players would still be better than classical ones is also dealt with.
Unitary Noise and the Mermin-GHZ Game
Institute of Scientific and Technical Information of China (English)
Ivan Fialík
2011-01-01
Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems. We speak of pseudo-telepathy when it is able to completely eliminate the need for communication. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of erroneously performed unitary transformations on the quantum winning strategy for the Mermin-GHZ game. The question of how strong the unitary noise can be so that quantum players would still be better than classical ones is also dealt with.
Unitary Noise and the Mermin-GHZ Game
Directory of Open Access Journals (Sweden)
Ivan Fialík
2010-06-01
Full Text Available Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems. We speak of pseudo-telepathy when it is able to completely eliminate the need for communication. Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game, quantum players are almost certain to make errors even though they use a winning strategy. After introducing a model for pseudo-telepathy games, we investigate the impact of erroneously performed unitary transformations on the quantum winning strategy for the Mermin-GHZ game. The question of how strong the unitary noise can be so that quantum players would still be better than classical ones is also dealt with.
Houlihan, S. R.
1992-01-01
Data were obtained on a 3-percent model of the Space Shuttle launch vehicle in the NASA/Ames Research Center 11x11-foot and 9x7-foot Unitary Plan Wind Tunnels. This test series has been identified as IA19OA/B and was conducted from 7 Feb. 1980 to 19 Feb. 1980 (IA19OA) and from 17 March 1980 to 19 March 1980 and from 8 May 1980 to 30 May 1980 (IA19OB). The primary test objective was to obtain structural loads on the following external tank protuberances: (1) LO2 feedline; (2) GO2 pressure line; (3) LO2 antigeyser line; (4) GH2 pressure line; (5) LH2 tank cable tray; (6) LO2 tank cable tray; (7) Bipod; (8) ET/SRB cable tray; and (9) Crossbeam/Orbiter cable tray. To fulfill these objectives the following steps were taken: Eight 3-component balances were used to measure forces on various sections of 1 thru 6 above; 315 pressure orifices were distributed over all 9 above items. The LO2 feedline was instrumented with 96 pressure taps and was rotated to four positions to yield 384 pressure measurements. The LO2 antigeyser line was instrumented with 64 pressure taps and was rotated to two positions to yield 128 pressure measurements; Three Chrysler miniature flow direction probes were mounted on a traversing mechanism on the tank upper surface centerline to obtain flow field data between the forward and aft attach structures; and Schlieren photographs and ultraviolet flow photographs were taken at all test conditions. Data from each of the four test phases are presented.
Houlihan, S. R.
1992-01-01
Data were obtained on a 3-percent model of the Space Shuttle launch vehicle in the NASA/Ames Research Center 11x11-foot and 9x7-foot Unitary Plan Wind Tunnels. This test series has been identified as IA190A/B and was conducted from 7 Feb. 1980 to 19 Feb. 1980 (IA190A) and from 17 March 1980 to 19 March 1980 and from 8 May 1980 to 30 May 1980 (IA190B). The primary test objective was to obtain structural loads on the following external tank protuberances: (1) LO2 feedline, (2) GO2 pressure line, (3) LO2 antigeyser line, (4) GH2 pressure line, (5) LH2 tank cable tray, (6) LO2 tank cable tray, (7) Bipod, (8) ET/SRB cable tray, and (9) Crossbeam/Orbiter cable tray. To fulfill these objectives the following steps were taken: (1) Eight 3-component balances were used to measure forces on various sections of 1 thru 6 above. (2) 315 pressure orifices were distributed over all 9 above items. The LO2 feedline was instrumented with 96 pressure taps and was rotated to four positions to yield 384 pressure measurements. The LO2 antigeyser line was instrumented with 64 pressure taps and was rotated to two positions to yield 128 pressure measurements. (3) Three Chrysler miniature flow direction probes were mounted on a traversing mechanism on the tank upper surface centerline to obtain flow field data between the forward and aft attach structures. (4) Schlieren photographs and ultraviolet flow photographs were taken at all test conditions. Data from each of the four test phases are presented.
Multiphase modeling of tumor growth with matrix remodeling and fibrosis
Tosin, Andrea
2009-01-01
We present a multiphase mathematical model for tumor growth which incorporates the remodeling of the extracellular matrix and describes the formation of fibrotic tissue by tumor cells. We also detail a full qualitative analysis of the spatially homogeneous problem, and study the equilibria of the system in order to characterize the conditions under which fibrosis may occur.
Quantum spectral curve for (q,t)-matrix model
Zenkevich, Yegor
2015-01-01
We derive quantum spectral curve equation for (q,t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin chain. This chain is spectral dual to the Seiberg-Witten integrable system associated with the AGT dual gauge theory.
Matrix models for 5d super Yang-Mills
Minahan, Joseph A
2016-01-01
In this contribution to the review on localization in gauge theories we investigate the matrix models derived from localizing N=1 super Yang-Mills on S^5. We consider the large-N limit and attempt to solve the matrix model by a saddle-point approximation. In general it is not possible to find an analytic solution, but at the weak and the strong limits of the 't Hooft coupling there are dramatic simplifications that allows us to extract most of the interesting information. At weak coupling we show that the matrix model is close to the Gaussian matrix model and that the free-energy scales as N^2. At strong coupling we show that if the theory contains one adjoint hypermultiplet then the free-energy scales as N^3. We also find the expectation value of a supersymmetric Wilson loop that wraps the equator. We demonstrate how to extract the effective couplings and reproduce results of Seiberg. Finally, we compare to results for the six-dimensional (2,0) theory derived using the AdS/CFT correspondence. We show that by...
Uncertainty relations for general unitary operators
Bagchi, Shrobona; Pati, Arun Kumar
2016-10-01
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the uncertainty relation for the unitary operators, we obtain the tight state-independent lower bound for the uncertainty of two Pauli observables and anticommuting observables in higher dimensions. With regard to the minimum-uncertainty states, we derive the minimum-uncertainty state equation by the analytic method and relate this to the ground-state problem of the Harper Hamiltonian. Furthermore, the higher-dimensional limit of the uncertainty relations and minimum-uncertainty states are explored. From an operational point of view, we show that the uncertainty in the unitary operator is directly related to the visibility of quantum interference in an interferometer where one arm of the interferometer is affected by a unitary operator. This shows a principle of preparation uncertainty, i.e., for any quantum system, the amount of visibility for two general noncommuting unitary operators is nontrivially upper bounded.
Quantum Entanglement Growth Under Random Unitary Dynamics
Nahum, Adam; Vijay, Sagar; Haah, Jeongwan
2016-01-01
Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time--dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the `entanglement tsunami' in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar--Parisi--Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like $(\\text{time})^{1/3}$ and are spatially correlated over a distance $\\propto (\\text{time})^{2/3}$. We derive KPZ universal behaviour in three complementary ways, by mapping random entanglement growth to: (i) a stochastic model of a growing surface; (ii) a `minimal cut' picture, reminisce...
Learning Hidden Markov Models using Non-Negative Matrix Factorization
Cybenko, George
2008-01-01
The Baum-Welsh algorithm together with its derivatives and variations has been the main technique for learning Hidden Markov Models (HMM) from observational data. We present an HMM learning algorithm based on the non-negative matrix factorization (NMF) of higher order Markovian statistics that is structurally different from the Baum-Welsh and its associated approaches. The described algorithm supports estimation of the number of recurrent states of an HMM and iterates the non-negative matrix factorization (NMF) algorithm to improve the learned HMM parameters. Numerical examples are provided as well.
Error correcting codes for binary unitary channels on multipartite quantum systems
Choi, M D; Kribs, D W; Zyczkowski, K; Choi, Man-Duen; Holbrook, John A.; Kribs, David W.; Zyczkowski, Karol
2006-01-01
We conduct an analysis of ideal error correcting codes for randomized unitary channels determined by two unitary error operators -- what we call ``binary unitary channels'' -- on multipartite quantum systems. In a wide variety of cases we give a complete description of the code structure for such channels. Specifically, we find a practical geometric technique to determine the existence of codes of arbitrary dimension, and then derive an explicit construction of codes of a given dimension when they exist. For instance, given any binary unitary noise model on an n-qubit system, we design codes that support n-2 qubits. We accomplish this by verifying a conjecture for higher rank numerical ranges of normal operators in many cases.
Novel differential unitary space-time modulation schemes for fast fading channels
Institute of Scientific and Technical Information of China (English)
Tian Jifeng; Jiang Haining; Song Wentao; Luo Hanwen
2006-01-01
Differential unitary space-time modulation (DUSTM), which obtains full transmit diversity in slowly flat-fading channels without channel state information, has generated significant interests recently. To combat frequency-selective fading, DUSTM has been applied to each subcarrier of an OFDM system and DUSTM-OFDM system was proposed. Both DUSTM and DUSTM-OFDM, however, are designed for slowly fading channels and suffer performance deterioration in fast fading channels. In this paper, two novel differential unitary space-time modulation schemes are proposed for fast fading channels. For fast flat-fading channels, a sub-matrix interleaved DUSTM (SMI-DUSTM) scheme is proposed, in which matrix-segmentation and sub-matrix based interleaving are introduced into DUSTM system. For fast frequency-selective fading channels, a differential unitary space-frequency modulation (DUSFM) scheme is proposed, in which existing unitary space-time codes are employed across transmit antennas and OFDM subcarriers simultaneously and differential modulation is performed between two adjacent OFDM blocks. Compared with DUSTM and DUSTM-OFDM schemes, SMI-DUSTM and DUSFM-OFDM are more robust to fast channel fading with low decoding complexity, which is demonstrated by performance analysis and simulation results.
Klein, A.A.B.; Melard, G.; Zahaf, T.
2000-01-01
The Fisher information matrix is of fundamental importance for the analysis of parameter estimation of time series models. In this paper the exact information matrix of a multivariate Gaussian time series model expressed in state space form is derived. A computationally efficient procedure is used b
Klein, A.A.B.; Melard, G.; Zahaf, T.
2000-01-01
The Fisher information matrix is of fundamental importance for the analysis of parameter estimation of time series models. In this paper the exact information matrix of a multivariate Gaussian time series model expressed in state space form is derived. A computationally efficient procedure is used b
D=0 Matrix Model as Conjugate Field Theory
Ben-Menahem, S
1993-01-01
The D=0 matrix model is reformulated as a 2d nonlocal quantum field theory. The interactions occur on the one-dimensional line of hermitian matrix eigenvalues. The field is conjugate to the density of matrix eigenvalues which appears in the Jevicki-Sakita collective field theory. The classical solution of the field equation is either unique or labeled by a discrete index. Such a solution corresponds to the Dyson sea modified by an entropy term. The modification smoothes the sea edges, and interpolates between different eigenvalue bands for multiple-well potentials. Our classical eigenvalue density contains nonplanar effects, and satisfies a local nonlinear Schr\\"odinger equation with similarities to the Marinari-Parisi $D=1$ reformulation. The quantum fluctuations about a classical solution are computable, and the IR and UV divergences are manifestly removed to all orders. The quantum corrections greatly simplify in the double scaling limit, and include both string-perturbative and nonperturbative effects.
Modelling of packet traffic with matrix analytic methods
DEFF Research Database (Denmark)
Andersen, Allan T.
1995-01-01
scenario was modelled using Markovian models. The Ordinary Differential Equations arising from these models were solved numerically. The results obtained seemed very similar to those obtained using a different method in previous work by Akinpelu & Skoog 1985. Recent measurement studies of packet traffic...... process. A heuristic formula for the tail behaviour of a single server queue fed by a superposition of renewal processes has been evaluated. The evaluation was performed by applying Matrix Analytic methods. The heuristic formula has applications in the Call Admission Control (CAC) procedure of the future...... network services i.e. 800 and 900 calls and advanced mobile communication services. The Markovian Arrival Process (MAP) has been used as a versatile tool to model the packet arrival process. Applying the MAP facilitates the use of Matrix Analytic methods to obtain performance measures associated...
Democratic Seesaw Mass Matrix Model and New Physics
Koide, Y
1998-01-01
A seesaw mass matrix model is reviewed as a unification model of quark and lepton mass matrices. The model can understand why top-quark mass m_t is so singularly enhanced compared with other quark masses, especially, why m_t >> m_b in contrast to m_u = O(m_d), and why only top-quark mass is of the order of the electroweak scale Lambda_W, i.e., m_t = O(Lambda_W). The model predicts the fourth up-quark t' with a mass m_{t'}= O(m_{W_R}), and an abnormal structure of the right-handed up-quark mixing matrix U_R^u. Possible new physics is discussed.
Black holes, quantum information, and unitary evolution
Giddings, Steven B
2012-01-01
The unitary crisis for black holes indicates an apparent need to modify local quantum field theory. This paper explores the idea that quantum mechanics and in particular unitarity are fundamental principles, but at the price of familiar locality. Thus, one should seek to parameterize unitary evolution, extending the field theory description of black holes, such that their quantum information is transferred to the external state. This discussion is set in a broader framework of unitary evolution acting on Hilbert spaces comprising subsystems. Here, various constraints can be placed on the dynamics, based on quantum information-theoretic and other general physical considerations, and one can seek to describe dynamics with "minimal" departure from field theory. While usual spacetime locality may not be a precise concept in quantum gravity, approximate locality seems an important ingredient in physics. In such a Hilbert space approach an apparently "coarser" form of localization can be described in terms of tenso...
Experimental Status of the CKM Matrix
Porter, Frank C
2016-01-01
The CKM matrix, V, relates the quark mass and flavor bases. In the standard model, V is unitary 3X3, and specified by four arbitrary parameters, including a phase allowing for $CP$ violation. We review the experimental determination of V, including the four parameters in the standard model context. This is an active field; the precision of experimental measurements and theoretical inputs continues to improve. The consistency of the determination with the standard model unitarity is investigated. While there remain some issues the overall agreement with standard model unitarity is good.
Color Energy Of A Unitary Cayley Graph
Directory of Open Access Journals (Sweden)
Adiga Chandrashekar
2014-11-01
Full Text Available Let G be a vertex colored graph. The minimum number χ(G of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G and computed the color energy of few families of graphs with χ(G colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xnc and some gcd-graphs.
Higher genus correlators from the hermitian one-matrix model
Energy Technology Data Exchange (ETDEWEB)
Ambjoern, J. (Niels Bohr Inst., Copenhagen (Denmark)); Chekhov, L. (Steklov Mathematical Inst., Moscow (Russia)); Makeenko, Yu. (Inst. of Theoretical and Experimental Physics, Moscow (Russia))
1992-05-28
We develop an iterative algorithm for the genus expansion of the hermitian NxN one-matrix model (is the Penner model in an external field). By introducing moments of the external field, we prove that the genus g contribution to the m-loop correlator depends only on 3g-2+m lower moments (3g-2 for the partition function). We present the explicit results for the partition function and the one-loop correlator in genus one. We compare the correlators for the hermitian one-matrix model with those at zero momenta for c=1 CFT and show an agreement of the one-loop correlators for genus zero. (orig.).
The CKM matrix from anti-SU(7 unification of GUT families
Directory of Open Access Journals (Sweden)
Jihn E. Kim
2015-10-01
Full Text Available We estimate the CKM matrix elements in the recently proposed minimal model, anti-SU(7 GUT for the family unification, [3]+2[2]+8[1¯]+(singlets. It is shown that the real angles of the right-handed unitary matrix diagonalizing the mass matrix can be determined to fit the Particle Data Group data. However, the phase in the right-handed unitary matrix is not constrained very much. At present, there are three classes of possible CKM parametrizations, δCKM=α,β, or γ of the unitarity triangle. For the choice of δCKM=α, it is easy to show that the phase is close to a maximal one, which has a parametrization-independent meaning.
The CKM matrix from anti-SU(7) unification of GUT families
Kim, Jihn E.; Mo, Doh Young; Seo, Min-Seok
2015-10-01
We estimate the CKM matrix elements in the recently proposed minimal model, anti-SU(7) GUT for the family unification, [ 3 ] + 2 [ 2 ] + 8 [ 1 bar ] +(singlets). It is shown that the real angles of the right-handed unitary matrix diagonalizing the mass matrix can be determined to fit the Particle Data Group data. However, the phase in the right-handed unitary matrix is not constrained very much. At present, there are three classes of possible CKM parametrizations, δCKM = α , β, or γ of the unitarity triangle. For the choice of δCKM = α, it is easy to show that the phase is close to a maximal one, which has a parametrization-independent meaning.
Universal Structure and Universal PDE for Unitary Ensembles
Rumanov, Igor
2009-01-01
An attempt is made to describe random matrix ensembles with unitary invariance of measure (UE) in a unified way, using a combination of Tracy-Widom (TW) and Adler-Shiota-Van Moerbeke (ASvM) approaches to derivation of partial differential equations (PDE) for spectral gap probabilities. First, general 3-term recurrence relations for UE restricted to subsets of real line, or, in other words, for functions in the resolvent kernel, are obtained. Using them, simple universal relations between all TW dependent variables and one-dimensional Toda lattice $\\tau$-functions are found. A universal system of PDE for UE is derived from previous relations, which leads also to a {\\it single independent PDE} for spectral gap probability of various UE. Thus, orthogonal function bases and Toda lattice are seen at the core of correspondence of different approaches. Moreover, Toda-AKNS system provides a common structure of PDE for unitary ensembles. Interestingly, this structure can be seen in two very different forms: one arises...
Boson-Faddeev in the Unitary Limit and Efimov States
K"\\ohler, H S
2010-01-01
A numerical study of the Faddeev equation for bosons is made with two-body interactions at or close to the Unitary limit. Separable interactions are obtained from phase-shifts defined by scattering length and effective range. In EFT-language this would correspond to NLO. Both ground and Efimov state energies are calculated. For effective ranges $r_0 > 0$ and rank-1 potentials the total energy $E_T$ is found to converge with momentum cut-off $\\Lambda$ for $\\Lambda > \\sim 10/r_0$ . In the Unitary limit ($1/a=r_0= 0$) the energy does however diverge. It is shown (analytically) that in this case $E_T=E_u\\Lambda^2$. Calculations give $E_u=-0.108$ for the ground state and $E_u=-1.\\times10^{-4}$ for the single Efimov state found. The cut-off divergence is remedied by modifying the off-shell t-matrix by replacing the rank-1 by a rank-2 phase-shift equivalent potential. This is somewhat similar to the counterterm method suggested by Bedaque et al. This investigation is exploratory and does not refer to any specific ph...
Matrix Factorizations for Local F-Theory Models
Omer, Harun
2016-01-01
I use matrix factorizations to describe branes at simple singularities as they appear in elliptic fibrations of local F-theory models. Each node of the corresponding Dynkin diagrams of the ADE-type singularities is associated with one indecomposable matrix factorization which can be deformed into one or more factorizations of lower rank. Branes with internal fluxes arise naturally as bound states of the indecomposable factorizations. Describing branes in such a way avoids the need to resolve singularities and encodes information which is neglected in conventional F-theory treatments. This paper aims to show how branes arising in local F-theory models around simple singularities can be described in this framework.
Four-point function in the IOP matrix model
Michel, Ben; Polchinski, Joseph; Rosenhaus, Vladimir; Suh, S. Josephine
2016-05-01
The IOP model is a quantum mechanical system of a large- N matrix oscillator and a fundamental oscillator, coupled through a quartic interaction. It was introduced previously as a toy model of the gauge dual of an AdS black hole, and captures a key property that at infinite N the two-point function decays to zero on long time scales. Motivated by recent work on quantum chaos, we sum all planar Feynman diagrams contributing to the four-point function. We find that the IOP model does not satisfy the more refined criteria of exponential growth of the out-of-time-order four-point function.
Four-point function in the IOP matrix model
Michel, Ben; Rosenhaus, Vladimir; Suh, S Josephine
2016-01-01
The IOP model is a quantum mechanical system of a large-$N$ matrix oscillator and a fundamental oscillator, coupled through a quartic interaction. It was introduced previously as a toy model of the gauge dual of an AdS black hole, and captures a key property that at infinite $N$ the two-point function decays to zero on long time scales. Motivated by recent work on quantum chaos, we sum all planar Feynman diagrams contributing to the four-point function. We find that the IOP model does not satisfy the more refined criteria of exponential growth of the out-of-time-order four-point function.
Bayes linear covariance matrix adjustment for multivariate dynamic linear models
Wilkinson, Darren J
2008-01-01
A methodology is developed for the adjustment of the covariance matrices underlying a multivariate constant time series dynamic linear model. The covariance matrices are embedded in a distribution-free inner-product space of matrix objects which facilitates such adjustment. This approach helps to make the analysis simple, tractable and robust. To illustrate the methods, a simple model is developed for a time series representing sales of certain brands of a product from a cash-and-carry depot. The covariance structure underlying the model is revised, and the benefits of this revision on first order inferences are then examined.
Developmental Dyspraxia: Is It a Unitary Function?
Ayres, A. Jean; And Others
1987-01-01
A group of 182 children (ages four through nine) with known or suspected sensory integrative dysfunction were assessed using tests and clinical observations to examine developmental dyspraxia. The study did not justify the existence of either a unitary function or different types of developmental dyspraxia. (Author/CH)
Renormalization of 3d quantum gravity from matrix models
Ambjørn, Jan; Loll, R
2004-01-01
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively non-renormalizable even in three dimensions. By mapping the three-dimensional theory to a two-matrix model with ABAB interaction we show that both the cosmological and the (perturbatively) non-renormalizable gravitational coupling constant undergo additive renormalizations consistent with canonical quantization.
M(atrix) model interaction with 11D supergravity
Bandos, Igor A
2010-01-01
We present the equations of motion for multiple M0-brane (mM0) system in an arbitrary curved supergravity superspace which generalizes the M(atrix) model equations for the case of arbitrary supergravity background. Although these were obtained in the frame of superembedding approach to mM0, we do not make a review of this approach in this contribution but concentrate discussion on the structure of the equations.
Fuzzy Spacetime with SU(3) Isometry in IIB Matrix Model
Kaneko, H; Tomino, D
2005-01-01
A group of fuzzy spacetime with SU(3) isometry is studied at the two loop level in IIB matrix model. It consists of spacetime from 4 to 6 dimensions, namely from CP2 to SU(3)/U(1)x U(1). The effective action scales in a universal manner in the large N limit as N and N^{4/3} on 4 and 6 dimensional manifolds respectively. The 4 dimensional spacetime CP2 possesses the smallest effective action in this class.
Free energy topological expansion for the 2-matrix model
Energy Technology Data Exchange (ETDEWEB)
Chekhov, Leonid [Steklov Mathematical Institute, ITEP and Poncelet Laboratoire, Moscow (Russian Federation); Eynard, Bertrand [Service de Physique Theorique de Saclay, F-91191 Gif-sur-Yvette Cedex (France); Orantin, Nicolas [Service de Physique Theorique de Saclay, F-91191 Gif-sur-Yvette Cedex (France)
2006-12-15
We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/N expansion of the nonmixed correlation functions and give a new formulation of the spectral curve. We extend these rules obtaining a closed formula for correlation functions in all orders of topological expansion. We then integrate it to obtain the free energy in terms of residues on the associated Riemann surface.
Dirac cohomology of unitary representations of equal rank exceptional groups
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we consider the unitary representations of equal rank exceptional groups of type E with a regular lambda-lowest K-type and classify those unitary representations with the nonzero Dirac cohomology.
Alvarez-Gaumé, Luís; Marino, M; Wadia, S R; Alvarez-Gaume, Luis; Basu, Pallab; Marino, Marcos; Wadia, Spenta R.
2006-01-01
In this paper we discuss the blackhole-string transition of the small Schwarzschild blackhole of $AdS_5 \\times S^5$ using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak {\\it and} strong coupling, can be expressed entirely in terms of constant Polyakov lines which are $SU (N)$ matrices. In showing this we have taken into account that there are no Nambu-Goto modes associated with the fact that the 10 dimensional blackhole solution sits at a point in $S^5$. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order $N = \\infty$ phase transition with the blackhole-string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of $N^{-2/3}$. The $N = \\infty$ transition now becomes a smooth crossover in terms of a renormalized string c...
Unitary evolution for a quantum Kantowski-Sachs cosmology
Pal, Sridip
2015-01-01
It is shown that like Bianchi I, V and IX models, a Kantowski-Sachs cosmological model also allows a unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of the anisotropy. Non-unitarity, if there is any, cannot escape notice in this as the evolution is studied against a properly oriented time parameter fixed by the evolution of the fluid. Furthermore, we have constructed a wave-packet by superposing different energy eigenstates, thereby establishing unitarity in a non-trivial way, which is a stronger result than an energy eigenstate trivially giving time independent probability density. For $\\alpha\
Chiral matrix model of the semi-QGP in QCD
Pisarski, Robert D.; Skokov, Vladimir V.
2016-08-01
Previously, a matrix model of the region near the transition temperature, in the "semi"quark gluon plasma, was developed for the theory of S U (3 ) gluons without quarks. In this paper we develop a chiral matrix model applicable to QCD by including dynamical quarks with 2 +1 flavors. This requires adding a nonet of scalar fields, with both parities, and coupling these to quarks through a Yukawa coupling, y . Treating the scalar fields in mean field approximation, the effective Lagrangian is computed by integrating out quarks to one loop order. As is standard, the potential for the scalar fields is chosen to be symmetric under the flavor symmetry of S U (3 )L×S U (3 )R×Z (3 )A, except for a term linear in the current quark mass, mqk. In addition, at a nonzero temperature T it is necessary to add a new term, ˜mqkT2. The parameters of the gluon part of the matrix model are identical to those for the pure glue theory without quarks. The parameters in the chiral matrix model are fixed by the values, at zero temperature, of the pion decay constant and the masses of the pions, kaons, η , and η'. The temperature for the chiral crossover at Tχ=155 MeV is determined by adjusting the Yukawa coupling y . We find reasonable agreement with the results of numerical simulations on the lattice for the pressure and related quantities. In the chiral limit, besides the divergence in the chiral susceptibility there is also a milder divergence in the susceptibility between the Polyakov loop and the chiral order parameter, with critical exponent β -1 . We compute derivatives with respect to a quark chemical potential to determine the susceptibilities for baryon number, the χ2 n. Especially sensitive tests are provided by χ4-χ2 and by χ6, which changes in sign about Tχ. The behavior of the susceptibilities in the chiral matrix model strongly suggests that as the temperature increases from Tχ, that the transition to deconfinement is significantly quicker than indicated by the
Mechanical model for a collagen fibril pair in extracellular matrix.
Chan, Yue; Cox, Grant M; Haverkamp, Richard G; Hill, James M
2009-04-01
In this paper, we model the mechanics of a collagen pair in the connective tissue extracellular matrix that exists in abundance throughout animals, including the human body. This connective tissue comprises repeated units of two main structures, namely collagens as well as axial, parallel and regular anionic glycosaminoglycan between collagens. The collagen fibril can be modeled by Hooke's law whereas anionic glycosaminoglycan behaves more like a rubber-band rod and as such can be better modeled by the worm-like chain model. While both computer simulations and continuum mechanics models have been investigated for the behavior of this connective tissue typically, authors either assume a simple form of the molecular potential energy or entirely ignore the microscopic structure of the connective tissue. Here, we apply basic physical methodologies and simple applied mathematical modeling techniques to describe the collagen pair quantitatively. We found that the growth of fibrils was intimately related to the maximum length of the anionic glycosaminoglycan and the relative displacement of two adjacent fibrils, which in return was closely related to the effectiveness of anionic glycosaminoglycan in transmitting forces between fibrils. These reveal the importance of the anionic glycosaminoglycan in maintaining the structural shape of the connective tissue extracellular matrix and eventually the shape modulus of human tissues. We also found that some macroscopic properties, like the maximum molecular energy and the breaking fraction of the collagen, were also related to the microscopic characteristics of the anionic glycosaminoglycan.
Ren, Shiwei; Ma, Xiaochuan; Yan, Shefeng; Hao, Chengpeng
2013-03-28
A unitary transformation-based algorithm is proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals. The problem is solved by reorganizing the covariance matrix into a block Hankel one for decorrelation first and then reconstructing a new matrix to facilitate the unitary transformation. By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly. In addition, a fast and computationally attractive realization of the 2-D unitary transformation is given by making a Kronecker product of the 1-D matrices. Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry. The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signalsmore thoroughly. Simulation results and computational order analysis are presented to verify the validity and effectiveness of the proposed algorithm.
Directory of Open Access Journals (Sweden)
Chengpeng Hao
2013-03-01
Full Text Available A unitary transformation-based algorithm is proposed for two-dimensional (2-D direction-of-arrival (DOA estimation of coherent signals. The problem is solved by reorganizing the covariance matrix into a block Hankel one for decorrelation first and then reconstructing a new matrix to facilitate the unitary transformation. By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly. In addition, a fast and computationally attractive realization of the 2-D unitary transformation is given by making a Kronecker product of the 1-D matrices. Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry. The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT-Like method and the forward-backward averaging, which can decorrelate the impinging signalsmore thoroughly. Simulation results and computational order analysis are presented to verify the validity and effectiveness of the proposed algorithm.
Liu, Alan S.; Wang, Hailong; Copeland, Craig R.; Chen, Christopher S.; Shenoy, Vivek B.; Reich, Daniel H.
2016-01-01
The biomechanical behavior of tissues under mechanical stimulation is critically important to physiological function. We report a combined experimental and modeling study of bioengineered 3D smooth muscle microtissues that reveals a previously unappreciated interaction between active cell mechanics and the viscoplastic properties of the extracellular matrix. The microtissues’ response to stretch/unstretch actuations, as probed by microcantilever force sensors, was dominated by cellular actomyosin dynamics. However, cell lysis revealed a viscoplastic response of the underlying model collagen/fibrin matrix. A model coupling Hill-type actomyosin dynamics with a plastic perfectly viscoplastic description of the matrix quantitatively accounts for the microtissue dynamics, including notably the cells’ shielding of the matrix plasticity. Stretch measurements of single cells confirmed the active cell dynamics, and were well described by a single-cell version of our model. These results reveal the need for new focus on matrix plasticity and its interactions with active cell mechanics in describing tissue dynamics. PMID:27671239
H∞ /H2 model reduction through dilated linear matrix inequalities
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
2012-01-01
This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field...... not satisfactorily approximates the original system, an iterative algorithm based on dilated LMIs is proposed to significantly improve the approximation bound. The effectiveness of the method is accessed by numerical experiments. The method is also applied to the $H_2$ order reduction of a flexible wind turbine...
Topological expansion for the Cauchy two-matrix model
Energy Technology Data Exchange (ETDEWEB)
Bertola, M [Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve W, Montreal, Quebec H3G 1M8 (Canada); Ferrer, A Prats [Centre de recherches mathematiques, Universite de Montreal, 2920 Chemin de la tour, Montreal, Quebec H3T 1J4 (Canada)], E-mail: bertola@crm.umontreal.ca, E-mail: pratsferrer@crm.umontreal.ca
2009-08-21
Recently, a two-matrix model with a new type of interaction (Bertola et al 2009 Commun. Math. Phys. 287 983-1014) has been introduced and analyzed using bi-orthogonal polynomial techniques. Here we present the complete 1/N{sup 2} expansion for the formal version of this model, following the spirit of Eynard and Orantin (2005 J. High Energy Phys. JHEP12(2005)034), and Chekhov and Eynard (2006 J. High Energy Phys. JHEP03(2006)014), i.e. the full expansion for the non-mixed resolvent correlators and for the free energies.
Derivation of stiffness matrix in constitutive modeling of magnetorheological elastomer
Leng, D.; Sun, L.; Sun, J.; Lin, Y.
2013-02-01
Magnetorheological elastomers (MREs) are a class of smart materials whose mechanical properties change instantly by the application of a magnetic field. Based on the specially orthotropic, transversely isotropic stress-strain relationships and effective permeability model, the stiffness matrix of constitutive equations for deformable chain-like MRE is considered. To valid the components of shear modulus in this stiffness matrix, the magnetic-structural simulations with finite element method (FEM) are presented. An acceptable agreement is illustrated between analytical equations and numerical simulations. For the specified magnetic field, sphere particle radius, distance between adjacent particles in chains and volume fractions of ferrous particles, this constitutive equation is effective to engineering application to estimate the elastic behaviour of chain-like MRE in an external magnetic field.
Random Matrix Model for Nakagami-Hoyt Fading
Kumar, Santosh; 10.1109/TIT.2010.2044060
2011-01-01
Random matrix model for the Nakagami-q (Hoyt) fading in multiple-input multiple-output (MIMO) communication channels with arbitrary number of transmitting and receiving antennas is considered. The joint probability density for the eigenvalues of H{\\dag}H (or HH{\\dag}), where H is the channel matrix, is shown to correspond to the Laguerre crossover ensemble of random matrices and is given in terms of a Pfaffian. Exact expression for the marginal density of eigenvalues is obtained as a series consisting of associated Laguerre polynomials. This is used to study the effect of fading on the Shannon channel capacity. Exact expressions for higher order density correlation functions are also given which can be used to study the distribution of channel capacity.
Identical Wells, Symmetry Breaking, and the Near-Unitary Limit
Harshman, N. L.
2017-03-01
Energy level splitting from the unitary limit of contact interactions to the near unitary limit for a few identical atoms in an effectively one-dimensional well can be understood as an example of symmetry breaking. At the unitary limit in addition to particle permutation symmetry there is a larger symmetry corresponding to exchanging the N! possible orderings of N particles. In the near unitary limit, this larger symmetry is broken, and different shapes of traps break the symmetry to different degrees. This brief note exploits these symmetries to present a useful, geometric analogy with graph theory and build an algebraic framework for calculating energy splitting in the near unitary limit.
Unitary cycles on Shimura curves and the Shimura lift II
Sankaran, Siddarth
2013-01-01
We consider two families of arithmetic divisors defined on integral models of Shimura curves. The first was studied by Kudla, Rapoport and Yang, who proved that if one assembles these divisors in a formal generating series, one obtains the q-expansion of a modular form of weight 3/2. The present work concerns the Shimura lift of this modular form: we identify the Shimura lift with a generating series comprised of unitary divisors, which arose in recent work of Kudla and Rapoport regarding cyc...
Directory of Open Access Journals (Sweden)
N. A. Vunder
2016-03-01
Full Text Available Subject of Research.The paper deals with the problem of required placement of state matrix modes in the system being designed.Methods.The problem has been solved with the use of vector matrix formalism of state space method with the dominant attention at the algebraic properties of the object control matrix. Main Results. Algebraic conditions have been obtained imposed on the matrix components of control plant and system models, which has helped to create the algorithms for solving the tasks without necessarily resorting to matrix Sylvester equation and Ackermann's formula. Practical Relevance. User’s base of algorithms for synthesis procedures of control systems with specified quality indices has been extended.
Reduced M(atrix) theory models: ground state solutions
López, J L
2015-01-01
We propose a method to find exact ground state solutions to reduced models of the SU($N$) invariant matrix model arising from the quantization of the 11-dimensional supermembrane action in the light-cone gauge. We illustrate the method by applying it to lower dimensional toy models and for the SU(2) group. This approach could, in principle, be used to find ground state solutions to the complete 9-dimensional model and for any SU($N$) group. The Hamiltonian, the supercharges and the constraints related to the SU($2$) symmetry are built from operators that generate a multicomponent spinorial wave function. The procedure is based on representing the fermionic degrees of freedom by means of Dirac-like gamma matrices, as was already done in the first proposal of supersymmetric (SUSY) quantum cosmology. We exhibit a relation between these finite $N$ matrix theory ground state solutions and SUSY quantum cosmology wave functions giving a possible physical significance of the theory even for finite $N$.
A hint on the external field problem for matrix models
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L. (Steklov Mathematical Inst., Moscow (USSR)); Makeenko, Y. (Niels Bohr Inst., Copenhagen (Denmark) Inst. of Theoretical and Experimental Physics, Moscow (USSR))
1992-03-26
We reexamine the external field problem for NxN hermitian one-matrix model. We prove an equivalence of the models with the potentials tr ((1/2N)X{sup 2}+log X-{Lambda}X) and {Sigma}{sub k=1}{sup {infinity}}t{sub k} to X{sup k} provided the matrix {Lambda} is related to {l brace}t{sub k}{r brace} by t{sub k}=(1/k)tr{Lambda}{sup -k}-(N/2){delta}{sub k2}. Based on this equivalence we formulate a method for calculating the partition function by solving the Schwinger-Dyson equations order by order of genus expansion. Explicit calculations of the partition function and of correlators of conformal operators with the puncture operator are presented in genus one. These results support the conjecture that our models are associated with the c=1 case in the same sense as the Kontsevich model describes c=0. (orig.).
Matrix population models from 20 studies of perennial plant populations
Ellis, Martha M.; Williams, Jennifer L.; Lesica, Peter; Bell, Timothy J.; Bierzychudek, Paulette; Bowles, Marlin; Crone, Elizabeth E.; Doak, Daniel F.; Ehrlen, Johan; Ellis-Adam, Albertine; McEachern, Kathryn; Ganesan, Rengaian; Latham, Penelope; Luijten, Sheila; Kaye, Thomas N.; Knight, Tiffany M.; Menges, Eric S.; Morris, William F.; den Nijs, Hans; Oostermeijer, Gerard; Quintana-Ascencio, Pedro F.; Shelly, J. Stephen; Stanley, Amanda; Thorpe, Andrea; Tamara, Ticktin; Valverde, Teresa; Weekley, Carl W.
2012-01-01
Demographic transition matrices are one of the most commonly applied population models for both basic and applied ecological research. The relatively simple framework of these models and simple, easily interpretable summary statistics they produce have prompted the wide use of these models across an exceptionally broad range of taxa. Here, we provide annual transition matrices and observed stage structures/population sizes for 20 perennial plant species which have been the focal species for long-term demographic monitoring. These data were assembled as part of the 'Testing Matrix Models' working group through the National Center for Ecological Analysis and Synthesis (NCEAS). In sum, these data represent 82 populations with >460 total population-years of data. It is our hope that making these data available will help promote and improve our ability to monitor and understand plant population dynamics.
Bang, Jeongho; Yoo, Seokwon
2014-12-01
We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the "genetic parameter vector" of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the often-called Deutsch problem. By numerical simulations, we can faithfully find the appropriate unitary transformations to solve the problem by using our method. We analyze the quantum algorithms identified by the found unitary transformations and generalize the variant models of the original Deutsch's algorithm.
Energy Technology Data Exchange (ETDEWEB)
Bang, Jeongho [Seoul National University, Seoul (Korea, Republic of); Hanyang University, Seoul (Korea, Republic of); Yoo, Seokwon [Hanyang University, Seoul (Korea, Republic of)
2014-12-15
We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the 'genetic parameter vector' of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the often-called Deutsch problem. By numerical simulations, we can faithfully find the appropriate unitary transformations to solve the problem by using our method. We analyze the quantum algorithms identified by the found unitary transformations and generalize the variant models of the original Deutsch's algorithm.
An Uncertainty Structure Matrix for Models and Simulations
Green, Lawrence L.; Blattnig, Steve R.; Hemsch, Michael J.; Luckring, James M.; Tripathi, Ram K.
2008-01-01
Software that is used for aerospace flight control and to display information to pilots and crew is expected to be correct and credible at all times. This type of software is typically developed under strict management processes, which are intended to reduce defects in the software product. However, modeling and simulation (M&S) software may exhibit varying degrees of correctness and credibility, depending on a large and complex set of factors. These factors include its intended use, the known physics and numerical approximations within the M&S, and the referent data set against which the M&S correctness is compared. The correctness and credibility of an M&S effort is closely correlated to the uncertainty management (UM) practices that are applied to the M&S effort. This paper describes an uncertainty structure matrix for M&S, which provides a set of objective descriptions for the possible states of UM practices within a given M&S effort. The columns in the uncertainty structure matrix contain UM elements or practices that are common across most M&S efforts, and the rows describe the potential levels of achievement in each of the elements. A practitioner can quickly look at the matrix to determine where an M&S effort falls based on a common set of UM practices that are described in absolute terms that can be applied to virtually any M&S effort. The matrix can also be used to plan those steps and resources that would be needed to improve the UM practices for a given M&S effort.
Scrambling with matrix black holes
Brady, Lucas; Sahakian, Vatche
2013-08-01
If black holes are not to be dreaded sinks of information but rather fully described by unitary evolution, they must scramble in-falling data and eventually leak it through Hawking radiation. Sekino and Susskind have conjectured that black holes are fast scramblers; they generate entanglement at a remarkably efficient rate, with the characteristic time scaling logarithmically with the entropy. In this work, we focus on Matrix theory—M-theory in the light-cone frame—and directly probe the conjecture. We develop a concrete test bed for quantum gravity using the fermionic variables of Matrix theory and show that the problem becomes that of chains of qubits with an intricate network of interactions. We demonstrate that the black hole system evolves much like a Brownian quantum circuit, with strong indications that it is indeed a fast scrambler. We also analyze the Berenstein-Maldacena-Nastase model and reach the same tentative conclusion.
On unitary reconstruction of linear optical networks
Tillmann, Max; Walther, Philip
2015-01-01
Linear optical elements are pivotal instruments in the manipulation of classical and quantum states of light. The vast progress in integrated quantum photonic technology enables the implementation of large numbers of such elements on chip while providing interferometric stability. As a trade-off these structures face the intrinsic challenge of characterizing their optical transformation as individual optical elements are not directly accessible. Thus the unitary transformation needs to be reconstructed from a dataset generated with having access to the input and output ports of the device only. Here we present a novel approach to unitary reconstruction that significantly improves upon existing approaches. We compare its performance to several approaches via numerical simulations for networks up to 14 modes. We show that an adapted version of our approach allows to recover all mode-dependent losses and to obtain highest reconstruction fidelities under such conditions.
Unitary and room air-conditioners
Energy Technology Data Exchange (ETDEWEB)
Christian, J.E.
1977-09-01
The scope of this technology evaluation on room and unitary air conditioners covers the initial investment and performance characteristics needed for estimating the operating cost of air conditioners installed in an ICES community. Cooling capacities of commercially available room air conditioners range from 4000 Btu/h to 36,000 Btu/h; unitary air conditioners cover a range from 6000 Btu/h to 135,000 Btu/h. The information presented is in a form useful to both the computer programmer in the construction of a computer simulation of the packaged air-conditioner's performance and to the design engineer, interested in selecting a suitably sized and designed packaged air conditioner.
Scalable Noise Estimation with Random Unitary Operators
Emerson, J; Zyczkowski, K; Emerson, Joseph; Alicki, Robert; Zyczkowski, Karol
2005-01-01
We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random unitary operators. In the simplest case our method enables direct estimation of the average gate fidelity. The more general fidelities are characterized by a universal exponential rate of fidelity loss. In all cases the measurable fidelity decrease is directly related to the strength of the noise affecting the implementation -- quantified by the trace of the superoperator describing the non--unitary dynamics. While the scalability of our stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), our method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device. By varying over different experimental arrangements and error-correction strategies a...
Scalable noise estimation with random unitary operators
Energy Technology Data Exchange (ETDEWEB)
Emerson, Joseph [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Alicki, Robert [Institute of Theoretical Physics and Astrophysics, University of Gdansk, Wita Stwosza 57, PL 80-952 Gdansk (Poland); Zyczkowski, Karol [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2005-10-01
We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random unitary operators. In the simplest case our method enables direct estimation of the average gate fidelity. The more general fidelities are characterized by a universal exponential rate of fidelity loss. In all cases the measurable fidelity decrease is directly related to the strength of the noise affecting the implementation, quantified by the trace of the superoperator describing the non-unitary dynamics. While the scalability of our stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), our method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device. By varying over different experimental arrangements and error-correction strategies, additional information about the noise can be determined.
Generalized Unitaries and the Picard Group
Indian Academy of Sciences (India)
Michael Skeide
2006-11-01
After discussing some basic facts about generalized module maps, we use the representation theory of the algebra $\\mathscr{B}^a(E)$ of adjointable operators on a Hilbert $\\mathcal{B}$-module to show that the quotient of the group of generalized unitaries on and its normal subgroup of unitaries on is a subgroup of the group of automorphisms of the range ideal $\\mathcal{B}_E$ of in $\\mathcal{B}$. We determine the kernel of the canonical mapping into the Picard group of $\\mathcal{B}_E$ in terms of the group of quasi inner automorphisms of $\\mathcal{B}_E$. As a by-product we identify the group of bistrict automorphisms of the algebra of adjointable operators on modulo inner automorphisms as a subgroup of the (opposite of the) Picard group.
Recurrence for discrete time unitary evolutions
Grünbaum, F A; Werner, A H; Werner, R F
2012-01-01
We consider quantum dynamical systems specified by a unitary operator U and an initial state vector \\phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We call the system recurrent if this eventually happens with probability one. We show that recurrence is equivalent to the absence of an absolutely continuous part from the spectral measure of U with respect to \\phi. We also show that in the recurrent case the expected first return time is an integer or infinite, for which we give a topological interpretation. A key role in our theory is played by the first arrival amplitudes, which turn out to be the (complex conjugated) Taylor coefficients of the Schur function of the spectral measure. On the one hand, this provides a direct dynamical interpretation of these coefficients; on the other hand it links our definition of first return times to a large body of mathematical literature.
Kitaev honeycomb tensor networks: exact unitary circuits and applications
Schmoll, Philipp
2016-01-01
The Kitaev honeycomb model is a paradigm of exactly-solvable models, showing non-trivial physical properties such as topological quantum order, abelian and non-abelian anyons, and chirality. Its solution is one of the most beautiful examples of the interplay of different mathematical techniques in condensed matter physics. In this paper, we show how to derive a tensor network (TN) description of the eigenstates of this spin-1/2 model in the thermodynamic limit, and in particular for its ground state. In our setting, eigenstates are naturally encoded by an exact 3d TN structure made of fermionic unitary operators, corresponding to the unitary quantum circuit building up the many-body quantum state. In our derivation we review how the different "solution ingredients" of the Kitaev honeycomb model can be accounted for in the TN language, namely: Jordan-Wigner transformation, braidings of Majorana modes, fermionic Fourier transformation, and Bogoliubov transformation. The TN built in this way allows for a clear u...
Complex saddles in the Gross-Witten-Wadia matrix model
Álvarez, Gabriel; Medina, Elena
2016-01-01
We give an exhaustive characterization of the complex saddle point configurations of the Gross-Witten-Wadia matrix model in the large-N limit. In particular, we characterize the cases in which the saddles accumulate in one, two, or three arcs, in terms of the values of the coupling constant and of the fraction of the total unit density that is supported in one of the arcs, and derive an explicit condition for gap closing associated to nonvacuum saddles. By applying the idea of large-N instanton we also give direct analytic derivations of the weak-coupling and strong-coupling instanton actions.
Scale invariant behavior in a large N matrix model
Narayanan, Rajamani
2016-01-01
Eigenvalue distributions of properly regularized Wilson loop operators are used to study the transition from ultra-violet (UV) behavior to infra-red (IR) behavior in gauge theories coupled to matter that potentially have an IR fixed point (FP). We numerically demonstrate emergence of scale invariance in a matrix model that describes $SU(N)$ gauge theory coupled to two flavors of massless adjoint fermions in the large $N$ limit. The eigenvalue distribution of Wilson loops of varying sizes cannot be described by a universal lattice beta-function connecting the UV to the IR.
Approximate State Transition Matrix and Secular Orbit Model
Directory of Open Access Journals (Sweden)
M. P. Ramachandran
2015-01-01
Full Text Available The state transition matrix (STM is a part of the onboard orbit determination system. It is used to control the satellite’s orbital motion to a predefined reference orbit. Firstly in this paper a simple orbit model that captures the secular behavior of the orbital motion in the presence of all perturbation forces is derived. Next, an approximate STM to match the secular effects in the orbit due to oblate earth effect and later in the presence of all perturbation forces is derived. Numerical experiments are provided for illustration.
Transfer matrix methods in the Blume-Emery-Griffiths model
Koza, Zbigniew; Jasiukiewicz, Czesa̵w; Pȩkalski, Andrzej
1990-03-01
The critical properties of the plane Blume-Emery-Griffiths (BEG) model are analyzed using two transfer matrix approaches. The two methods and the domains of their applicability are discussed. The phase diagram is derived and compared with the one obtained by the position-space renormalization group (PSRG). The critical indices η i and conformal anomaly c are computed at Ising-like and Potts-like critical points and a good agreement with the conformal invariance predictions is found. A new, very effective method of estimating critical points is introduced and an attempt to estimate critical end points is also made.
THE BONUS-MALUS SYSTEM MODELLING USING THE TRANSITION MATRIX
Directory of Open Access Journals (Sweden)
SANDRA TEODORESCU
2012-05-01
Full Text Available The motor insurance is an important branch of non-life insurance in many countries; in some of them, coming first in total premium income category (in Romania, for example. The Bonus-Malus system implementation is one of the solutions chosen by the insurance companies in order to increase the efficiency in the motor insurance domain. This system has been recently introduced by the Romanian insurers as well. In this paper I present the means for modelling the bonus-malus system using the transition matrix.
Integral Compressor/Generator/Fan Unitary Structure
Dreiman, Nelik
2016-01-01
INTEGRAL COMPRESSOR / GENERATOR / FAN UNITARY STRUCTURE.*) Dr. Nelik Dreiman Consultant, P.O.Box 144, Tipton, MI E-mail: An extremely compact, therefore space saving single compressor/generator/cooling fan structure of short axial length and light weight has been developed to provide generation of electrical power with simultaneous operation of the compressor when power is unavailable or function as a regular AC compressor powered by a power line. The generators and ai...
Unitary representations and harmonic analysis an introduction
Sugiura, M
1990-01-01
The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou''s theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.
Matrix models with Penner interaction inspired by interacting ribonucleic acid
Indian Academy of Sciences (India)
Pradeep Bhadola; N Deo
2015-02-01
The Penner interaction known in studies of moduli space of punctured Riemann surfaces is introduced and studied in the context of random matrix model of homo RNA. An analytic derivation of the generating function is given and the corresponding partition function is derived numerically. An additional dependence of the structure combinatorics factor on (related to the size of the matrix and the interaction strength) is obtained. This factor has a strong effect on the structure combinatorics in the low regime. Databases are scanned for real ribonucleic acid (RNA) structures and pairing information for these RNA structures is computationally extracted. Then the genus is calculated for every structure and plotted as a function of length. The genus distribution function is compared with the prediction from the nonlinear (NL) model. The specific heat and distribution of structure with temperature calculated from the NL model shows that the NL inter-action is biased towards planar structures. The second derivative of specific heat changes phase from a double peaked function for small to a single peak for large . Detailed analysis reveals the presence of the double peak only for genus 0 structures, the higher genii behave normally with . Comparable behaviour is found in studies involving interactions of RNA with osmolytes and monovalent cations in unfolding experiments.
Chiral condensate in the Schwinger model with matrix product operators
Energy Technology Data Exchange (ETDEWEB)
Banuls, Mari Carmen [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Poznan Univ. (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, Hana [Tsukuba Univ. (Japan). Center for Computational Sciences
2016-03-15
Tensor network (TN) methods, in particular the Matrix Product States (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the non-zero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chiral symmetry breaking in the massless and massive cases and show that the method works very well and gives good control over a broad range of temperatures, essentially from zero to infinite temperature.
Modeling cell-matrix traction forces in Keratinocyte colonies
Banerjee, Shiladitya
2013-03-01
Crosstalk between cell-cell and cell-matrix adhesions plays an essential role in the mechanical function of tissues. The traction forces exerted by cohesive keratinocyte colonies with strong cell-cell adhesions are mostly concentrated at the colony periphery. In contrast, for weak cadherin-based intercellular adhesions, individual cells in a colony interact with their matrix independently, with a disorganized distribution of traction forces extending throughout the colony. In this talk I will present a minimal physical model of the colony as contractile elastic media linked by springs and coupled to an elastic substrate. The model captures the spatial distribution of traction forces seen in experiments. For cell colonies with strong cell-cell adhesions, the total traction force of the colony measured in experiments is found to scale with the colony's geometrical size. This scaling suggests the emergence of an effective surface tension of magnitude comparable to that measured for non-adherent, three-dimensional cell aggregates. The physical model supports the scaling and indicates that the surface tension may be controlled by acto-myosin contractility. Supported by the NSF through grant DMR-1004789. This work was done in collaboration with Aaron F. Mertz, Eric R. Dufresne and Valerie Horsley (Yale University) and M. Cristina Marchetti (Syracuse University).
Chiral condensate in the Schwinger model with Matrix Product Operators
Bañuls, Mari Carmen; Jansen, Karl; Saito, Hana
2016-01-01
Tensor network (TN) methods, in particular the Matrix Product States (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the non-zero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chir...
Chiral condensate in the Schwinger model with matrix product operators
Bañuls, Mari Carmen; Cichy, Krzysztof; Jansen, Karl; Saito, Hana
2016-05-01
Tensor network (TN) methods, in particular the matrix product states (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the nonzero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chiral symmetry breaking in the massless and massive cases and show that the method works very well and gives good control over a broad range of temperatures, essentially from zero to infinite temperature.
Optimal control theory for unitary transformations
Palao, J P; Palao, Jose P.
2003-01-01
The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory (OCT) is used to solve the inversion problem irrespective of the initial input state. A unified formalism, based on the Krotov method is developed leading to a new scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X^1\\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\\Sigma^+_u$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-...
Equivalence of Matrix Models for Complex QCD Dirac Spectra
Akemann, G
2003-01-01
Two different matrix models for QCD with a non-vanishing quark chemical potential are shown to be equivalent by mapping the corresponding partition functions. The equivalence holds in the phase with broken chiral symmetry. It is exact in the limit of weak non-Hermiticity, where the chemical potential squared is rescaled with the volume. At strong non-Hermiticity it holds only for small chemical potential. The first model proposed by Stephanov is directly related to QCD and allows to analyze the QCD phase diagram. In the second model suggested by the author all microscopic spectral correlation functions of complex Dirac operators can be calculated in the broken phase. We briefly compare those predictions to complex Dirac eigenvalues from quenched QCD lattice simulations.
Recent developments in the type IIB matrix model
Nishimura, Jun
2014-01-01
We review recent developments in the type IIB matrix model, which was conjectured to be a nonperturbative formulation of superstring theory. In the first part we review the recent results for the Euclidean model, which suggest that SO(10) symmetry is spontaneously broken. In the second part we review the recent results for the Lorentzian model. In particular, we discuss Monte Carlo results, which suggest that (3+1)-dimensional expanding universe emerges dynamically. We also discuss some results suggesting the emergence of exponential expansion and the power-law expansion at later times. The behaviors at much later times are studied by the classical equation of motion. We discuss a solution representing 3d expanding space, which suggests a possible solution to the cosmological constant problem.
The smallest matrix black hole model in the classical limit
Berenstein, David
2016-01-01
We study the smallest non-trivial matrix model that can be considered to be a (toy) model of a black hole. The model consists of a pair of $2\\times 2$ traceless hermitian matrices with a commutator squared potential and an $SU(2)$ gauge symmetry, plus an $SO(2)$ rotation symmetry. We show that using the symmetries of the system, all but two of the variables can be separated. The two variables that remain display chaos and a transition from chaos to integrability when a parameter related to an $SO(2)$ angular momentum is tuned to a critical value. We compute the Lyapunov exponents near this transition and study the critical exponent of the Lyapunov exponents near the critical point. We compare this transition to extremal rotating black holes.
Bulk Universality and Related Properties of Hermitian Matrix Models
Pastur, L
2007-01-01
We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function (see Theorem \\ref{t:U.t1}). The proof as our previous proof in \\cite{Pa-Sh:97} is based on the orthogonal polynomial techniques but does not use asymptotics of orthogonal polynomials. Rather, we obtain the $sin$-kernel as a unique solution of a certain non-linear integro-differential equation that follows from the determinant formulas for the correlation functions of the model. We also give a simplified and strengthened version of paper \\cite{BPS:95} on the existence and properties of the limiting Normalized Counting Measure of eigenvalues. We use these results in the proof of universality and we believe that they are of independent interest.
Matrix Model for Choosing Green Marketing Sustainable Strategic Alternatives
Directory of Open Access Journals (Sweden)
Cătălina Sitnikov
2015-08-01
Full Text Available Green marketing examines the symbiotic role played by marketing in ensuring sustainable business, exploring issues concerning the environment and the way strategic decisions can influence it. At present, the environmental issues concern more and more the competitive approach any organization can implement. Based on this approach, organizations can gain competitive advantage by managing environmental variables and by developing and implementing green marketing strategies. Considering the importance and impact of green marketing, by using theoretical concepts and defining a set of research directions, the paper and the research conducted were focused on creating a matrix model for choosing the optimal green marketing strategy, oriented towards competitive advantage. The model is based on the correlation that can be established among the generic strategies of competitive advantage, the variables of extended marketing mix (7Ps and the green marketing strategy matrix. There are also analyzed the implications that may be generated within a company by the adoption of a green marketing strategy and its role in promoting the environmental benefits of products.
Unitary Representations of Gauge Groups
Huerfano, Ruth Stella
I generalize to the case of gauge groups over non-trivial principal bundles representations that I. M. Gelfand, M. I. Graev and A. M. Versik constructed for current groups. The gauge group of the principal G-bundle P over M, (G a Lie group with an euclidean structure, M a compact, connected and oriented manifold), as the smooth sections of the associated group bundle is presented and studied in chapter I. Chapter II describes the symmetric algebra associated to a Hilbert space, its Hilbert structure, a convenient exponential and a total set that later play a key role in the construction of the representation. Chapter III is concerned with the calculus needed to make the space of Lie algebra valued 1-forms a Gaussian L^2-space. This is accomplished by studying general projective systems of finitely measurable spaces and the corresponding systems of sigma -additive measures, all of these leading to the description of a promeasure, a concept modeled after Bourbaki and classical measure theory. In the case of a locally convex vector space E, the corresponding Fourier transform, family of characters and the existence of a promeasure for every quadratic form on E^' are established, so the Gaussian L^2-space associated to a real Hilbert space is constructed. Chapter III finishes by exhibiting the explicit Hilbert space isomorphism between the Gaussian L ^2-space associated to a real Hilbert space and the complexification of its symmetric algebra. In chapter IV taking as a Hilbert space H the L^2-space of the Lie algebra valued 1-forms on P, the gauge group acts on the motion group of H defining in an straight forward fashion the representation desired.
Stable unitary integrators for the numerical implementation of continuous unitary transformations
Savitz, Samuel; Refael, Gil
2017-09-01
The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge-Kutta numerical integration algorithms, suffers from both severe inefficiency due to stiffness and the loss of unitarity. After reviewing the formalism of continuous unitary transformations and Wegner's original choice for the infinitesimal generator of the flow, we present a number of approaches to resolving these issues including a choice of generator which induces what we call the "uniform tangent decay flow" and three numerical integrators specifically designed to perform continuous unitary transformations efficiently while preserving the unitarity of flow. We conclude by applying one of the flow algorithms to a simple calculation that visually demonstrates the many-body localization transition.
On matrix model partition functions for QCD with chemical potential
Akemann, G; Vernizzi, G
2004-01-01
Partition functions of two different matrix models for QCD with chemical potential are computed for an arbitrary number of quark and complex conjugate anti-quark flavors. In the large-N limit of weak nonhermiticity complete agreement is found between the two models. This supports the universality of such fermionic partition functions, that is of products of characteristic polynomials in the complex plane. In the strong nonhermiticity limit agreement is found for an equal number of quark and conjugate flavours. For a general flavor content the equality of partition functions holds only for small chemical potential. The chiral phase transition is analyzed for an arbitrary number of quarks, where the free energy presents a discontinuity of first order at a critical chemical potential. In the case of nondegenerate flavors there is first order phase transition for each separate mass scale.
Matrix models, noncommutative gauge theory and emergent gravity
Energy Technology Data Exchange (ETDEWEB)
Steinacker, Harold [Fakultaet fuer Physik, Universitaet Wien (Austria)
2009-07-01
Matrix Models of Yang-Mills type are studied with focus on the effective geometry. It is shown that SU(n) gauge fields and matter on general 4-dimensional noncommutative branes couple to an effective metric, leading to emergent gravity. The effective metric is reminiscent of the open string metric, and depends on the dynamical Poisson structure. Covariant equations of motion are derived, which are protected from quantum corrections due to an underlying Noether theorem. The quantization is discussed qualitatively, which singles out the IKKT model as a candidate for a quantum theory of gravity coupled to matter. UV/IR mixing plays a central role. A mechanism for avoiding the cosmological constant problem is exhibited.
Modeling oxidation damage of continuous fiber reinforced ceramic matrix composites
Institute of Scientific and Technical Information of China (English)
Cheng-Peng Yang; Gui-Qiong Jiao; Bo Wang
2011-01-01
For fiber reinforced ceramic matrix composites (CMCs), oxidation of the constituents is a very important damage type for high temperature applications. During the oxidizing process, the pyrolytic carbon interphase gradually recesses from the crack site in the axial direction of the fiber into the interior of the material. Carbon fiber usually presents notch-like or local neck-shrink oxidation phenomenon, causing strength degradation. But, the reason for SiC fiber degradation is the flaw growth mechanism on its surface. A micromechanical model based on the above mechanisms was established to simulate the mechanical properties of CMCs after high temperature oxidation. The statistic and shearlag theory were applied and the calculation expressions for retained tensile modulus and strength were deduced, respectively. Meanwhile, the interphase recession and fiber strength degradation were considered. And then, the model was validated by application to a C/SiC composite.
An Empirically Based Method of Q-Matrix Validation for the DINA Model: Development and Applications
de la Torre, Jimmy
2008-01-01
Most model fit analyses in cognitive diagnosis assume that a Q matrix is correct after it has been constructed, without verifying its appropriateness. Consequently, any model misfit attributable to the Q matrix cannot be addressed and remedied. To address this concern, this paper proposes an empirically based method of validating a Q matrix used…
Random matrix models of stochastic integral type for free infinitely divisible distributions
Molina, J Armando Domínguez
2010-01-01
The Bercovici-Pata bijection maps the set of classical infinitely divisible distributions to the set of free infinitely divisible distributions. The purpose of this work is to study random matrix models for free infinitely divisible distributions under this bijection. First, we find a specific form of the polar decomposition for the L\\'{e}vy measures of the random matrix models considered in Benaych-Georges who introduced the models through their measures. Second, random matrix models for free infinitely divisible distributions are built consisting of infinitely divisible matrix stochastic integrals whenever their corresponding classical infinitely divisible distributions admit stochastic integral representations. These random matrix models are realizations of random matrices given by stochastic integrals with respect to matrix-valued L\\'{e}vy processes. Examples of these random matrix models for several classes of free infinitely divisible distributions are given. In particular, it is shown that any free sel...
Hygrothermal modeling and testing of polymers and polymer matrix composites
Xu, Weiqun
2000-10-01
The dissertation, consisting of four papers, presents the results of the research investigation on environmental effects on polymers and polymer matrix composites. Hygrothermal models were developed that would allow characterization of non-Fickian diffusion coefficients from moisture weight gain data. Hygrothermal testing was also conducted to provide the necessary data for characterizing of model coefficients and model verification. In part 1, a methodology is proposed that would allow characterization of non-Fickian diffusion coefficients from moisture weight gain data for a polymer adhesive below its Tg. Subsequently, these diffusion coefficients are used for predicting moisture concentration profiles through the thickness of a polymer. In part 2, a modeling methodology based on irreversible thermodynamics applied within the framework of composite macro-mechanics is presented, that would allow characterization of non-Fickian diffusion coefficients from moisture weight gain data for laminated composites with distributed uniaxial damage. Comparisons with test data for a 5-harness satin textile composite with uniaxial micro-cracks are provided for model verifications. In part 3, the same modeling methodology based on irreversible thermodynamics is extended to the case of a bi-axially damaged laminate. The model allows characterization of nonFickian diffusion coefficients as well as moisture saturation level from moisture weight gain data for laminates with pre-existing damage. Comparisons with test data for a bi-axially damaged Graphite/Epoxy woven composite are provided for model verifications. Finally, in part 4, hygrothermal tests conducted on AS4/PR500 5HS textile composite laminates are summarized. The objectives of the hygrothermal tests are to determine the diffusivity and maximum moisture content of the laminate.
Study of optical techniques for the Ames unitary wind tunnel, part 7
Lee, George
1993-01-01
A summary of optical techniques for the Ames Unitary Plan wind tunnels are discussed. Six optical techniques were studied: Schlieren, light sheet and laser vapor screen, angle of attack, model deformation, infrared imagery, and digital image processing. The study includes surveys and reviews of wind tunnel optical techniques, some conceptual designs, and recommendations for use of optical methods in the Ames Unitary Plan wind tunnels. Particular emphasis was placed on searching for systems developed for wind tunnel use and on commercial systems which could be readily adapted for wind tunnels. This final report is to summarize the major results and recommendations.
A matrix model for Misner universe and closed string tachyons
She, Jian-Huang
2006-01-01
We use D-instantons to probe the geometry of Misner universe, and calculate the world volume field theory action, which is of the 1+0 dimensional form and highly non-local. Turning on closed string tachyons, we see from the deformed moduli space of the D-instantons that the spacelike singularity is removed and the region near the singularity becomes a fuzzy cone, where space and time do not commute. When realized cosmologically there can be controllable trans-planckian effects. And the infinite past is now causally connected with the infinite future, thus also providing a model for big crunch/big bang transition. In the spirit of IKKT matrix theory, we propose that the D-instanton action here provides a holographic description for Misner universe and time is generated dynamically. In addition we show that winding string production from the vacua and instability of D-branes have simple uniform interpretations in this second quantized formalism.
Thermal evolution of the Schwinger model with Matrix Product Operators
Bañuls, M C; Cirac, J I; Jansen, K; Saito, H
2015-01-01
We demonstrate the suitability of tensor network techniques for describing the thermal evolution of lattice gauge theories. As a benchmark case, we have studied the temperature dependence of the chiral condensate in the Schwinger model, using matrix product operators to approximate the thermal equilibrium states for finite system sizes with non-zero lattice spacings. We show how these techniques allow for reliable extrapolations in bond dimension, step width, system size and lattice spacing, and for a systematic estimation and control of all error sources involved in the calculation. The reached values of the lattice spacing are small enough to capture the most challenging region of high temperatures and the final results are consistent with the analytical prediction by Sachs and Wipf over a broad temperature range.
Thermal evolution of the Schwinger model with matrix product operators
Energy Technology Data Exchange (ETDEWEB)
Banuls, M.C.; Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik, Garching (Germany); Cichy, K. [Frankfurt am Main Univ. (Germany). Inst. fuer Theoretische Physik; Poznan Univ. (Poland). Faculty of Physics; DESY Zeuthen (Germany). John von Neumann-Institut fuer Computing (NIC); Jansen, K.; Saito, H. [DESY Zeuthen (Germany). John von Neumann-Institut fuer Computing (NIC)
2015-10-15
We demonstrate the suitability of tensor network techniques for describing the thermal evolution of lattice gauge theories. As a benchmark case, we have studied the temperature dependence of the chiral condensate in the Schwinger model, using matrix product operators to approximate the thermal equilibrium states for finite system sizes with non-zero lattice spacings. We show how these techniques allow for reliable extrapolations in bond dimension, step width, system size and lattice spacing, and for a systematic estimation and control of all error sources involved in the calculation. The reached values of the lattice spacing are small enough to capture the most challenging region of high temperatures and the final results are consistent with the analytical prediction by Sachs and Wipf over a broad temperature range.
Matrix product states and the nonabelian rotor model
Milsted, Ashley
2015-01-01
We use uniform matrix product states (MPS) to study the (1+1)D $O(2)$ and $O(4)$ rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free nonabelian lattice gauge theory on a "hawaiian earring" graph for $U(1)$ and $SU(2)$, respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the $\\beta$-function, we find excellent agreement with known strong results, locating the BKT transition for $O(2)$ and successfully entering the asymptotic weak-coupling regime for $O(4)$. To obtain a finite local Hilbert space, we truncate in the space of irreducible representations (irreps) of the gauge group, comparing the effects of different cutoff values. We find that higher irreps become important in the crossover and weak-coupling regimes of the nonabelian theory, where entanglement also suddenly increases. This could have important consequences for TNS studies of Yang-Mills on higher dimensional graphs.
Higher Rank ABJM Wilson Loops from Matrix Models
Cookmeyer, Jonathan; Liu, James; Zayas, Leopoldo
2017-01-01
We compute the expectation values of 1/6 supersymmetric Wilson Loops in ABJM theory in higher rank representations. Using standard matrix model techniques, we calculate the expectation value in the rank m fully symmetric and fully antisymmetric representation where m is scaled with N. To leading order, we find agreement with the classical action of D6 and D2 branes in AdS4 ×CP3 respectively. Further, we compute the first subleading order term, which, on the AdS side, makes a prediction for the one-loop effective action of the corresponding D6 and D2 branes. Supported by the National Science Foundation under Grant No. PHY 1559988 and the US Department of Energy under Grant No. DE-SC0007859.
A matrix model for Misner universe and closed string tachyons
Energy Technology Data Exchange (ETDEWEB)
She Jianhuang [Institute of Theoretical Physics, Chinese Academy of Science, P.O.Box 2735, Beijing 100080 (China); Graduate School of the Chinese Academy of Sciences, Beijing 100080 (China)
2006-01-15
We use D-instantons to probe the geometry of Misner universe, and calculate the world volume field theory action, which is of the 1+0 dimensional form and highly non-local. Turning on closed string tachyons, we see from the deformed moduli space of the D-instantons that the spacelike singularity is removed and the region near the singularity becomes a fuzzy cone, where space and time do not commute. When realized cosmologically there can be controllable trans-planckian effects. And the infinite past is now causally connected with the infinite future, thus also providing a model for big crunch/big bang transition. In the spirit of IKKT matrix theory, we propose that the D-instanton action here provides a holographic description for Misner universe and time is generated dynamically. In addition we show that winding string production from the vacua and instability of D-branes have simple uniform interpretations in this second quantized formalism.
Analytical Model of Water Flow in Coal with Active Matrix
Siemek, Jakub; Stopa, Jerzy
2014-12-01
This paper presents new analytical model of gas-water flow in coal seams in one dimension with emphasis on interactions between water flowing in cleats and coal matrix. Coal as a flowing system, can be viewed as a solid organic material consisting of two flow subsystems: a microporous matrix and a system of interconnected macropores and fractures. Most of gas is accumulated in the microporous matrix, where the primary flow mechanism is diffusion. Fractures and cleats existing in coal play an important role as a transportation system for macro scale flow of water and gas governed by Darcy's law. The coal matrix can imbibe water under capillary forces leading to exchange of mass between fractures and coal matrix. In this paper new partial differential equation for water saturation in fractures has been formulated, respecting mass exchange between coal matrix and fractures. Exact analytical solution has been obtained using the method of characteristics. The final solution has very simple form that may be useful for practical engineering calculations. It was observed that the rate of exchange of mass between the fractures and the coal matrix is governed by an expression which is analogous to the Newton cooling law known from theory of heat exchange, but in present case the mass transfer coefficient depends not only on coal and fluid properties but also on time and position. The constant term of mass transfer coefficient depends on relation between micro porosity and macro porosity of coal, capillary forces, and microporous structure of coal matrix. This term can be expressed theoretically or obtained experimentally. W artykule zaprezentowano nowy model matematyczny przepływu wody i gazu w jednowymiarowej warstwie węglowej z uwzględnieniem wymiany masy między systemem szczelin i matrycą węglową. Węgiel jako system przepływowy traktowany jest jako układ o podwójnej porowatości i przepuszczalności, składający się z mikroporowatej matrycy węglowej oraz z
On unitary representability of topological groups
Galindo Pastor, Jorge
2006-01-01
We prove that the additive group $(E^\\ast,\\tau_k(E))$ of an $\\mathscr{L}_\\infty$-Banach space $E$, with the topology $\\tau_k(E)$ of uniform convergence on compact subsets of $E$, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is \\emph{unitarily representable}). This is the same as proving that the topological group $(E^\\ast,\\tau_k(E))$ is uniformly homeomorphic to a subset of $\\ell_2^\\kappa$ for some $\\kappa$. As an immediate consequence, preduals of com...
Quantum remote control Teleportation of unitary operations
Huelga, S F; Chefles, A; Plenio, M B
2001-01-01
We consider the implementation of an unknown arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as a quantum remote control. We investigate the protocols which achieve this using local operations, classical communication and shared entanglement (LOCCSE). Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation.
Unitary Gas Constraints on Nuclear Symmetry Energy
Kolomeitsev, Evgeni E; Ohnishi, Akira; Tews, Ingo
2016-01-01
We show the existence of a lower bound on the volume symmetry energy parameter $S_0$ from unitary gas considerations. We further demonstrate that values of $S_0$ above this minimum imply upper and lower bounds on the symmetry energy parameter $L$ describing its lowest-order density dependence. The bounds are found to be consistent with both recent calculations of the energies of pure neutron matter and constraints from nuclear experiments. These results are significant because many equations of state in active use for simulations of nuclear structure, heavy ion collisions, supernovae, neutron star mergers, and neutron star structure violate these constraints.
Shear Viscosity of a Unitary Fermi Gas
Wlazłowski, Gabriel; Magierski, Piotr; Drut, Joaquín E.
2012-01-01
We present the first ab initio determination of the shear viscosity eta of the Unitary Fermi Gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity to entropy density ratio eta/s. The minimum of eta/s appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being eta/s approx 0.2 hbar/kB, which almost saturates...
Universal dynamics in a Unitary Bose Gas
Klauss, Catherine; Xie, Xin; D'Incao, Jose; Jin, Deborah; Cornell, Eric
2016-05-01
We investigate the dynamics of a unitary Bose gas with an 85 Rb BEC, specifically to determine whether the dynamics scale universally with density. We find that the initial density affects both the (i) projection of the strongly interacting many-body wave-function onto the Feshbach dimer state when the system is rapidly ramped to a weakly interacting value of the scattering length a and (ii) the overall decay rate to deeper bound states. We will present data on both measurements across two orders of magnitude in density, and will discuss how the data illustrate the competing roles of universality and Efimov physics.
Unitary Quantum Lattice Algorithms for Turbulence
2016-05-23
collision operator, based on the 3D relativistic Dirac particle dynamics theory of Yepez, ĈD = cosθ x( ) −i sinθ x( ) −i sinθ x( ) cosθ x... based algorithm it will result in a finite difference representation of the GP Eq. (24) provided the parameters are so chosen to yield diffusion-like...Fluid Dynamics, ed. H. W. Oh, ( InTech Publishers, Croatia, 2012) [20] “Unitary qubit lattice simulations of complex vortex structures
Unitary water-to-air heat pumps
Energy Technology Data Exchange (ETDEWEB)
Christian, J.E.
1977-10-01
Performance and cost functions for nine unitary water-to-air heat pumps ranging in nominal size from /sup 1///sub 2/ to 26 tons are presented in mathematical form for easy use in heat pump computer simulations. COPs at nominal water source temperature of 60/sup 0/F range from 2.5 to 3.4 during the heating cycle; during the cooling cycle EERs range from 8.33 to 9.09 with 85/sup 0/F entering water source temperatures. The COP and EER values do not include water source pumping power or any energy requirements associated with a central heat source and heat rejection equipment.
Quantum mechanics with non-unitary symmetries
Bistrovic, B
2000-01-01
This article shows how to properly extend symmetries of non-relativistic quantum mechanics to include non-unitary representations of Lorentz group for all spins. It follows from this that (almost) all existing relativistic single particle Lagrangians and equations are incorrect. This is shown in particular for Dirac's equation and Proca equations. It is shown that properly constructed relativistic extensions have no negative energies, zitterbewegung effects and have proper symmetric energy-momentum tensor and angular momentum density tensor. The downside is that states with negative norm are inevitable in all representations.
Unitary appreciative inquiry: evolution and refinement.
Cowling, W Richard; Repede, Elizabeth
2010-01-01
Unitary appreciative inquiry (UAI), developed over the past 20 years, provides an orientation and process for uncovering human wholeness and discovering life patterning in individuals and groups. Refinements and a description of studies using UAI are presented. Assumptions and conceptual underpinnings of the method distinguishing its contributions from other methods are reported. Data generation strategies that capture human wholeness and elucidate life patterning are proposed. Data synopsis as an alternative to analysis is clarified and explicated. Standards that suggest enhancing the legitimacy of knowledge and credibility of research are specified. Potential expansions of UAI offer possibilities for extending epistemologies, aesthetic integration, and theory development.
Endoscopic classification of representations of quasi-split unitary groups
Mok, Chung Pang
2015-01-01
In this paper the author establishes the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.
Momentum Distribution in the Unitary Bose Gas from First Principles
Comparin, Tommaso; Krauth, Werner
2016-11-01
We consider a realistic bosonic N -particle model with unitary interactions relevant for Efimov physics. Using quantum Monte Carlo methods, we find that the critical temperature for Bose-Einstein condensation is decreased with respect to the ideal Bose gas. We also determine the full momentum distribution of the gas, including its universal asymptotic behavior, and compare this crucial observable to recent experimental data. Similar to the experiments with different atomic species, differentiated solely by a three-body length scale, our model only depends on a single parameter. We establish a weak influence of this parameter on physical observables. In current experiments, the thermodynamic instability of our model from the atomic gas towards an Efimov liquid could be masked by the dynamical instability due to three-body losses.
Particular Matrix in the Study of the Index Hour Mathematical Model
Directory of Open Access Journals (Sweden)
Mihaela Poienar
2014-09-01
Full Text Available The three phase transformer clock hour figure mathematical model can be conceived in his regular form as a 3X3 square matrix, called matrix code, or as a matrix equation, called code equation and is conceived through the elementary matrices: Ma, Mb, Mc or by defining matrices: M100, M10, M1. The code equation expression is dependent on the definition function: the sgn function or the trivalent variable function. Interrelated with the two possibilities are shown, defined and explained the following particular matrix: transfer matrix T. Finally are presented the interrelation between these particular matrixes and highlighted the possibilities of exploitation.
Filter-matrix lattice Boltzmann model for microchannel gas flows.
Zhuo, Congshan; Zhong, Chengwen
2013-11-01
The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.
Kitaev honeycomb tensor networks: Exact unitary circuits and applications
Schmoll, Philipp; Orús, Román
2017-01-01
The Kitaev honeycomb model is a paradigm of exactly solvable models, showing nontrivial physical properties such as topological quantum order, Abelian and non-Abelian anyons, and chirality. Its solution is one of the most beautiful examples of the interplay of different mathematical techniques in condensed matter physics. In this paper, we show how to derive a tensor network (TN) description of the eigenstates of this spin-1/2 model in the thermodynamic limit, and in particular for its ground state. In our setting, eigenstates are naturally encoded by an exact 3d TN structure made of fermionic unitary operators, corresponding to the unitary quantum circuit building up the many-body quantum state. In our derivation we review how the different "solution ingredients" of the Kitaev honeycomb model can be accounted for in the TN language, namely, Jordan-Wigner transformation, braidings of Majorana modes, fermionic Fourier transformation, and Bogoliubov transformation. The TN built in this way allows for a clear understanding of several properties of the model. In particular, we show how the fidelity diagram is straightforward both at zero temperature and at finite temperature in the vortex-free sector. We also show how the properties of two-point correlation functions follow easily. Finally, we also discuss the pros and cons of contracting of our 3d TN down to a 2d projected entangled pair state (PEPS) with finite bond dimension. The results in this paper can be extended to generalizations of the Kitaev model, e.g., to other lattices, spins, and dimensions.
Critical endpoint for deconfinement in matrix and other effective models
Kashiwa, Kouji; Skokov, Vladimir V
2012-01-01
We consider the position of the deconfining critical endpoint, where the first order transition for deconfinement is washed out by the presence of massive, dynamical quarks. We use an effective matrix model, employed previously to analyze the transition in the pure glue theory. If the param- eters of the pure glue theory are unaffected by the presence of dynamical quarks, and if the quarks only contribute perturbatively, then for three colors and three degenerate quark flavors this quark mass is very heavy, m_de \\sim 2.5 GeV, while the critical temperature, T_de, barely changes, \\sim 1% below that in the pure glue theory. The location of the deconfining critical endpoint is a sensitive test to differentiate between effective models. For example, models with a logarithmic potential for the Polyakov loop give much smaller values of the quark mass, m_de \\sim 1 GeV, and a large shift in T_de \\sim 10% lower than that in the pure glue theory.
Garron, Nicolas; Lytle, Andew T
2016-01-01
We compute the hadronic matrix elements of the four-quark operators relevant for $K^0-{\\bar K^0}$ mixing beyond the Standard Model. Our results are from lattice QCD simulations with $n_f=2+1$ flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing ($a\\sim0.08$ and $a\\sim 0.11 \\, \\fm $) and with lightest unitary pion mass $\\sim 300\\, \\MeV$. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description of the renormalisation procedure is presented in a companion paper. We argue that the intermediate renormalisation scheme is responsible for the discrepancies found by different collaborations. We also study different normalisations and determine the matrix elements of the relevant four-quark operators with a precision of $\\sim 5\\%$ or better.
Energy Technology Data Exchange (ETDEWEB)
Garron, Nicolas [Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool,Brownlow Hill, Liverpool, L69 3BX (United Kingdom); Hudspith, Renwick J. [Department of Physics and Astronomy, York University,4700 Keele Street, Toronto, Ontario, M3J 1P3 (Canada); Lytle, Andrew T. [SUPA, School of Physics and Astronomy, University of Glasgow,University Avenue, Glasgow, G12 8QQ (United Kingdom); Collaboration: The RBC/UKQCD collaboration
2016-11-02
We compute the hadronic matrix elements of the four-quark operators relevant for K{sup 0}−K̄{sup 0} mixing beyond the Standard Model. Our results are from lattice QCD simulations with n{sub f}=2+1 flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing (a∼0.08 and a∼0.11 fm) and with lightest unitary pion mass ∼300 MeV. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description of the renormalisation procedure is presented in a companion paper. We argue that the intermediate renormalisation scheme is responsible for the discrepancies found by different collaborations. We also study different normalisations and determine the matrix elements of the relevant four-quark operators with a precision of ∼5% or better.
Multiscale modeling of PVDF matrix carbon fiber composites
Greminger, Michael; Haghiashtiani, Ghazaleh
2017-06-01
Self-sensing carbon fiber reinforced composites have the potential to enable structural health monitoring that is inherent to the composite material rather than requiring external or embedded sensors. It has been demonstrated that a self-sensing carbon fiber reinforced polymer composite can be created by using the piezoelectric polymer polyvinylidene difluoride (PVDF) as the matrix material and using a Kevlar layer to separate two carbon fiber layers. In this configuration, the electrically conductive carbon fiber layers act as electrodes and the Kevlar layer acts as a dielectric to prevent the electrical shorting of the carbon fiber layers. This composite material has been characterized experimentally for its effective d 33 and d 31 piezoelectric coefficients. However, for design purposes, it is desirable to obtain a predictive model of the effective piezoelectric coefficients for the final smart composite material. Also, the inverse problem can be solved to determine the degree of polarization obtained in the PVDF material during polarization by comparing the effective d 33 and d 31 values obtained in experiment to those predicted by the finite element model. In this study, a multiscale micromechanics and coupled piezoelectric-mechanical finite element modeling approach is introduced to predict the mechanical and piezoelectric performance of a plain weave carbon fiber reinforced PVDF composite. The modeling results show good agreement with the experimental results for the mechanical and electrical properties of the composite. In addition, the degree of polarization of the PVDF component of the composite is predicted using this multiscale modeling approach and shows that there is opportunity to drastically improve the smart composite’s performance by improving the polarization procedure.
Beamspace Unitary ESPRIT Algorithm for Angle Estimation in Bistatic MIMO Radar
Directory of Open Access Journals (Sweden)
Dang Xiaofang
2015-01-01
Full Text Available The beamspace unitary ESPRIT (B-UESPRIT algorithm for estimating the joint direction of arrival (DOA and the direction of departure (DOD in bistatic multiple-input multiple-output (MIMO radar is proposed. The conjugate centrosymmetrized DFT matrix is utilized to retain the rotational invariance structure in the beamspace transformation for both the receiving array and the transmitting array. Then the real-valued unitary ESPRIT algorithm is used to estimate DODs and DOAs which have been paired automatically. The proposed algorithm does not require peak searching, presents low complexity, and provides a significant better performance compared to some existing methods, such as the element-space ESPRIT (E-ESPRIT algorithm and the beamspace ESPRIT (B-ESPRIT algorithm for bistatic MIMO radar. Simulation results are conducted to show these conclusions.
M-P invertible matrices and unitary groups over Fq2
Institute of Scientific and Technical Information of China (English)
戴宗铎; 万哲先
2002-01-01
The Moor-Penrose generalized inverses (M-P inverses for short) of matrices over a finite field Fq2, which is a generalization of the Moor-Penrose generalized inverses over the complex field, are studied in the present paper. Some necessary and sufficient conditions for an m×n matrix A over Fq2 having an M-P inverse are obtained, which make clear the set of m×n matrices over Fq2 having M-P inverses and reduce the problem of constructing and enumerating the M-P invertible matrices to that of constructing and enumerating the non-isotropic subspaces with respect to the unitary group. Based on this reduction, both the construction problem and the enumeration problem are solved by borrowing the results in geometry of unitary groups over finite fields.
Cubic constraints for the resolvents of the ABJM matrix model and its cousins
Itoyama, Hiroshi; Suyama, Takao; Yoshioka, Reiji
2016-01-01
A set of Schwinger-Dyson equations forming constraints for at most three resolvent functions are considered for a class of Chern-Simons matter matrix models with two nodes labelled by a non-vanishing number $n$. The two cases $n=2$ and $n= -2$ label respectively the ABJM matrix model, which is the hyperbolic lift of the affine $A_1^{(1)}$ quiver matrix model, and the lens space matrix model. In the planar limit, we derive two cubic loop equations for the two planar resolvents. One of these reduces to the quadratic one when $n = \\pm 2$.
Stage-structured matrix models for organisms with non-geometric development times
Andrew Birt; Richard M. Feldman; David M. Cairns; Robert N. Coulson; Maria Tchakerian; Weimin Xi; James M. Guldin
2009-01-01
Matrix models have been used to model population growth of organisms for many decades. They are popular because of both their conceptual simplicity and their computational efficiency. For some types of organisms they are relatively accurate in predicting population growth; however, for others the matrix approach does not adequately model...
Perfect state transfer in unitary Cayley graphs over local rings
Directory of Open Access Journals (Sweden)
Yotsanan Meemark
2014-12-01
Full Text Available In this work, using eigenvalues and eigenvectors of unitary Cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing PST occurring in its unitary Cayley graph. Moreover, we have some developments when $R$ is a product of local rings.
D-Brane Probes in the Matrix Model
Ferrari, Frank
2013-01-01
Recently, a new approach to large N gauge theories, based on a generalization of the concept of D-brane probes to any gauge field theory, was proposed. In the present note, we compute the probe action in the one matrix model with a quartic potential. This allows to illustrate several non-trivial aspects of the construction in an exactly solvable set-up. One of our main goal is to test the bare bubble approximation. The approximate free energy found in this approximation, which can be derived from a back-of-an-envelope calculation, matches the exact result for all values of the 't Hooft coupling with a surprising accuracy. Another goal is to illustrate the remarkable properties of the equivariant partial gauge-fixing procedure, which is at the heart of the formalism. For this we use a general xi-gauge to compute the brane action. The action depends on xi in a very non-trivial way, yet we show explicitly that its critical value does not and coincide with twice the free energy, as required by general consistency...
Matrix product states and the non-Abelian rotor model
Milsted, Ashley
2016-04-01
We use uniform matrix product states to study the (1 +1 )D O (2 ) and O (4 ) rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free non-Abelian lattice gauge theory on a "Hawaiian earring" graph for U (1 ) and S U (2 ), respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the β function, we find excellent agreement with known results, locating the Berezinskii-Kosterlitz-Thouless transition for O (2 ) and successfully entering the asymptotic weak-coupling regime for O (4 ). To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the non-Abelian theory, where entanglement also suddenly increases. This could have important consequences for tensor network state studies of Yang-Mills on higher-dimensional graphs.
Institute of Scientific and Technical Information of China (English)
LI Chunxiang; ZHOU Dai
2004-01-01
The polynomial matrix using the block coefficient matrix representation auto-regressive moving average (referred to as the PM-ARMA) model is constructed in this paper for actively controlled multi-degree-of-freedom (MDOF) structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization. The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average (ARMA) model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators. (The sensors and actuators are required to maintain the identical number.) under any dimensional stationary stochastic excitation.
C T for non-unitary CFTs in higher dimensions
Osborn, Hugh; Stergiou, Andreas
2016-06-01
The coefficient C T of the conformal energy-momentum tensor two-point function is determined for the non-unitary scalar CFTs with four- and six-derivative kinetic terms. The results match those expected from large- N calculations for the CFTs arising from the O( N) non-linear sigma and Gross-Neveu models in specific even dimensions. C T is also calculated for the CFT arising from ( n - 1)-form gauge fields with derivatives in 2 n + 2 dimensions. Results for ( n - 1)-form theory extended to general dimensions as a non-gauge-invariant CFT are also obtained; the resulting C T differs from that for the gauge-invariant theory. The construction of conformal primaries by subtracting descendants of lower-dimension primaries is also discussed. For free theories this also leads to an alternative construction of the energy-momentum tensor, which can be quite involved for higher-derivative theories.
Biphoton transmission through non-unitary objects
Reichert, Matthew; Sun, Xiaohang; Fleischer, Jason W
2016-01-01
Losses should be accounted for in a complete description of quantum imaging systems, and yet they are often treated as undesirable and largely neglected. In conventional quantum imaging, images are built up by coincidence detection of spatially entangled photon pairs (biphotons) transmitted through an object. However, as real objects are non-unitary (absorptive), part of the transmitted state contains only a single photon, which is overlooked in traditional coincidence measurements. The single photon part has a drastically different spatial distribution than the two-photon part. It contains information both about the object, and, remarkably, the spatial entanglement properties of the incident biphotons. We image the one- and two-photon parts of the transmitted state using an electron multiplying CCD array both as a traditional camera and as a massively parallel coincidence counting apparatus, and demonstrate agreement with theoretical predictions. This work may prove useful for photon number imaging and lead ...
Lorentz Spin-Foam with Non Unitary Representations by use of Holomorphic Peter-Weyl Theorem
Perlov, Leonid
2013-01-01
We use the non-unitary spinor representations of SL(2,C) and the recently proved Holomorphic Peter-Weyl theorem to define the Hilbert space based on the holomorphic spin-networks, the non-unitary spin-foam, solve the simplicity constraints and calculate the vertex amplitude. The diagonal simplicity constraint provides two solutions. The first solution: Immirzi $\\gamma = i$ with the irreducible representations $(j_1, j_2)$ projected to $(0, j)$ and the second solution: Immirzi $\\gamma = -i$ and the irreducible non-unitary representations projected to $(j, 0)$. The off-diagonal constraint selects only the first of these two solutions. The solution is interesting in two aspects: a) it turns to be a topological BF model. b) Immirzi parameter $\\gamma = i$ corresponds to Ashtekar's self-dual connection of the complexified algebra $sl(2,C)\\otimes C$. The transition amplitude is finite and very similar to BF Euclidean model. We discuss the inner product Lorentz invariance and the viability of the non-unitary represen...
Random matrix theory and the zeros of {zeta}'(s)
Energy Technology Data Exchange (ETDEWEB)
Mezzadri, Francesco [School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK (United Kingdom)
2003-03-28
We study the density of the roots of the derivative of the characteristic polynomial Z(U, z) of an N x N random unitary matrix with distribution given by Haar measure on the unitary group. Based on previous random matrix theory models of the Riemann zeta function {zeta}(s), this is expected to be an accurate description for the horizontal distribution of the zeros of {zeta}'(s) to the right of the critical line. We show that as N {yields} {infinity} the fraction of the roots of Z'(U, z) that lie in the region 1 - x/(N - 1) {<=} vertical bar z vertical bar < 1 tends to a limit function. We derive asymptotic expressions for this function in the limits x {yields} {infinity} and x {yields} 0 and compare them with numerical experiments.
Compactifications of the Heterotic string with unitary bundles
Energy Technology Data Exchange (ETDEWEB)
Weigand, T.
2006-05-23
In this thesis we investigate a large new class of four-dimensional supersymmetric string vacua defined as compactifications of the E{sub 8} x E{sub 8} and the SO(32) heterotic string on smooth Calabi-Yau threefolds with unitary gauge bundles and heterotic five-branes. The first part of the thesis discusses the implementation of this idea into the E{sub 8} x E{sub 8} heterotic string. After specifying a large class of group theoretic embeddings featuring unitary bundles, we analyse the effective four-dimensional N=1 supergravity upon compactification. From the gauge invariant Kaehler potential for the moduli fields we derive a modification of the Fayet-Iliopoulos D-terms arising at one-loop in string perturbation theory. From this we conjecture a one-loop deformation of the Hermitian Yang-Mills equation and introduce the idea of {lambda}-stability as the perturbatively correct stability concept generalising the notion of Mumford stability valid at tree-level. We then proceed to a definition of SO(32) heterotic vacua with unitary gauge bundles in the presence of heterotic five-branes and find agreement of the resulting spectrum with the S-dual framework of Type I/Type IIB orientifolds. A similar analysis of the effective four-dimensional supergravity is performed. Further evidence for the proposed one-loop correction to the stability condition is found by identifying the heterotic corrections as the S-dual of the perturbative part of {pi}-stability as the correct stability concept in Type IIB theory. After reviewing the construction of holomorphic stable vector bundles on elliptically fibered Calabi-Yau manifolds via spectral covers, we provide semi-realistic examples for SO(32) heterotic vacua with Pati-Salam and MSSM-like gauge sectors. We finally discuss the construction of realistic vacua with flipped SU(5) GUT and MSSM gauge group within the E{sub 8} x E{sub 8} framework, based on the embedding of line bundles into both E{sub 8} factors. Some of the appealing
Neutrinoless Double Beta Nuclear Matrix Elements Around Mass 80 in the Nuclear Shell Model
Yoshinaga, Naotaka; Higashiyama, Koji; Taguchi, Daisuke; Teruya, Eri
The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. In its theoretical nuclear side it is particularly important to estimate three types of nuclear matrix elements, namely, Fermi (F), Gamow-Teller (GT), and tensor (T) types matrix elements. The shell model calculations and also the pair-truncated shell model calculations are carried out to check the model dependence on nuclear matrix elements. In this work the neutrinoless double-beta decay for mass A = 82 nuclei is studied. It is found that the matrix elements are quite sensitive to the ground state wavefunctions.
How random are matrix elements of the nuclear shell model Hamiltonian?
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper we study the general behavior of matrix elements of the nuclear shell model Hamiltonian.We find that nonzero off-diagonal elements exhibit a regular pattern,if one sorts the diagonal matrix elements from smaller to larger values.The correlation between eigenvalues and diagonal matrix elements for the shell model Hamiltonian is more remarkable than that for random matrices with the same distribution unless the dimension is small.
How random are matrix elements of the nuclear shell model Hamiltonian?
Institute of Scientific and Technical Information of China (English)
SHEN JiaJie; ZHAO YuMing
2009-01-01
In this paper we study the general behavior of matrix elements of the nuclear shell model Hamiltonlan.We find that nonzero off-diagonal elements exhibit a regular pattern,if one sorts the diagonal matrix elements from smaller to larger values.The correlation between eigenvalues and diagonal matrix elements for the shell model Hamiltonian is more remarkable than that for random matrices with the same distribution unless the dimension is small.
Neutron matter at low density and the unitary limit
Baldo, M
2007-01-01
Neutron matter at low density is studied within the hole-line expansion. Calculations are performed in the range of Fermi momentum $k_F$ between 0.4 and 0.8 fm$^{-1}$. It is found that the Equation of State is determined by the $^1S_0$ channel only, the three-body forces contribution is quite small, the effect of the single particle potential is negligible and the three hole-line contribution is below 5% of the total energy and indeed vanishing small at the lowest densities. Despite the unitary limit is actually never reached, the total energy stays very close to one half of the free gas value throughout the considered density range. A rank one separable representation of the bare NN interaction, which reproduces the physical scattering length and effective range, gives results almost indistinguishable from the full Brueckner G-matrix calculations with a realistic force. The extension of the calculations below $k_F = 0.4$ fm$^{-1}$ does not indicate any pathological behavior of the neutron Equation of State.
Deformation behavior of SiC particle reinforced Al matrix composites based on EMA model
Institute of Scientific and Technical Information of China (English)
CHENG Nan-pu; ZENG Su-min; YU Wen-bin; LIU Zhi-yi; CHEN Zhi-qian
2007-01-01
Effects of the matrix properties, particle size distribution and interfacial matrix failure on the elastoplastic deformation behavior in Al matrix composites reinforced by SiC particles with an average size of 5 μm and volume fraction of 12% were quantitatively calculated by using the expanded effective assumption(EMA) model. The particle size distribution naturally brings about the variation of matrix properties and the interfacial matrix failure due to the presence of SiC particles. The theoretical results coincide well with those of the experiment. The current research indicates that the load transfer between matrix and reinforcements, grain refinement in matrix, and enhanced dislocation density originated from the thermal mismatch between SiC particles and Al matrix increase the flow stress of the composites, but the interfacial matrix failure is opposite. It also proves that the load transfer, grain refinement and dislocation strengthening are the main strengthening mechanisms, and the interfacial matrix failure and ductile fracture of matrix are the dominating fracture modes in the composites. The mechanical properties of the composites strongly depend on the metal matrix.
The classical r-matrix method for nonlinear sigma-model
Sevostyanov, Alexey
1995-01-01
The canonical Poisson structure of nonlinear sigma-model is presented as a Lie-Poisson r-matrix bracket on coadjoint orbits. It is shown that the Poisson structure of this model is determined by some `hidden singularities' of the Lax matrix.
Neutron diffraction measurements and modeling of residual strains in metal matrix composites
Saigal, A.; Leisk, G. G.; Hubbard, C. R.; Misture, S. T.; Wang, X. L.
1996-01-01
Neutron diffraction measurements at room temperature are used to characterize the residual strains in tungsten fiber-reinforced copper matrix, tungsten fiber-reinforced Kanthal matrix, and diamond particulate-reinforced copper matrix composites. Results of finite element modeling are compared with the neutron diffraction data. In tungsten/Kanthal composites, the fibers are in compression, the matrix is in tension, and the thermal residual strains are a strong function of the volume fraction of fibers. In copper matrix composites, the matrix is in tension and the stresses are independent of the volume fraction of tungsten fibers or diamond particles and the assumed stress free temperature because of the low yield strength of the matrix phase.
On the complete classification of unitary N=2 minimal superconformal field theories
Energy Technology Data Exchange (ETDEWEB)
Gray, Oliver
2009-08-03
Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each candidate for a modular invariant partition function of such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models demonstrates that there exists a unitary N=2 minimal model for every one of the allowed partition functions in the list obtained from Gannon's work. Kreuzer and Schellekens' conjecture that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N=2 minimal models by simple counting arguments. We nd a nice characterisation of the projection from the Hilbert space of a minimal model with k odd to its modular invariant subspace, and we present a new simple proof of the superconformal version of the Verlinde formula for the minimal models using simple currents. Finally we demonstrate a curious relation between the generating function of simple current invariants and the Riemann zeta function. (orig.)
Modeling the Mechanical Behavior of Ceramic Matrix Composite Materials
Jordan, William
1998-01-01
Ceramic matrix composites are ceramic materials, such as SiC, that have been reinforced by high strength fibers, such as carbon. Designers are interested in using ceramic matrix composites because they have the capability of withstanding significant loads while at relatively high temperatures (in excess of 1,000 C). Ceramic matrix composites retain the ceramic materials ability to withstand high temperatures, but also possess a much greater ductility and toughness. Their high strength and medium toughness is what makes them of so much interest to the aerospace community. This work concentrated on two different tasks. The first task was to do an extensive literature search into the mechanical behavior of ceramic matrix composite materials. This report contains the results of this task. The second task was to use this understanding to help interpret the ceramic matrix composite mechanical test results that had already been obtained by NASA. Since the specific details of these test results are subject to the International Traffic in Arms Regulations (ITAR), they are reported in a separate document (Jordan, 1997).
Sequential scheme for locally discriminating bipartite unitary operations without inverses
Li, Lvzhou
2017-08-01
Local distinguishability of bipartite unitary operations has recently received much attention. A nontrivial and interesting question concerning this subject is whether there is a sequential scheme for locally discriminating between two bipartite unitary operations, because a sequential scheme usually represents the most economic strategy for discrimination. An affirmative answer to this question was given in the literature, however with two limitations: (i) the unitary operations to be discriminated were limited to act on d ⊗d , i.e., a two-qudit system, and (ii) the inverses of the unitary operations were assumed to be accessible, although this assumption may be unrealizable in experiment. In this paper, we improve the result by removing the two limitations. Specifically, we show that any two bipartite unitary operations acting on dA⊗dB can be locally discriminated by a sequential scheme, without using the inverses of the unitary operations. Therefore, this paper enhances the applicability and feasibility of the sequential scheme for locally discriminating unitary operations.
Perturbation semigroup of matrix algebras
Neumann, N.; Suijlekom, W.D. van
2016-01-01
In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-algebra and extends the group of unitary elements of this *-algebra. We compute the perturbation semigroup for all matrix algebras.
Open intersection numbers, matrix models and MKP hierarchy
Alexandrov, A
2014-01-01
In this paper we claim that the generating function of the intersection numbers on the moduli spaces of Riemann surfaces with boundary, constructed recently by R. Pandharipande, J. Solomon and R. Tessler and extended by A. Buryak, is a tau-function of the KP integrable hierarchy. Moreover, it is given by a simple modification of the Kontsevich matrix integral so that the generating functions of open and closed intersection numbers are described by the MKP integrable hierarchy. Virasoro constraints for the open intersection numbers naturally follow from the matrix integral representation.
Open intersection numbers, matrix models and MKP hierarchy
Energy Technology Data Exchange (ETDEWEB)
Alexandrov, A. [Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg,Albertstrasse 19, 79104 Freiburg (Germany); Mathematics Institute, University of Freiburg,Eckerstrasse 1, 79104 Freiburg (Germany); ITEP,Bolshaya Cheremushkinskaya 25, 117218 Moscow (Russian Federation)
2015-03-09
In this paper we conjecture that the generating function of the intersection numbers on the moduli spaces of Riemann surfaces with boundary, constructed recently by R. Pandharipande, J. Solomon and R. Tessler and extended by A. Buryak, is a tau-function of the KP integrable hierarchy. Moreover, it is given by a simple modification of the Kontsevich matrix integral so that the generating functions of open and closed intersection numbers are described by the MKP integrable hierarchy. Virasoro constraints for the open intersection numbers naturally follow from the matrix integral representation.
Multidisciplinary Product Decomposition and Analysis Based on Design Structure Matrix Modeling
DEFF Research Database (Denmark)
Habib, Tufail
2014-01-01
Design structure matrix (DSM) modeling in complex system design supports to define physical and logical configuration of subsystems, components, and their relationships. This modeling includes product decomposition, identification of interfaces, and structure analysis to increase the architectural...
High-Strain-Rate Constitutive Characterization and Modeling of Metal Matrix Composites
2014-03-07
impact fracture of carbon fiber reinforced 7075 -T6 aluminum matrix composite , Materials Transactions, Japan Institute of Metals, 41, 1055-1063...MODELING OF METAL MATRIX COMPOSITES Report Title The mechanical response of three different types of materials are examined: unidirectionally...conditions. This report also documents some of the highlights of the material response of Saffil filled aluminum matrix composite and a Nextel satin
Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
Ueda, K.; Otani, R.; Nishio, Y; Gendiar, A.; Nishino, T
2004-01-01
We report a way of obtaining a spin configuration snapshot, which is one of the representative spin configurations in canonical ensemble, in a finite area of infinite size two-dimensional (2D) classical lattice models. The corner transfer matrix renormalization group (CTMRG), a variant of the density matrix renormalization group (DMRG), is used for the numerical calculation. The matrix product structure of the variational state in CTMRG makes it possible to stochastically fix spins each by ea...
Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry
Energy Technology Data Exchange (ETDEWEB)
Novaes, Marcel, E-mail: marcel.novaes@gmail.com
2015-10-15
We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.
Localization in band random matrix models with and without increasing diagonal elements.
Wang, Wen-ge
2002-06-01
It is shown that localization of eigenfunctions in the Wigner band random matrix model with increasing diagonal elements can be related to localization in a band random matrix model with random diagonal elements. The relation is obtained by making use of a result of a generalization of Brillouin-Wigner perturbation theory, which shows that reduced Hamiltonian matrices with relatively small dimensions can be introduced for nonperturbative parts of eigenfunctions, and by employing intermediate basis states, which can improve the method of the reduced Hamiltonian matrix. The latter model deviates from the standard band random matrix model mainly in two aspects: (i) the root mean square of diagonal elements is larger than that of off-diagonal elements within the band, and (ii) statistical distributions of the matrix elements are close to the Lévy distribution in their central parts, except in the high top regions.
Comparative analysis of mathematical models of the matrix photodetector used in digital holography
Grebenyuk, K. A.
2017-08-01
It is established, that in modern works on digital holography, three fundamentally different mathematical models of a matrix photodetector are used. Comparative analysis of these models, including analysis of the formula of each model and test calculations, has been conducted. The possibility of using these models to account for the influence of geometrical parameters of a matrix photodetector on the properties of recorded digital holograms is considered.
Fortran code for generating random probability vectors, unitaries, and quantum states
Directory of Open Access Journals (Sweden)
Jonas eMaziero
2016-03-01
Full Text Available The usefulness of generating random configurations is recognized in many areas of knowledge. Fortran was born for scientific computing and has been one of the main programming languages in this area since then. And several ongoing projects targeting towards its betterment indicate that it will keep this status in the decades to come. In this article, we describe Fortran codes produced, or organized, for the generation of the following random objects: numbers, probability vectors, unitary matrices, and quantum state vectors and density matrices. Some matrix functions are also included and may be of independent interest.
A new derivation of the highest-weight polynomial of a unitary lie algebra
Energy Technology Data Exchange (ETDEWEB)
P Chau, Huu-Tai; P Van, Isacker [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2000-07-01
A new method is presented to derive the expression of the highest-weight polynomial used to build the basis of an irreducible representation (IR) of the unitary algebra U(2J+1). After a brief reminder of Moshinsky's method to arrive at the set of equations defining the highest-weight polynomial of U(2J+1), an alternative derivation of the polynomial from these equations is presented. The method is less general than the one proposed by Moshinsky but has the advantage that the determinantal expression of the highest-weight polynomial is arrived at in a direct way using matrix inversions. (authors)
Random Matrix theory approach to Quantum mechanics
Chaitanya, K. V. S. Shiv
2015-01-01
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of random matrix theory. This study helps in identify the potential appear in the joint probability distribution function in the random matrix theory as a super potential. This approach allows to extend the random matrix theory to the newly discovered exceptional ...
A unitary test of the Ratios Conjecture
Goes, John; Miller, Steven J; Montague, David; Ninsuwan, Kesinee; Peckner, Ryan; Pham, Thuy
2009-01-01
The Ratios Conjecture of Conrey, Farmer and Zirnbauer predicts the answers to numerous questions in number theory, ranging from n-level densities and correlations to mollifiers to moments and vanishing at the central point. The conjecture gives a recipe to generate these answers, which are believed to be correct up to square-root cancelation. These predictions have been verified, for suitably restricted test functions, for the 1-level density of orthogonal and symplectic families of L-functions. In this paper we verify the conjecture's predictions for the unitary family of all Dirichlet $L$-functions with prime conductor; we show square-root agreement between prediction and number theory if the support of the Fourier transform of the test function is in (-1,1), and for support up to (-2,2) we show agreement up to a power savings in the family's cardinality. The interesting feature in this family (which has not surfaced in previous investigations) is determining what is and what is not a diagonal term in the R...
Quantum metrology with unitary parametrization processes.
Liu, Jing; Jing, Xiao-Xing; Wang, Xiaoguang
2015-02-24
Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. In this representation, all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. Furthermore, H can be expressed in an expanded form. The highlights of this form is that it can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Moreover, for an exponential form initial state, an analytical expression of quantum Fisher information by H operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation.
Unitary Evolution and Cosmological Fine-Tuning
Carroll, Sean M
2010-01-01
Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville's theorem implies that no dynamical process can evolve a large number of initial states into a small number of final states. We use the invariant measure on solutions to Einstein's equation to quantify the problems of cosmological fine-tuning. The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are spatially flat. The homogeneity of the early universe, however, does represent a substantial fine-tuning; the horizon problem is real. When perturbations are taken into account, inflation only occurs in a negligibly small fraction of cosmological histories, less than $10^{-6.6\\times 10^7}$. We argue that while inflation does not affect the number of initial conditions that evolve into a late universe like our own, it neve...
Unified continuum damage model for matrix cracking in composite rotor blades
Energy Technology Data Exchange (ETDEWEB)
Pollayi, Hemaraju; Harursampath, Dineshkumar [Nonlinear Multifunctional Composites - Analysis and Design Lab (NMCAD Lab) Department of Aerospace Engineering Indian Institute of Science Bangalore - 560012, Karnataka (India)
2015-03-10
This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic load.
Improved Porosity and Permeability Models with Coal Matrix Block Deformation Effect
Zhou, Yinbo; Li, Zenghua; Yang, Yongliang; Zhang, Lanjun; Qi, Qiangqiang; Si, Leilei; Li, Jinhu
2016-09-01
Coal permeability is an important parameter in coalbed methane (CBM) exploration and greenhouse gas storage. A reasonable theoretical permeability model is helpful for analysing the influential factors of gas flowing in a coalbed. As an unconventional reservoir, the unique feature of a coal structure deformation determines the state of gas seepage. The matrix block and fracture change at the same time due to changes in the effective stress and adsorption; the porosity and permeability also change. Thus, the matrix block deformation must be ignored in the theoretical model. Based on the cubic model, we analysed the characteristics of matrix block deformation and fracture deformation. The new models were developed with the change in matrix block width a. We compared the new models with other models, such as the Palmer-Manson (P-M) model and the Shi-Durucan (S-D) model, and used a constant confining stress. By matching the experimental data, our model matches quite well and accurately predicts the evolution of permeability. The sorption-induced strain coefficient f differs between the strongly adsorbing gases and weakly adsorbing gases because the matrix block deformation is more sensitive for the weakly adsorbing gases and the coefficient f is larger. The cubic relationship between porosity and permeability overlooks the importance of the matrix block deformation. In our model, the matrix block deformation suppresses the permeability ratio growth. With a constant confining stress, the weight of the matrix block deformation for the strongly adsorbing gases is larger than that for weakly adsorbing gases. The weight values increase as the pore pressure increases. It can be concluded that the matrix block deformation is an important phenomenon for researching coal permeability and can be crucial for the prediction of CBM production due to the change in permeability.
A comparison between the fission matrix method, the diffusion model and the transport model
Energy Technology Data Exchange (ETDEWEB)
Dehaye, B.; Hugot, F. X.; Diop, C. M. [Commissariat a l' Energie Atomique et aux Energies Alternatives, Direction de l' Energie Nucleaire, Departement de Modelisation des Systemes et Structures, CEA DEN/DM2S, PC 57, F-91191 Gif-sur-Yvette cedex (France)
2013-07-01
The fission matrix method may be used to solve the critical eigenvalue problem in a Monte Carlo simulation. This method gives us access to the different eigenvalues and eigenvectors of the transport or fission operator. We propose to compare the results obtained via the fission matrix method with those of the diffusion model, and an approximated transport model. To do so, we choose to analyse the mono-kinetic and continuous energy cases for a Godiva-inspired critical sphere. The first five eigenvalues are computed with TRIPOLI-4{sup R} and compared to the theoretical ones. An extension of the notion of the extrapolation distance is proposed for the modes other than the fundamental one. (authors)
Goldberg, Robert K.; Stouffer, Donald C.
1998-01-01
Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this second paper of a two part report, a three-dimensional composite micromechanical model is described which allows for the analysis of the rate dependent, nonlinear deformation response of a polymer matrix composite. Strain rate dependent inelastic constitutive equations utilized to model the deformation response of a polymer are implemented within the micromechanics method. The deformation response of two representative laminated carbon fiber reinforced composite materials with varying fiber orientation has been predicted using the described technique. The predicted results compare favorably to both experimental values and the response predicted by the Generalized Method of Cells, a well-established micromechanics analysis method.
Transitioning to Low-GWP Alternatives in Unitary Air Conditioning
This fact sheet provides current information on low-Global Warming Potential (GWP) refrigerant alternatives used in unitary air-conditioning equipment, relevant to the Montreal Protocol on Substances that Deplete the Ozone Layer.
Virial theorem and universality in a unitary fermi gas.
Thomas, J E; Kinast, J; Turlapov, A
2005-09-16
Unitary Fermi gases, where the scattering length is large compared to the interparticle spacing, can have universal properties, which are independent of the details of the interparticle interactions when the range of the scattering potential is negligible. We prepare an optically trapped, unitary Fermi gas of 6Li, tuned just above the center of a broad Feshbach resonance. In agreement with the universal hypothesis, we observe that this strongly interacting many-body system obeys the virial theorem for an ideal gas over a wide range of temperatures. Based on this result, we suggest a simple volume thermometry method for unitary gases. We also show that the observed breathing mode frequency, which is close to the unitary hydrodynamic value over a wide range of temperature, is consistent with a universal hydrodynamic gas with nearly isentropic dynamics.
Exact and Approximate Unitary 2-Designs: Constructions and Applications
Dankert, C; Emerson, J; Livine, E; Dankert, Christoph; Cleve, Richard; Emerson, Joseph; Livine, Etera
2006-01-01
We consider an extension of the concept of spherical t-designs to the unitary group in order to develop a unified framework for analyzing the resource requirements of randomized quantum algorithms. We show that certain protocols based on twirling require a unitary 2-design. We describe an efficient construction for an exact unitary 2-design based on the Clifford group, and then develop a method for generating an epsilon-approximate unitary 2-design that requires only O(n log(1/epsilon)) gates, where n is the number of qubits and epsilon is an appropriate measure of precision. These results lead to a protocol with exponential resource savings over existing experimental methods for estimating the characteristic fidelities of physical quantum processes.
Aoki, Yasunori; Nordgren, Rikard; Hooker, Andrew C
2016-03-01
As the importance of pharmacometric analysis increases, more and more complex mathematical models are introduced and computational error resulting from computational instability starts to become a bottleneck in the analysis. We propose a preconditioning method for non-linear mixed effects models used in pharmacometric analyses to stabilise the computation of the variance-covariance matrix. Roughly speaking, the method reparameterises the model with a linear combination of the original model parameters so that the Hessian matrix of the likelihood of the reparameterised model becomes close to an identity matrix. This approach will reduce the influence of computational error, for example rounding error, to the final computational result. We present numerical experiments demonstrating that the stabilisation of the computation using the proposed method can recover failed variance-covariance matrix computations, and reveal non-identifiability of the model parameters.
A program for computing the exact Fisher information matrix of a Gaussian VARMA model
Klein, A.; Mélard, G.; Niemczyk, J.; Zahaf, T.
2004-01-01
A program in the MATLAB environment is described for computing the Fisher information matrix of the exact information matrix of a Gaussian vector autoregressive moving average (VARMA) model. A computationally efficient procedure is used on the basis of a state space representation. It relies heavily
S-matrix Fluctuations in a model with Classical Diffusion and Quantum Localization
Borgonovi, F; Borgonovi, Fausto; Guarneri, Italo
1993-01-01
Abstract: The statistics of S-matrix fluctuations are numerically investigated on a model for irregular quantum scattering in which a classical chaotic diffusion takes place within the interaction region. Agreement with various random-matrix theoretic predictions is discussed in the various regimes (ballistic, diffusive, localized).
Markov Model of Wind Power Time Series UsingBayesian Inference of Transition Matrix
DEFF Research Database (Denmark)
Chen, Peiyuan; Berthelsen, Kasper Klitgaard; Bak-Jensen, Birgitte
2009-01-01
This paper proposes to use Bayesian inference of transition matrix when developing a discrete Markov model of a wind speed/power time series and 95% credible interval for the model verification. The Dirichlet distribution is used as a conjugate prior for the transition matrix. Three discrete Markov...... models are compared, i.e. the basic Markov model, the Bayesian Markov model and the birth-and-death Markov model. The proposed Bayesian Markov model shows the best accuracy in modeling the autocorrelation of the wind power time series....
Modeling of effects of matrix on actuation characteristics of embedded shape memory alloy wires
Institute of Scientific and Technical Information of China (English)
CUI Xiao-long; ZHENG Yan-jun; CUI Li-shan
2005-01-01
Effects of matrix properties on the actuation characteristics of embedded shape memory alloy wires were studied. The coefficient of thermal expansion and the modulus of matrix have significant effect on the maximum recovery stress. The thermal strain rate of the SMA wires upon heating is more sensitive to the matrix properties than the stress rate does. Additional fibers embedded in the matrix have significant effect on the stress distribution between the SMA wires and the matrix, and thus affect the interface quality significantly. Fibers with negative thermal expansion coefficient are beneficial to the interface between shape memory alloy wires and the epoxy matrix. All conclusions based on the numerical modeling can find experimental supports.
The Theory of Unitary Development of Chengdu and Chongqing
Institute of Scientific and Technical Information of China (English)
HuangQing
2005-01-01
Chengdu and Chongqing are two megalopolises with the synthesized economic strength and the strongest urban competitiveness in the entire western region, which have very important positions in the development of western China. Through horizontal contrast of social economic developing level of the two cities, the two cities' economic foundation of unitary development is analyzed from complementary and integrative relationship. Then the policies and measures of economic unitary development of two cities is put forward.
Free Energies and Fluctuations for the Unitary Brownian Motion
Dahlqvist, Antoine
2016-12-01
We show that the Laplace transforms of traces of words in independent unitary Brownian motions converge towards an analytic function on a non trivial disc. These results allow one to study the asymptotic behavior of Wilson loops under the unitary Yang-Mills measure on the plane with a potential. The limiting objects obtained are shown to be characterized by equations analogue to Schwinger-Dyson's ones, named here after Makeenko and Migdal.
A matrix model for the topological string II: The spectral curve and mirror geometry
Eynard, Bertrand; Marchal, Olivier
2010-01-01
In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing certain minimality assumptions on the spectral curve, the large volume limit of the BKMP "remodeling the B-model" conjecture, the claim that Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the spectral invariants of its mirror curve.
Neutrinoless double beta nuclear matrix elements around mass 80 in the nuclear shell-model
Yoshinaga, N.; Higashiyama, K.; Taguchi, D.; Teruya, E.
2015-05-01
The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. For theoretical nuclear physics it is particularly important to estimate three types of matrix elements, namely Fermi (F), Gamow-Teller (GT), and tensor (T) matrix elements. In this paper, we carry out shell-model calculations and also pair-truncated shell-model calculations to check the model dependence in the case of mass A=82 nuclei.
Neutrinoless double beta nuclear matrix elements around mass 80 in the nuclear shell-model
Directory of Open Access Journals (Sweden)
Yoshinaga N.
2015-01-01
Full Text Available The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. For theoretical nuclear physics it is particularly important to estimate three types of matrix elements, namely Fermi (F, Gamow-Teller (GT, and tensor (T matrix elements. In this paper, we carry out shell-model calculations and also pair-truncated shell-model calculations to check the model dependence in the case of mass A=82 nuclei.
One- and two-matrix models and random cylindre with two-coloured boundaries
Orantin, Nicolas
2004-01-01
In this training course report, I briefly present the one- and two-matrix models as tools for the study of conformal field theories with boundaries. In a first part, after a short historical presentation of random matrices, I present the matrix models' formalism, their diagramatic interpretation, their link with random surfaces and conformal field theories and the "loop equations" method for the 2-matrix model. In a second part, I use this method for the calculation of the generating function of random cylindres whose boundaries are two-coloured, which was not know before.
Implementation of bipartite or remote unitary gates with repeater nodes
Yu, Li; Nemoto, Kae
2016-08-01
We propose some protocols to implement various classes of bipartite unitary operations on two remote parties with the help of repeater nodes in-between. We also present a protocol to implement a single-qubit unitary with parameters determined by a remote party with the help of up to three repeater nodes. It is assumed that the neighboring nodes are connected by noisy photonic channels, and the local gates can be performed quite accurately, while the decoherence of memories is significant. A unitary is often a part of a larger computation or communication task in a quantum network, and to reduce the amount of decoherence in other systems of the network, we focus on the goal of saving the total time for implementing a unitary including the time for entanglement preparation. We review some previously studied protocols that implement bipartite unitaries using local operations and classical communication and prior shared entanglement, and apply them to the situation with repeater nodes without prior entanglement. We find that the protocols using piecewise entanglement between neighboring nodes often require less total time compared to preparing entanglement between the two end nodes first and then performing the previously known protocols. For a generic bipartite unitary, as the number of repeater nodes increases, the total time could approach the time cost for direct signal transfer from one end node to the other. We also prove some lower bounds of the total time when there are a small number of repeater nodes. The application to position-based cryptography is discussed.
Cell-based modeling of cell-matrix interactions in angiogenesis
Directory of Open Access Journals (Sweden)
Merks Roeland M.H.
2015-01-01
Full Text Available The self-organization of endothelial cells into blood vessel networks and sprouts can be studied using computational, cell-based models. These take as input the behavior of individual, endothelial cells, as observed in experiments, and gives as output the resulting, collective behavior, i.e. the formation of shapes and tissue structures. Many cell-based models ignore the extracellular matrix, i.e., the fibrous or homogeneous materials that surround cells and gives tissue structural support. In this extended abstract, we highlight two approaches that we have taken to explore the role of the extracellular matrix in our cellular Potts models of blood vessel formation (angiogenesis: first we discuss a model considering chemical endothelial cell-matrix interactions, then we discuss a model that include mechanical cell-matrix interactions. We end by discussing some potential new directions.
Unitary fermions and Lüscher's formula on a crystal
Valiente, Manuel; Zinner, Nikolaj T.
2016-11-01
We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the naïve continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak, intermediate and unitary limits. These may be used to significantly ease the extraction of scattering information, and therefore effective interactions in condensed matter systems in realistic periodic potentials. This can achieved via exact diagonalisation or Monte Carlo methods, without the need to solve challenging, genuine multichannel collisional problems with very restricted symmetry simplifications.
Analytical Micromechanics Modeling Technique Developed for Ceramic Matrix Composites Analysis
Min, James B.
2005-01-01
Ceramic matrix composites (CMCs) promise many advantages for next-generation aerospace propulsion systems. Specifically, carbon-reinforced silicon carbide (C/SiC) CMCs enable higher operational temperatures and provide potential component weight savings by virtue of their high specific strength. These attributes may provide systemwide benefits. Higher operating temperatures lessen or eliminate the need for cooling, thereby reducing both fuel consumption and the complex hardware and plumbing required for heat management. This, in turn, lowers system weight, size, and complexity, while improving efficiency, reliability, and service life, resulting in overall lower operating costs.
The black hole S-Matrix from quantum mechanics
Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga
2016-11-01
We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory & c = 1 Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model — of waves scattering off inverted harmonic oscillator potentials — that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.
The Black Hole S-Matrix from Quantum Mechanics
Betzios, Panagiotis; Papadoulaki, Olga
2016-01-01
We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory \\& $c=1$ Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model\\textemdash of waves scattering off inverted harmonic oscillator potentials\\textemdash that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.
Study of optical techniques for the Ames unitary wind tunnel. Part 5: Infrared imagery
Lee, George
1992-01-01
A survey of infrared thermography for aerodynamics was made. Particular attention was paid to boundary layer transition detection. IR thermography flow visualization of 2-D and 3-D separation was surveyed. Heat transfer measurements and surface temperature measurements were also covered. Comparisons of several commercial IR cameras were made. The use of a recently purchased IR camera in the Ames Unitary Plan Wind Tunnels was studied. Optical access for these facilities and the methods to scan typical models was investigated.
Probing Models of Neutrino Masses via the Flavor Structure of the Mass Matrix
Kanemura, Shinya
2015-01-01
We discuss what kinds of combinations of Yukawa interactions can generate the Majorana neutrino mass matrix. We concentrate on the flavor structure of the neutrino mass matrix because it does not depend on details of the models except for Yukawa interactions while determination of the overall scale of the mass matrix requires to specify also the scalar potential and masses of new particles. Thus, models to generate Majorana neutrino mass matrix can be efficiently classified according to the combination of Yukawa interactions. We first investigate the case where Yukawa interactions with only leptons are utilized. Next, we consider the case with Yukawa interactions between leptons and gauge singlet fermions, which have the odd parity under the unbroken Z_2 symmetry. We show that combinations of Yukawa interactions for these cases can be classified into only three groups. Our classification would be useful for the efficient discrimination of models via experimental tests for not each model but just three groups ...
Space-Time Quantization and Nonlocal Field Theory -Relativistic Second Quantization of Matrix Model
Tanaka, S
2000-01-01
We propose relativistic second quantization of matrix model of D particles in a general framework of nonlocal field theory based on Snyder-Yang's quantized space-time. Second-quantized nonlocal field is in general noncommutative with quantized space-time, but conjectured to become commutative with light cone time $X^+$. This conjecture enables us to find second-quantized Hamiltonian of D particle system and Heisenberg's equation of motion of second-quantized {\\bf D} field in close contact with Hamiltonian given in matrix model. We propose Hamilton's principle of Lorentz-invariant action of {\\bf D} field and investigate what conditions or approximations are needed to reproduce the above Heisenberg's equation given in light cone time. Both noncommutativities appearing in position coordinates of D particles in matrix model and in quantized space-time will be eventually unified through second quantization of matrix model.
National Research Council Canada - National Science Library
Aoki, Yasunori; Nordgren, Rikard; Hooker, Andrew C
2016-01-01
... a bottleneck in the analysis. We propose a preconditioning method for non-linear mixed effects models used in pharmacometric analyses to stabilise the computation of the variance-covariance matrix...
A Random Matrix Approach for Quantifying Model-Form Uncertainties in Turbulence Modeling
Xiao, Heng; Ghanem, Roger G
2016-01-01
With the ever-increasing use of Reynolds-Averaged Navier--Stokes (RANS) simulations in mission-critical applications, the quantification of model-form uncertainty in RANS models has attracted attention in the turbulence modeling community. Recently, a physics-based, nonparametric approach for quantifying model-form uncertainty in RANS simulations has been proposed, where Reynolds stresses are projected to physically meaningful dimensions and perturbations are introduced only in the physically realizable limits. However, a challenge associated with this approach is to assess the amount of information introduced in the prior distribution and to avoid imposing unwarranted constraints. In this work we propose a random matrix approach for quantifying model-form uncertainties in RANS simulations with the realizability of the Reynolds stress guaranteed. Furthermore, the maximum entropy principle is used to identify the probability distribution that satisfies the constraints from available information but without int...
Matrix model and Holographic Baryons in the D0-D4 background
Li, Si-Wen
2015-01-01
We study on the spectrum and short-distance two-body force of holographic baryons by the matrix model derived from Sakai-Sugimoto model in D0-D4 background (D0-D4/D8 system). The matrix model is derived by using the standard technique in string theory which can describe multi-baryon system. We rederive the action of the matrix model from open string theory on the wrapped baryon vertex which is embedded in the D0- D4/D8 system. In this matrix model, the positions of $k$ baryons are described by $k\\times k$ matrices, and the spins and isospins are encoded in a set of $k$-vectors. The matrix model offers a systematic approach to the dynamics of the baryons at short distances. In our system, we find that the matrix model describe stable baryonic states only if $\\zeta=U_{Q_{0}}^{3}/U_{KK}^{3}2$, which may consistently correspond to the existence of unstable baryonic states.
Snorradóttir, Bergthóra S; Jónsdóttir, Fjóla; Sigurdsson, Sven Th; Másson, Már
2014-08-01
A model is presented for transdermal drug delivery from single-layered silicone matrix systems. The work is based on our previous results that, in particular, extend the well-known Higuchi model. Recently, we have introduced a numerical transient model describing matrix systems where the drug dissolution can be non-instantaneous. Furthermore, our model can describe complex interactions within a multi-layered matrix and the matrix to skin boundary. The power of the modelling approach presented here is further illustrated by allowing the possibility of a donor solution. The model is validated by a comparison with experimental data, as well as validating the parameter values against each other, using various configurations with donor solution, silicone matrix and skin. Our results show that the model is a good approximation to real multi-layered delivery systems. The model offers the ability of comparing drug release for ibuprofen and diclofenac, which cannot be analysed by the Higuchi model because the dissolution in the latter case turns out to be limited. The experiments and numerical model outlined in this study could also be adjusted to more general formulations, which enhances the utility of the numerical model as a design tool for the development of drug-loaded matrices for trans-membrane and transdermal delivery.
Directory of Open Access Journals (Sweden)
Soldatova S.
2015-12-01
Full Text Available This article addresses the task of creating a regional Social Accounting Matrix (SAM in the Kaliningrad region. Analyzing the behavior of economic systems of national and sub-national levels in the changing environment is one of the main objectives of macroeconomic research. Matrices are used in examining the flow of financial resources, which makes it possible to conduct a comprehensive analysis of commodity and cash flows at the regional level. The study identifies key data sources for matrix development and presents its main results: the data sources for the accounts development and filling the social accounting matrix are identified, regional accounts consolidated, the structure of regional matrix devised, and the multiplier of the regional social accounting matrix calculated. An important aspect of this approach is the set target, which determines the composition of matrix accounts representing different aspects of regional performance. The calculated multiplier suggests the possibility of modelling of a socioeconomic system for the region using a social accounting matrix. The regional modelling approach ensures the matrix compliance with the methodological requirements of the national system.
Directory of Open Access Journals (Sweden)
Soldatova S.
2015-08-01
Full Text Available This article addresses the task of creating a regional Social Accounting Matrix (SAM in the Kaliningrad region. Analyzing the behavior of economic systems of national and sub-national levels in the changing environment is one of the main objectives of macroeconomic research. Matrices are used in examining the flow of financial resources, which makes it possible to conduct a comprehensive analysis of commodity and cash flows at the regional level. The study identifies key data sources for matrix development and presents its main results: the data sources for the accounts development and filling the social accounting matrix are identified, regional accounts consolidated, the structure of regional matrix devised, and the multiplier of the regional social accounting matrix calculated. An important aspect of this approach is the set target, which determines the composition of matrix accounts representing different aspects of regional performance. The calculated multiplier suggests the possibility of modelling of a socioeconomic system for the region using a social accounting matrix. The regional modelling approach ensures the matrix compliance with the methodological requirements of the national system
Directory of Open Access Journals (Sweden)
Soldatova Svetlana
2015-09-01
Full Text Available This article addresses the task of creating a regional Social Accounting Matrix (SAM in the Kaliningrad region. Analyzing the behavior of economic systems of national and sub-national levels in the changing environment is one of the main objectives of macroeconomic research. Matrices are used in examining the flow of financial resources, which makes it possible to conduct a comprehensive analysis of commodity and cash flows at the regional level. The study identifies key data sources for matrix development and presents its main results: the data sources for the accounts development and filling the social accounting matrix are identified, regional accounts consolidated, the structure of regional matrix devised, and the multiplier of the regional social accounting matrix calculated. An important aspect of this approach is the set target, which determines the composition of matrix accounts representing different aspects of regional performance. The calculated multiplier suggests the possibility of modelling of a socioeconomic system for the region using a social accounting matrix. The regional modelling approach ensures the matrix compliance with the methodological requirements of the national system
Seeking Texture Zeros in the Quark Mass Matrix Sector of the Standard Model
Giraldo, Yithsbey
2015-01-01
Here we show that the Weak Basis Transformation is an appropriate mathematical tool that can be used to find texture zeros in the quark mass matrix sector of the Standard Model. So, starting with the most general quark mass matrices and taking physical data into consideration, is possible to obtain more than three texture zeros by any weak basis transformation. Where the most general quark mass matrices considered in the model, were obtained through a special weak basis wherein the mass matrix $M_u$~(or $M_d$) has been taken to be diagonal and only the matrix $M_d$~(or $M_u$) is considered to be most general.
A Mathematical Model for Diffusion-Controlled Monolithic Matrix Coated with outer Membrane System
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A release model for diffusion-controlled monolithic matrix coated with outer membrane system is proposed and solved by using the refined double integral method. The calculated results are in satisfactory agreement with the experimental release data. The present model can be well used to describe the release process for all cd/cs values. In addition, the release effects of the monolithic matrix coated with outer membrane system are discussed theoretically.
A Model for Estimating Nonlinear Deformation and Damage in Ceramic Matrix Composites (Preprint)
2011-07-01
AFRL-RX-WP-TP-2011-4232 A MODEL FOR ESTIMATING NONLINEAR DEFORMATION AND DAMAGE IN CERAMIC MATRIX COMPOSITES (PREPRINT) Unni Santhosh and...5a. CONTRACT NUMBER In-house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62102F 6. AUTHOR(S) Unni Santhosh and Jalees Ahmad 5d. PROJECT...Composite Materials, 2010 A Model for Estimating Nonlinear Deformation and Damage in Ceramic Matrix Composites Unni Santhosh and Jalees Ahmad Research
Massless ground state for a compact SU(2 matrix model in 4D
Directory of Open Access Journals (Sweden)
Lyonell Boulton
2015-09-01
Full Text Available We show the existence and uniqueness of a massless supersymmetric ground state wavefunction of a SU(2 matrix model in a bounded smooth domain with Dirichlet boundary conditions. This is a gauge system and we provide a new framework to analyze the quantum spectral properties of this class of supersymmetric matrix models subject to constraints which can be generalized for arbitrary number of colors.
Boundary form factors in the Smirnov--Fateev model with a diagonal boundary $S$ matrix
Lashkevich, Michael
2008-01-01
The boundary conditions with diagonal boundary $S$ matrix and the boundary form factors for the Smirnov--Fateev model on a half line has been considered in the framework of the free field representation. In contrast to the case of the sine-Gordon model, in this case the free field representation is shown to impose severe restrictions on the boundary $S$ matrix, so that a finite number of solutions is only consistent with the free field realization.
On Correlation Numbers in 2D Minimal Gravity and Matrix Models
Belavin, A A
2008-01-01
We test recent results for the four-point correlation numbers in Minimal Liouville Gravity against calculations in the one-Matrix Models, and find full agreement. In the process, we construct the resonance transformation which relates coupling parameters of the Liouville Gravity with the couplings of the Matrix Models, up to the terms of the order 4. We also conjecture the general form of this transformation.
Unitary Networks from the Exact Renormalization of Wave Functionals
Fliss, Jackson R; Parrikar, Onkar
2016-01-01
The exact renormalization group (ERG) for $O(N)$ vector models (at large $N$) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on $AdS_{d+1}$. This was established in the sense that at large $N$ the generating functional of correlation functions of single trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the $O(N)$ vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared rece...
Holographic Fluctuations from Unitary de Sitter Invariant Field Theory
Banks, Tom; Torres, T J; Wainwright, Carroll L
2013-01-01
We continue the study of inflationary fluctuations in Holographic Space Time models of inflation. We argue that the holographic theory of inflation provides a physical context for what is often called dS/CFT. The holographic theory is a quantum theory which, in the limit of a large number of e-foldings, gives rise to a field theory on $S^3$, which is the representation space for a unitary representation of SO(1,4). This is not a conventional CFT, and we do not know the detailed non-perturbative axioms for correlation functions. However, the two- and three-point functions are completely determined by symmetry, and coincide up to a few constants (really functions of the background FRW geometry) with those calculated in a single field slow-roll inflation model. The only significant deviation from slow roll is in the tensor fluctuations. We predict zero tensor tilt and roughly equal weight for all three conformally invariant tensor 3-point functions (unless parity is imposed as a symmetry). We discuss the relatio...
Spectral Characteristics of the Unitary Critical Almost-Mathieu Operator
Fillman, Jake; Ong, Darren C.; Zhang, Zhenghe
2016-10-01
We discuss spectral characteristics of a one-dimensional quantum walk whose coins are distributed quasi-periodically. The unitary update rule of this quantum walk shares many spectral characteristics with the critical Almost-Mathieu Operator; however, it possesses a feature not present in the Almost-Mathieu Operator, namely singularity of the associated cocycles (this feature is, however, present in the so-called Extended Harper's Model). We show that this operator has empty absolutely continuous spectrum and that the Lyapunov exponent vanishes on the spectrum; hence, this model exhibits Cantor spectrum of zero Lebesgue measure for all irrational frequencies and arbitrary phase, which in physics is known as Hofstadter's butterfly. In fact, we will show something stronger, namely, that all spectral parameters in the spectrum are of critical type, in the language of Avila's global theory of analytic quasiperiodic cocycles. We further prove that it has empty point spectrum for each irrational frequency and away from a frequency-dependent set of phases having Lebesgue measure zero. The key ingredients in our proofs are an adaptation of Avila's Global Theory to the present setting, self-duality via the Fourier transform, and a Johnson-type theorem for singular dynamically defined CMV matrices which characterizes their spectra as the set of spectral parameters at which the associated cocycles fail to admit a dominated splitting.
MODELLING THE LESOTHO ECONOMY: A SOCIAL ACCOUNTING MATRIX APPROACH
Directory of Open Access Journals (Sweden)
Yonas Tesfamariam Bahta
2013-07-01
Full Text Available Using a 2000 Social Accounting Matrix (SAM for Lesotho, this paper investigates the key features of the Lesotho economy and the role played by the agricultural sector. A novel feature of the SAM is the elaborate disaggregation of the agricultural sector into finer subcategories. The fundamental importance of agriculture development emerges clearly from a descriptive review and from SAM multiplier analysis. It is dominant with respect to income generation and value of production. It contributes 23 percent of gross domestic product and 12 percent of the total value of production. It employs 26 percent of labour and 24 percent of capital. The construction sector has the highest open SAM output multiplier (1,588 and SAM output multiplier (1.767. The household multipliers indicate that in the rural and urban areas, agriculture and mining respectively generate most household income. Agriculture has the highest employment coefficient. Agriculture and mining sectors also have the largest employment multipliers in Lesotho.
A Random Matrix Model of Adiabatic Quantum Computing
Mitchell, D R; Lue, W; Williams, C P; Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.
2004-01-01
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances, i.e., those having a critical ratio of clauses to variables, the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathemat...
Transient Analysis of Hysteresis Queueing Model Using Matrix Geometric Method
Directory of Open Access Journals (Sweden)
Wajiha Shah
2011-10-01
Full Text Available Various analytical methods have been proposed for the transient analysis of a queueing system in the scalar domain. In this paper, a vector domain based transient analysis is proposed for the hysteresis queueing system with internal thresholds for the efficient and numerically stable analysis. In this system arrival rate of customer is controlled through the internal thresholds and the system is analyzed as a quasi-birth and death process through matrix geometric method with the combination of vector form Runge-Kutta numerical procedure which utilizes the special matrices. An arrival and service process of the system follows a Markovian distribution. We analyze the mean number of customers in the system when the system is in transient state against varying time for a Markovian distribution. The results show that the effect of oscillation/hysteresis depends on the difference between the two internal threshold values.
Time series, correlation matrices and random matrix models
Energy Technology Data Exchange (ETDEWEB)
Vinayak [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca (Mexico); Seligman, Thomas H. [Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca, México and Centro Internacional de Ciencias, C.P. 62210 Cuernavaca (Mexico)
2014-01-08
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.
Modelling of polypropylene fibre-matrix composites using finite element analysis
Directory of Open Access Journals (Sweden)
2009-01-01
Full Text Available Polypropylene (PP fibre-matrix composites previously prepared and studied experimentally were modelled using finite element analysis (FEA in this work. FEA confirmed that fibre content and composition controlled stress distribution in all-PP composites. The stress concentration at the fibre-matrix interface became greater with less fibre content. Variations in fibre composition were more significant in higher stress regions of the composites. When fibre modulus increased, the stress concentration at the fibres decreased and the shear stress at the fibre-matrix interface became more intense. The ratio between matrix modulus and fibre modulus was important, as was the interfacial stress in reducing premature interfacial failure and increasing mechanical properties. The model demonstrated that with low fibre concentration, there were insufficient fibres to distribute the applied stress. Under these conditions the matrix yielded when the applied stress reached the matrix yield stress, resulting in increased fibre axial stress. When the fibre content was high, there was matrix depletion and stress transfer was inefficient. The predictions of the FEA model were consistent with experimental and published data.
Spicer, Graham L. C.; Azarin, Samira M.; Yi, Ji; Young, Scott T.; Ellis, Ronald; Bauer, Greta M.; Shea, Lonnie D.; Backman, Vadim
2016-10-01
In cancer biology, there has been a recent effort to understand tumor formation in the context of the tissue microenvironment. In particular, recent progress has explored the mechanisms behind how changes in the cell-extracellular matrix ensemble influence progression of the disease. The extensive use of in vitro tissue culture models in simulant matrix has proven effective at studying such interactions, but modalities for non-invasively quantifying aspects of these systems are scant. We present the novel application of an imaging technique, Inverse Spectroscopic Optical Coherence Tomography, for the non-destructive measurement of in vitro biological samples during matrix remodeling. Our findings indicate that the nanoscale-sensitive mass density correlation shape factor D of cancer cells increases in response to a more crosslinked matrix. We present a facile technique for the non-invasive, quantitative study of the micro- and nano-scale structure of the extracellular matrix and its host cells.
Abnormal Structure of Fermion Mixings in a Seesaw Quark Mass Matrix Model
Koide, Y
1997-01-01
It is pointed out that in a seesaw quark mass matrix model which yields a singular enhancement of the top-quark mass, the right-handed fermion-mixing matrix U_R^u for the up-quark sector has a peculiar structure in contrast to the left-handed one U_L^u. As an example of the explicit structures of U_L^u and U_R^u, a case in which the heavy fermion mass matrix M_F is given by a form [(unit matrix)+(rank-one matrix)] is investigated. As a consequence, one finds observable signatures at projected high energy accelerators like the production of a fourth heavy quark family.
The $\\Xi^* \\bar{K}$ and $\\Omega \\eta$ interaction within a chiral unitary approach
Xu, Siqi; Chen, Xurong; Jia, Duojie
2015-01-01
In this work we study the interaction of the coupled channels $\\Omega \\eta$ and $\\Xi^* \\bar{K}$ within the chiral unitary approach. The systems under consideration have total isospins $0$, strangeness $S = -3$, and spin $3/2$. We studied the $s$ wave interaction which implies that the possible resonances generated in the system can have spin-parity $J^P = 3/2^-$. The unitary amplitudes in coupled channels develop poles that can be associated with some known baryonic resonances. We find there is a dynamically generated $3/2^-$ $\\Omega$ state with mass around $1800$ MeV, which is in agreement with the predictions of the five-quark model.
Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2002-03-19
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.
DEFF Research Database (Denmark)
Terp, G E; Christensen, I T; Jørgensen, Flemming Steen
2000-01-01
Matrix metalloproteinases are extracellular enzymes taking part in the remodeling of extracellular matrix. The structures of the catalytic domain of MMP1, MMP3, MMP7 and MMP8 are known, but structures of enzymes belonging to this family still remain to be determined. A general approach...... to the homology modeling of matrix metalloproteinases, exemplified by the modeling of MMP2, MMP9, MMP12 and MMP14 is described. The models were refined using an energy minimization procedure developed for matrix metalloproteinases. This procedure includes incorporation of parameters for zinc and calcium ions...... in the AMBER 4.1 force field, applying a non-bonded approach and a full ion charge representation. Energy minimization of the apoenzymes yielded structures with distorted active sites, while reliable three-dimensional structures of the enzymes containing a substrate in active site were obtained. The structural...
Energy Technology Data Exchange (ETDEWEB)
B. Julia-Diaz, H. Kamano, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki
2009-04-01
Within the relativistic quantum field theory, we analyze the differences between the $\\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2002-03-12
Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle-antiparticle amplitude. This process differs from conventional on-shell Mandelstam s,t,u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel nonperturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle-antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the nonrelativistic Coulomb problem, including the forward scattering singularity , the essential singularity in the phase, and the Bohr bound-state spectrum.
A matrix approach to the statistics of longevity in heterogeneous frailty models
Directory of Open Access Journals (Sweden)
Hal Caswell
2014-09-01
Full Text Available Background: The gamma-Gompertz model is a fixed frailty model in which baseline mortality increasesexponentially with age, frailty has a proportional effect on mortality, and frailty at birth follows a gamma distribution. Mortality selects against the more frail, so the marginal mortality rate decelerates, eventually reaching an asymptote. The gamma-Gompertz is one of a wider class of frailty models, characterized by the choice of baseline mortality, effects of frailty, distributions of frailty, and assumptions about the dynamics of frailty. Objective: To develop a matrix model to compute all the statistical properties of longevity from thegamma-Gompertz and related models. Methods: I use the vec-permutation matrix formulation to develop a model in which individuals are jointly classified by age and frailty. The matrix is used to project the age and frailty dynamicsof a cohort and the fundamental matrix is used to obtain the statistics of longevity. Results: The model permits calculation of the mean, variance, coefficient of variation, skewness and all moments of longevity, the marginal mortality and survivorship functions, the dynamics of the frailty distribution, and other quantities. The matrix formulation extends naturally to other frailty models. I apply the analysis to the gamma-Gompertz model (for humans and laboratory animals, the gamma-Makeham model, and the gamma-Siler model, and to a hypothetical dynamic frailty model characterized by diffusion of frailty with reflecting boundaries.The matrix model permits partitioning the variance in longevity into components due to heterogeneity and to individual stochasticity. In several published human data sets, heterogeneity accounts for less than 10Š of the variance in longevity. In laboratory populations of five invertebrate animal species, heterogeneity accounts for 46Š to 83Š ofthe total variance in longevity.
Simplified prediction model for elastic modulus of particulate reinforced metal matrix composites
Institute of Scientific and Technical Information of China (English)
WANG Wen-ming; PAN Fu-sheng; LU Yun; ZENG Su-min
2006-01-01
Some structural parameters of the metal matrix composite, including particulate shape and distribution do not influence the elastic modulus. A prediction model for the elastic modulus of particulate reinforced metal matrix Al composite was developed and improved. Expressions of rigidity and flexibility of the rule of mixing were proposed. A five-zone model for elasticity performance calculation of the composite was proposed. The five-zone model is thought to be able to reflect the effects of the MMC interface on elastic modulus of the composite. The model overcomes limitations of the currently-understood rigidity and flexibility of the rule of mixing. The original idea of a five-zone model is to propose particulate/interface interactive zone and matrix/interface interactive zone. By integrating organically with the law of mixing, the new model is found to be capable of predicting the engineering elastic constants of the MMC composite.
The Area Law in Matrix Models for Large N QCD Strings
Anagnostopoulos, K N; Nishimura, J
2002-01-01
We study the question whether matrix models obtained in the zero volume limit of 4d Yang-Mills theories can describe large N QCD strings. The matrix model we use is a variant of the Eguchi-Kawai model in terms of Hermitian matrices, but without any twists or quenching. This model was originally proposed as a toy model of the IIB matrix model. In contrast to common expectations, we do observe the area law for Wilson loops in a significant range of scale of the loop area. Numerical simulations show that this range is stable as N increases up to 768, which strongly suggests that it persists in the large N limit. Hence the equivalence to QCD strings may hold for length scales inside a finite regime.
Efficient unitary designs with nearly time-independent Hamiltonian dynamics
Nakata, Yoshifumi; Koashi, Masato; Winter, Andreas
2016-01-01
We provide new constructions of unitary $t$-designs for general $t$ on one qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time, as a basic framework to investigate randomising time evolution in quantum many-body systems. The new constructions are based on recently proposed schemes of repeating random unitaires diagonal in mutually unbiased bases. We first show that, if a pair of the bases satisfies a certain condition, the process on one qudit approximately forms a unitary $t$-design after $O(t)$ repetitions. We then construct quantum circuits on $N$ qubits that achieve unitary $t$-designs for $t = o(N^{1/2})$ using $O(t N^2)$ gates, improving the previous result using $O(t^{10}N^2)$ gates in terms of $t$. Based on these results, we present a design Hamiltonian with periodically changing two-local spin-glass-type interactions, leading to fast and relatively natural realisations of unitary designs in complex many-bo...
Modeling social influence through network autocorrelation : constructing the weight matrix
Leenders, RTAJ
2002-01-01
Many physical and social phenomena are embedded within networks of interdependencies, the so-called 'context' of these phenomena. In network analysis, this type of process is typically modeled as a network autocorrelation model. Parameter estimates and inferences based on autocorrelation models, hin
A new coal-permeability model: Internal swelling stress and fracture-matrix interaction
Energy Technology Data Exchange (ETDEWEB)
Liu, H.H.; Rutqvist, J.
2009-10-01
We have developed a new coal-permeability model for uniaxial strain and constant confining stress conditions. The model is unique in that it explicitly considers fracture-matrix interaction during coal deformation processes and is based on a newly proposed internal-swelling stress concept. This concept is used to account for the impact of matrix swelling (or shrinkage) on fracture-aperture changes resulting from partial separation of matrix blocks by fractures that do not completely cut through the whole matrix. The proposed permeability model is evaluated with data from three Valencia Canyon coalbed wells in the San Juan Basin, where increased permeability has been observed during CH{sub 4} gas production, as well as with published data from laboratory tests. Model results are generally in good agreement with observed permeability changes. The importance of fracture-matrix interaction in determining coal permeability, demonstrated in this work using relatively simple stress conditions, underscores the need for a dual-continuum (fracture and matrix) mechanical approach to rigorously capture coal-deformation processes under complex stress conditions, as well as the coupled flow and transport processes in coal seams.
A Cellular Potts Model simulating cell migration on and in matrix environments.
Scianna, Marco; Preziosi, Luigi; Wolf, Katarina
2013-02-01
Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated into nucleus and cytosolic region, while the extracellular matrix is composed of a fibrous mesh and a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological extracellular matrix distribution and a biphasic dependence of migration on the matrix structure, density, adhesion, and stiffness, and, moreover, simulates that cell locomotion in highly constrained fibrillar obstacles requires the deformation of the cell's nucleus and/or the activity of cell-derived proteolysis. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomenon in healthy and diseased tissues and in engineering applications.
Jain, S
1996-01-01
Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and 2-d quantum gravity. We review the connection of RMT with these areas. We also discuss the method of loop equations for determining correlation functions in RMT, and smoothed global eigenvalue correlators in the 2-matrix model for gaussian orthogonal, unitary and symplectic ensembles.
Institute of Scientific and Technical Information of China (English)
江冰; 方岱宁; 黄克智
1999-01-01
Based on micromechanics and Laplace transformation, a constitutive model of ferroelectric composites with a linear elastic and linear dielectric matrix is developed and extended to the ferroelectric composites with a viscoelastic and dielectric relaxation matrix. Thus, a constitutive model for ferroelectric composites with a viscoelastic and dielectric relaxation matrix has been set up.
Culture Models to Define Key Mediators of Cancer Matrix Remodeling
Directory of Open Access Journals (Sweden)
Emily Suzanne Fuller
2014-03-01
Full Text Available High grade serous epithelial ovarian cancer (HG-SOC is one of the most devastating gynecological cancers affecting women worldwide, with a poor survival rate despite clinical treatment advances. HG-SOC commonly metastasizes within the peritoneal cavity, primarily to the mesothelial cells of the omentum which regulate an extracellular matrix (ECM rich in collagens type I, III and IV along with laminin, vitronectin and fibronectin. Cancer cells depend on their ability to penetrate and invade secondary tissue sites to spread, however a detailed understanding of the molecular mechanisms underlying these processes remain largely unknown. Given the high metastatic potential of HG-SOC and the associated poor clinical outcome, it is extremely important to identify the pathways and the components of which that are responsible for the progression of this disease. In-vitro methods of recapitulating human disease processes are the critical first step in such investigations. In this context, establishment of an in-vitro ‘tumor-like’ microenvironment, such as 3D culture, to study early disease and metastasis of human HG-SOC is an important and highly insightful method. In recent years many such methods have been established to investigate the adhesion and invasion of human ovarian cancer cell lines. The aim of this review is to summarize recent developments in ovarian cancer culture systems and their use to investigate clinically relevant findings concerning the key players in driving human HG-SOC.
A Multidimensional Nonnegative Matrix Factorization Model for Retweeting Behavior Prediction
Directory of Open Access Journals (Sweden)
Mengmeng Wang
2015-01-01
Full Text Available Today microblogging has increasingly become a means of information diffusion via user’s retweeting behavior. As a consequence, exploring on retweeting behavior is a better way to understand microblog’s transmissibility in the network. Hence, targeted at online microblogging, a directed social network, along with user-based features, this paper first built content-based features, which consisted of URL, hashtag, emotion difference, and interest similarity, based on time series of text information that user posts. And then we measure relationship-based factor in social network according to frequency of interactions and network structure which blend with temporal information. Finally, we utilize nonnegative matrix factorization to predict user’s retweeting behavior from user-based dimension and content-based dimension, respectively, by employing strength of social relationship to constrain objective function. The results suggest that our proposed method effectively increases retweeting behavior prediction accuracy and provides a new train of thought for retweeting behavior prediction in dynamic social networks.
Learning Item-Attribute Relationship in Q-Matrix Based Diagnostic Classification Models
Liu, Jingchen; Ying, Zhiliang
2011-01-01
Recent surge of interests in cognitive assessment has led to the developments of novel statistical models for diagnostic classification. Central to many such models is the well-known Q-matrix, which specifies the item-attribute relationship. This paper proposes a principled estimation procedure for the Q-matrix and related model parameters. Desirable theoretic properties are established through large sample analysis. The proposed method also provides a platform under which important statistical issues, such as hypothesis testing and model selection, can be addressed.
Chiral unitary theory: Application to nuclear problems
Indian Academy of Sciences (India)
E Oset; D Cabrera; H C Chiang; C Garcia Recio; S Hirenzaki; S S Kamalov; J Nieves; Y Okumura; A Ramos; H Toki; M J Vicente Vacas
2001-08-01
In this talk we brieﬂy describe some basic elements of chiral perturbation theory, , and how the implementation of unitarity and other novel elements lead to a better expansion of the -matrix for meson–meson and meson–baryon interactions. Applications are then done to the interaction in nuclear matter in the scalar and vector channels, antikaons in nuclei and - atoms, and how the meson properties are changed in a nuclear medium.
On reducibility and ergodicity of population projection matrix models
DEFF Research Database (Denmark)
Stott, Iain; Townley, Stuart; Carslake, David
2010-01-01
1. Population projection matrices (PPMs) are probably the most commonly used empirical population models. To be useful for predictive or prospective analyses, PPM models should generally be irreducible (the associated life cycle graph contains the necessary transition rates to facilitate pathways...... structure used in the population projection). In our sample of published PPMs, 15·6% are non-ergodic. 3. This presents a problem: reducible–ergodic models often defy biological rationale in their description of the life cycle but may or may not prove problematic for analysis as they often behave similarly...... to irreducible models. Reducible–non-ergodic models will usually defy biological rationale in their description of the both the life cycle and population dynamics, hence contravening most analytical methods. 4. We provide simple methods to evaluate reducibility and ergodicity of PPM models, present illustrative...
The Use of Scattering Matrix to Model Multi-Modal Array Inspection with the Tfm
Zhang, J.; Drinkwater, B. W.; Wilcox, P. D.
2009-03-01
The scattering coefficient matrix describes the far field amplitude of scattered signals from a scatterer as a function of incident and scattering angles. In this paper an FE model is used to predict scattering matrices. By combining the predicted scattering coefficient matrix with a ray tracing model to predict the full matrix of array data, an efficient forward model of the complete array inspection process is presented. Longitudinal wave, shear waves and wave mode conversions are considered in the model. The TFM images for various wave mode combination cases from a weld sample are predicted and measured. Results show that by selecting the optimum array mode combination a good image for a given defect in the weld sample can be produced using an array. It is also shown how the model can be used to optimize the array inspection configuration.
Energy Technology Data Exchange (ETDEWEB)
Jakob, A
2004-07-01
In this report a comprehensive overview on the matrix diffusion of solutes in fractured crystalline rocks is presented. Some examples from observations in crystalline bedrock are used to illustrate that matrix diffusion indeed acts on various length scales. Fickian diffusion is discussed in detail followed by some considerations on rock porosity. Due to the fact that the dual-porosity medium model is a very common and versatile method for describing solute transport in fractured porous media, the transport equations and the fundamental assumptions, approximations and simplifications are discussed in detail. There is a variety of geometrical aspects, processes and events which could influence matrix diffusion. The most important of these, such as, e.g., the effect of the flow-wetted fracture surface, channelling and the limited extent of the porous rock for matrix diffusion etc., are addressed. In a further section open issues and unresolved problems related to matrix diffusion are mentioned. Since matrix diffusion is one of the key retarding processes in geosphere transport of dissolved radionuclide species, matrix diffusion was consequently taken into account in past performance assessments of radioactive waste repositories in crystalline host rocks. Some issues regarding matrix diffusion are site-specific while others are independent of the specific situation of a planned repository for radioactive wastes. Eight different performance assessments from Finland, Sweden and Switzerland were considered with the aim of finding out how matrix diffusion was addressed, and whether a consistent picture emerges regarding the varying methodology of the different radioactive waste organisations. In the final section of the report some conclusions are drawn and an outlook is given. An extensive bibliography provides the reader with the key papers and reports related to matrix diffusion. (author)
General approach for modeling partial coherence in spectroscopic Mueller matrix polarimetry.
Hingerl, Kurt; Ossikovski, Razvigor
2016-01-15
We present a general formalism for modeling partial coherence in spectroscopic Mueller matrix measurements of stratified media. The approach is based on the statistical definition of a Mueller matrix, as well as, on the fundamental representation of the measurement process as the convolution of the sample response with a specific instrumental function. The formalism is readily extended to describe other measurement imperfections occurring jointly with partial coherence and resulting in depolarizing experimental Mueller matrices.
THE TRANSITION PROBABILITY MATRIX OF A MARKOV CHAIN MODEL IN AN ATM NETWORK
Institute of Scientific and Technical Information of China (English)
YUE Dequan; ZHANG Huachen; TU Fengsheng
2003-01-01
In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.
Compressor-fan unitary structure for air conditioning system
Dreiman, N.
2015-08-01
An extremely compact, therefore space saving unitary structure of short axial length is produced by radial integration of a revolving piston rotary compressor and an impeller of a centrifugal fan. The unitary structure employs single motor to run as the compressor so the airflow fan and eliminates duality of motors, related power supply and control elements. Novel revolving piston rotary compressor which provides possibility for such integration comprises the following: a suction gas delivery system which provides cooling of the motor and supplies refrigerant into the suction chamber under higher pressure (supercharged); a modified discharge system and lubricating oil supply system. Axial passages formed in the stationary crankshaft are used to supply discharge gas to a condenser, to return vaporized cooling agent from the evaporator to the suction cavity of the compressor, to pass a lubricant and to accommodate wiring supplying power to the unitary structure driver -external rotor electric motor.
Time reversal and exchange symmetries of unitary gate capacities
Harrow, A W; Harrow, Aram W.; Shor, Peter W.
2005-01-01
Unitary gates are an interesting resource for quantum communication in part because they are always invertible and are intrinsically bidirectional. This paper explores these two symmetries: time-reversal and exchange of Alice and Bob. We will present examples of unitary gates that exhibit dramatic separations between forward and backward capacities (even when the back communication is assisted by free entanglement) and between entanglement-assisted and unassisted capacities, among many others. Along the way, we will give a general time-reversal rule for relating the capacities of a unitary gate and its inverse that will explain why previous attempts at finding asymmetric capacities failed. Finally, we will see how the ability to erase quantum information and destroy entanglement can be a valuable resource for quantum communication.
Xing, Zhi-zhong
2012-01-01
In a simple extension of the standard electroweak theory where the phenomenon of lepton flavor mixing is described by a 3x3 unitary matrix V, the electric and magnetic dipole moments of three active neutrinos are suppressed not only by their tiny masses but also by the Glashow-Iliopoulos-Maiani (GIM) mechanism. We show that it is possible to lift the GIM suppression if the canonical seesaw mechanism of neutrino mass generation, which allows V to be slightly non-unitary, is taken into account. In view of current experimental constraints on the non-unitarity of V, we find that the effective electromagnetic dipole moments of three neutrinos and the rates of their radiative decays can be maximally enhanced by a factor of O(10^2) and a factor of O(10^4), respectively. This nontrivial observation reveals an intrinsic and presumably significant correlation between the electromagnetic properties of massive neutrinos and the origin of their small masses.
Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
Akemann, Gernot
2011-01-01
We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-n limit in the vicinity of the chGUE (which we denote by weakly non-chiral limit) this theory is in one to one correspondence to the partition function of Wilson chiral perturbation theory in the epsilon regime, such as the related two matrix-model previously introduced in refs. [20,21]. For a generic number of flavours and rectangular block matrices in the chGUE part we derive an eigenvalue representation for the partition function displaying a Pfaffian structure. In the quenched case with nu=0,1 we derive all spectral correlations functions in our model for finite-n, given in terms of skew-orthogonal polynomials. The latter are expressed as Gaussian integrals over standard Laguerre polynomials. In the weakly non-chira...
Directory of Open Access Journals (Sweden)
Akihito Soeda
2010-06-01
Full Text Available We study how two pieces of localized quantum information can be delocalized across a composite Hilbert space when a global unitary operation is applied. We classify the delocalization power of global unitary operations on quantum information by investigating the possibility of relocalizing one piece of the quantum information without using any global quantum resource. We show that one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent of a controlled-unitary operation. The delocalization power turns out to reveal different aspect of the non-local properties of global unitary operations characterized by their entangling power.
Random matrices and the six-vertex model
Bleher, Pavel
2013-01-01
This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wa...
Potential Energy Surfaces Using Algebraic Methods Based on Unitary Groups
Directory of Open Access Journals (Sweden)
Renato Lemus
2011-01-01
Full Text Available This contribution reviews the recent advances to estimate the potential energy surfaces through algebraic methods based on the unitary groups used to describe the molecular vibrational degrees of freedom. The basic idea is to introduce the unitary group approach in the context of the traditional approach, where the Hamiltonian is expanded in terms of coordinates and momenta. In the presentation of this paper, several representative molecular systems that permit to illustrate both the different algebraic approaches as well as the usual problems encountered in the vibrational description in terms of internal coordinates are presented. Methods based on coherent states are also discussed.
A construction of fully diverse unitary space-time codes
Institute of Scientific and Technical Information of China (English)
YU Fei; TONG HongXi
2009-01-01
Fully diverse unitary space-time codes are useful in multiantenna communications,especially in multiantenna differential modulation.Recently,two constructions of parametric fully diverse unitary space-time codes for three antennas system have been introduced.We propose a new construction method based on the constructions.In the present paper,fully diverse codes for systems of odd prime number antennas are obtained from this construction.Space-time codes from present construction are found to have better error performance than many best known ones.
Non-unitary probabilistic quantum computing circuit and method
Williams, Colin P. (Inventor); Gingrich, Robert M. (Inventor)
2009-01-01
A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained.
A construction of fully diverse unitary space-time codes
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Fully diverse unitary space-time codes are useful in multiantenna communications, especially in multiantenna differential modulation. Recently, two constructions of parametric fully diverse unitary space-time codes for three antennas system have been introduced. We propose a new construction method based on the constructions. In the present paper, fully diverse codes for systems of odd prime number antennas are obtained from this construction. Space-time codes from present construction are found to have better error performance than many best known ones.