Self-dual geometry of generalized Hermitian surfaces

International Nuclear Information System (INIS)

Arsen'eva, O E; Kirichenko, V F

1998-01-01

Several results on the geometry of conformally semiflat Hermitian surfaces of both classical and hyperbolic types (generalized Hermitian surfaces) are obtained. Some of these results are generalizations and clarifications of already known results in this direction due to Koda, Itoh, and other authors. They reveal some unexpected beautiful connections between such classical characteristics of conformally semiflat (generalized) Hermitian surfaces as the Einstein property, the constancy of the holomorphic sectional curvature, and so on. A complete classification of compact self-dual Hermitian RK-surfaces that are at the same time generalized Hopf manifolds is obtained. This provides a complete solution of the Chen problem in this class of Hermitian surfaces

Heralded Magnetism in Non-Hermitian Atomic Systems

Directory of Open Access Journals (Sweden)

Tony E. Lee

2014-10-01

Full Text Available Quantum phase transitions are usually studied in terms of Hermitian Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian because of spontaneous decay. Here, we show that non-Hermitian systems exhibit quantum phase transitions that are beyond the paradigm of Hermitian physics. We consider the non-Hermitian XY model, which can be implemented using three-level atoms with spontaneous decay. We exactly solve the model in one dimension and show that there is a quantum phase transition from short-range order to quasi-long-range order despite the absence of a continuous symmetry in the Hamiltonian. The ordered phase has a frustrated spin pattern. The critical exponent ν can be 1 or 1/2. Our results can be seen experimentally with trapped ions, cavity QED, and atoms in optical lattices.

General coupled mode theory in non-Hermitian waveguides.

Science.gov (United States)

Xu, Jing; Chen, Yuntian

2015-08-24

In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non-Hermitian. In such non-Hermitian waveguides, the standard coupled mode theory fails. We generalize the coupled mode theory with a properly defined inner product based on reaction conservation. We apply our theory to the non-Hermitian parity-time symmetric waveguides, and obtain excellent agreement with results obtained by finite element fullwave simulations. The theory presented here is typically formulated in space to study coupling between waveguides, which can be transformed into time domain by proper reformulation to study coupling between non-Hermitian resonators. Our theory has the strength of studying non-Hermitian optical systems with inclusion of the full vector fields, thus is useful to study and design non-Hermitian devices that support asymmetric and even nonreciprocal light propagations.

Pseudo-Hermitian continuous-time quantum walks

Energy Technology Data Exchange (ETDEWEB)

Salimi, S; Sorouri, A, E-mail: shsalimi@uok.ac.i, E-mail: a.sorouri@uok.ac.i [Department of Physics, University of Kurdistan, PO Box 66177-15175, Sanandaj (Iran, Islamic Republic of)

2010-07-09

In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum-mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it pseudo-Hermitian continuous-time quantum walk. We introduce a method to obtain the probability distribution of walk on any vertex and then study a specific system. We observe that the probability distribution on certain vertices increases compared to that of the Hermitian case. This formalism makes the transport process faster and can be useful for search algorithms.

Pseudo-Hermitian description of PT-symmetric systems defined on a complex contour

International Nuclear Information System (INIS)

Mostafazadeh, Ali

2005-01-01

We describe a method that allows for a practical application of the theory of pseudo-Hermitian operators to PT-symmetric systems defined on a complex contour. We apply this method to study the Hamiltonians H = p 2 + x 2 (ix) ν with ν ε (-2, ∞) that are defined along the corresponding anti-Stokes lines. In particular, we reveal the intrinsic non-Hermiticity of H for the cases that ν is an even integer, so that H p 2 ± x 2+ν , and give a proof of the discreteness of the spectrum of H for all ν ε (-2, ∞). Furthermore, we study the consequences of defining a square-well Hamiltonian on a wedge-shaped complex contour. This yields a PT-symmetric system with a finite number of real eigenvalues. We present a comprehensive analysis of this system within the framework of pseudo-Hermitian quantum mechanics. We also outline a direct pseudo-Hermitian treatment of PT-symmetric systems defined on a complex contour which clarifies the underlying mathematical structure of the formulation of PT-symmetric quantum mechanics based on the charge-conjugation operator. Our results provide conclusive evidence that pseudo-Hermitian quantum mechanics provides a complete description of general PT-symmetric systems regardless of whether they are defined along the real line or a complex contour

Designing non-Hermitian dynamics for conservative state evolution on the Bloch sphere

Science.gov (United States)

Yu, Sunkyu; Piao, Xianji; Park, Namkyoo

2018-03-01

An evolution on the Bloch sphere is the fundamental state transition, including optical polarization controls and qubit operations. Conventional evolution of a polarization state or qubit is implemented within a closed system that automatically satisfies energy conservation from the Hermitian formalism. Although particular forms of static non-Hermitian Hamiltonians, such as parity-time-symmetric Hamiltonians, allow conservative states in an open system, the criteria for the energy conservation in a dynamical open system have not been fully explored. Here, we derive the condition of conservative state evolution in open-system dynamics and its inverse design method, by developing the non-Hermitian modification of the Larmor precession equation. We show that the geometrically designed locus on the Bloch sphere can be realized by different forms of dynamics, leading to the isolocus family of non-Hermitian dynamics. This increased degree of freedom allows the complementary phenomena of error-robust and highly sensitive evolutions on the Bloch sphere, which could be applicable to stable polarizers, quantum gates, and optimized sensors in dynamical open systems.

Cotangent bundles over all the Hermitian symmetric spaces

International Nuclear Information System (INIS)

Arai, Masato; Baba, Kurando

2016-01-01

We construct the N = 2 supersymmetric nonlinear sigma models on the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces. In order to construct them we use the projective superspace formalism which is an N = 2 off-shell superfield formulation in four-dimensional space-time. This formalism allows us to obtain the explicit expression of N = 2 supersymmetric nonlinear sigma models on the cotangent bundles over any Hermitian symmetric spaces in terms of the N =1 superfields, once the Kähler potentials of the base manifolds are obtained. Starting with N = 1 supersymmetric Kähler nonlinear sigma models on the Hermitian symmetric spaces, we extend them into the N = 2 supersymmetric models by using the projective superspace formalism and derive the general formula for the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces. We apply to the formula for the non-compact Hermitian symmetric space E 7 /E 6 × U(1) 1 . (paper)

Extension of the CPT theorem to non-Hermitian Hamiltonians and unstable states

Energy Technology Data Exchange (ETDEWEB)

Mannheim, Philip D., E-mail: philip.mannheim@uconn.edu

2016-02-10

We extend the CPT theorem to quantum field theories with non-Hermitian Hamiltonians and unstable states. Our derivation is a quite minimal one as it requires only the time-independent evolution of scalar products, invariance under complex Lorentz transformations, and a non-standard but nonetheless perfectly legitimate interpretation of charge conjugation as an antilinear operator. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each other, and forces the Hamiltonian to admit of an antilinear symmetry. The latter two requirements then force this antilinear symmetry to be CPT, while forcing the Hamiltonian to be real rather than Hermitian. Our work justifies the use of the CPT theorem in establishing the equality of the lifetimes of unstable particles that are charge conjugates of each other. We show that the Euclidean time path integrals of a CPT-symmetric theory must always be real. In the quantum-mechanical limit the key results of the PT symmetry program of Bender and collaborators are recovered, with the C-operator of the PT symmetry program being identified with the linear component of the charge conjugation operator.

Non-Hermitian photonics based on parity-time symmetry

Science.gov (United States)

Feng, Liang; El-Ganainy, Ramy; Ge, Li

2017-12-01

Nearly one century after the birth of quantum mechanics, parity-time symmetry is revolutionizing and extending quantum theories to include a unique family of non-Hermitian Hamiltonians. While conceptually striking, experimental demonstration of parity-time symmetry remains unexplored in quantum electronic systems. The flexibility of photonics allows for creating and superposing non-Hermitian eigenstates with ease using optical gain and loss, which makes it an ideal platform to explore various non-Hermitian quantum symmetry paradigms for novel device functionalities. Such explorations that employ classical photonic platforms not only deepen our understanding of fundamental quantum physics but also facilitate technological breakthroughs for photonic applications. Research into non-Hermitian photonics therefore advances and benefits both fields simultaneously.

Hermitian self-dual quasi-abelian codes

Directory of Open Access Journals (Sweden)

Herbert S. Palines

2017-12-01

Full Text Available Quasi-abelian codes constitute an important class of linear codes containing theoretically and practically interesting codes such as quasi-cyclic codes, abelian codes, and cyclic codes. In particular, the sub-class consisting of 1-generator quasi-abelian codes contains large families of good codes. Based on the well-known decomposition of quasi-abelian codes, the characterization and enumeration of Hermitian self-dual quasi-abelian codes are given. In the case of 1-generator quasi-abelian codes, we offer necessary and sufficient conditions for such codes to be Hermitian self-dual and give a formula for the number of these codes. In the case where the underlying groups are some $p$-groups, the actual number of resulting Hermitian self-dual quasi-abelian codes are determined.

Hermitian versus anti-hermitian one-matrix models and their hierarchies

International Nuclear Information System (INIS)

Hollowood, T.; Miramontes, L.; Pasquinucci, A.; Nappi, C.

1992-01-01

Building on a recent work of C. Crnkovic, M. Douglas and G. Moore, a study of multi-critical multi-cut one-matrix models and their associated sl(2, C) integrable hierarchies, is further pursued. The double-scaling limits of hermitian matrix models with different scaling ansaetze, lead to the KdV hierarchy, to the modified KdV hierarchy and part of the non-linear Schroedinger hierarchy. Instead, the anti-hermitian matrix model, in the 2-arc sector, results in the Zakharov-Shabat hierarchy, which contains both KdV and mKdV as reductions. For all the hierarchies it is found that the Virasoro constraints act on the associated τ-functions. Whereas it is known that the ZS and KdV models lead to the Virasoro constraints of an sl(2, C) vacuum, we find that the mKdV model leads to the Virasoro constraints of a highest-weight state with arbitrary conformal dimension. (orig.)

Para-Hermitian and para-quaternionic manifolds

International Nuclear Information System (INIS)

Ivanov, S.; Zamkovoy, S.

2003-10-01

A set of canonical para-Hermitian connections on an almost para-Hermitian manifold is defined. A Para-hermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly para-Kaehler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the para-quaternionic case. A locally conformally hyper-para-Kaehler (hypersymplectic) flat structure with parallel Lee form on the Kodaira-Thurston complex surfaces modeled on S 1 x SL (2, R)-tilde is constructed. Anti-self-dual locally conformally hyper-para-Kaehler (hypersymplectic) neutral metrics with non vanishing Weyl tensor are obtained on the Inoe surfaces. An example of anti-self-dual neutral metric which is not locally conformally hyper-para-Kaehler (hypersymplectic) is constructed. (author)

Para-Hermitian and para-quaternionic manifolds

Energy Technology Data Exchange (ETDEWEB)

Ivanov, S [University of Sofia ' St. Kl. Ohridski' , Faculty of Mathematics and Informatics, Sofia (Bulgaria) and Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Zamkovoy, S [University of Sofia ' St. Kl. Ohridski' , Faculty of Mathematics and Informatics, Sofia (Bulgaria)

2003-10-01

A set of canonical para-Hermitian connections on an almost para-Hermitian manifold is defined. A Para-hermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly para-Kaehler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the para-quaternionic case. A locally conformally hyper-para-Kaehler (hypersymplectic) flat structure with parallel Lee form on the Kodaira-Thurston complex surfaces modeled on S{sup 1} x SL (2, R)-tilde is constructed. Anti-self-dual locally conformally hyper-para-Kaehler (hypersymplectic) neutral metrics with non vanishing Weyl tensor are obtained on the Inoe surfaces. An example of anti-self-dual neutral metric which is not locally conformally hyper-para-Kaehler (hypersymplectic) is constructed. (author)

PREFACE: 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics

Science.gov (United States)

Fring, Andreas; Jones, Hugh; Znojil, Miloslav

2008-06-01

growing community of this subject. It is, for instance, well understood that the reality of the spectrum can be attributed either to the unbroken PT-symmetry of the entire system, that is, invariance of the Hamiltonian and the corresponding wavefunctions under a simultaneous parity transformation and time reversal, or more generally to its pseudo-Hermiticity . When the spectrum is real and discrete the Hamiltonian is actually quasi-Hermitian, with a positive-definite metric operator, and can in principle be related by a similarity transformation to an isospectral Hermitian counterpart. For all approaches well-defined procedures have been developed, which allow one to construct metric operators and therefore a consistent description of the underlying quantum mechanical observables. Even though the general principles have been laid out, it remains a challenge in most concrete cases to implement the entire procedure. Solvable models in this sense, some of which may be found in this issue, remain a rare exception. Nonetheless, despite this progress some important questions are still unanswered. For instance, according to the current understanding the non-Hermitian Hamiltonian does not uniquely define the physics of the system since a meaningful metric can no longer be associated with the system in a non-trivial and unambiguous manner. A fully consistent scattering theory has also not yet been formulated. Other issues remain controversial, such as the quantum brachistochrone problem, the problem of forming a mixture between a Hermitian and non-Hermitian system, the new phenomenological possibilities of forming a kind of worm-hole effect, etc. We would like to acknowledge the financial support of the London Mathematical Society, the Institute of Physics, the Doppler Institute in Prague and the School of Engineering and Mathematical Science of City University London. We hope this special issue will be useful to the newcomer as well as to the expert in the subject. Workshop

A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field

International Nuclear Information System (INIS)

Castro-Alvaredo, Olalla A; Fring, Andreas

2009-01-01

We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT-symmetry, we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turn out to be unique with the sole assumption that the Dyson map is Hermitian. Finally, we analyse the magnetization of the chain in the z- and x-direction.

Balanced Hermitian metrics from SU(2)-structures

International Nuclear Information System (INIS)

Fernandez, M.; Tomassini, A.; Ugarte, L.; Villacampa, R.

2009-01-01

We study the intrinsic geometrical structure of hypersurfaces in six-manifolds carrying a balanced Hermitian SU(3)-structure, which we call balanced SU(2)-structure. We provide sufficient conditions, in terms of suitable evolution equations, which imply that a five-manifold with such structure can be isometrically embedded as a hypersurface in a balanced Hermitian SU(3)-manifold. Any five-dimensional compact nilmanifold has an invariant balanced SU(2)-structure, and we show how some of them can be evolved to give new explicit examples of balanced Hermitian SU(3)-structures. Moreover, for n=3,4, we present examples of compact solvmanifolds endowed with a balanced SU(n)-structure such that the corresponding Bismut connection has holonomy equal to SU(n)

New quasi-exactly solvable Hermitian as well as non-Hermitian PT ...

Indian Academy of Sciences (India)

Abstract. We start with quasi-exactly solvable (QES) Hermitian (and hence real) as ... the time reversal transformation t → −t and further, one replaces i → −i. One can ..... F M Fernandez, R Guardiola, J Ros and M Znojil, J. Phys. A32, 3105 ...

Decoding Hermitian Codes with Sudan's Algorithm

DEFF Research Database (Denmark)

Høholdt, Tom; Nielsen, Rasmus Refslund

1999-01-01

We present an efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Q-polynomial, and a reduct......We present an efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Q...

Non-Hermitian Heisenberg representation

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2015-01-01

Roč. 379, č. 36 (2015), s. 2013-2017 ISSN 0375-9601 Institutional support: RVO:61389005 Keywords : quantum mechanics * Non-Hermitian representation of observables * Generalized Heisenberg equations Subject RIV: BE - Theoretical Physics Impact factor: 1.677, year: 2015

Symmetries and conservation laws in non-Hermitian field theories

Science.gov (United States)

Alexandre, Jean; Millington, Peter; Seynaeve, Dries

2017-09-01

Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for P T -symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the P T -conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of P T -symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether's theorem, and we give specific examples for illustration.

Moyal products-a new perspective on quasi-Hermitian quantum mechanics

International Nuclear Information System (INIS)

Scholtz, F G; Geyer, H B

2006-01-01

The rationale for introducing non-Hermitian Hamiltonians and other observables is reviewed and open issues identified. We present a new approach based on Moyal products to compute the metric for quasi-Hermitian systems. This approach is not only an efficient method of computation, but also suggests a new perspective on quasi-Hermitian quantum mechanics which invites further exploration. In particular, we present some first results which link the Berry connection and curvature to non-perturbative properties and the metric

Infinite families of (non)-Hermitian Hamiltonians associated with exceptional Xm Jacobi polynomials

International Nuclear Information System (INIS)

Midya, Bikashkali; Roy, Barnana

2013-01-01

Using an appropriate change of variable, the Schrödinger equation is transformed into a second-order differential equation satisfied by recently discovered Jacobi-type X m exceptional orthogonal polynomials. This facilitates the derivation of infinite families of exactly solvable Hermitian as well as non-Hermitian trigonometric Scarf potentials and a finite number of Hermitian and an infinite number of non-Hermitian PT-symmetric hyperbolic Scarf potentials. The bound state solutions of all these potentials are associated with the aforesaid exceptional orthogonal polynomials. These infinite families of potentials are shown to be extensions of the conventional trigonometric and hyperbolic Scarf potentials by the addition of some rational terms characterized by the presence of classical Jacobi polynomials. All the members of a particular family of these ‘rationally extended polynomial-dependent’ potentials have the same energy spectrum and possess translational shape-invariant symmetry. The obtained non-Hermitian trigonometric Scarf potentials are shown to be quasi-Hermitian in nature ensuring the reality of the associated energy spectra. (paper)

Analytical results for non-Hermitian parity–time-symmetric and ...

Indian Academy of Sciences (India)

Abstract. We investigate both the non-Hermitian parity–time-(PT-)symmetric and Hermitian asymmetric volcano potentials, and present the analytical solution in terms of the confluent Heun function. Under certain special conditions, the confluent Heun function can be terminated as a polynomial, thereby leading to certain ...

Theory of superconductivity with non-Hermitian and parity-time reversal symmetric Cooper pairing symmetry

Science.gov (United States)

Ghatak, Ananya; Das, Tanmoy

2018-01-01

Recently developed parity (P ) and time-reversal (T ) symmetric non-Hermitian systems govern a rich variety of new and characteristically distinct physical properties, which may or may not have a direct analog in their Hermitian counterparts. We study here a non-Hermitian, PT -symmetric superconducting Hamiltonian that possesses a real quasiparticle spectrum in the PT -unbroken region of the Brillouin zone. Within a single-band mean-field theory, we find that real quasiparticle energies are possible when the superconducting order parameter itself is either Hermitian or anti-Hermitian. Within the corresponding Bardeen-Cooper-Schrieffer (BCS) theory, we find that several properties are characteristically distinct and novel in the non-Hermitian pairing case than its Hermitian counterpart. One of our significant findings is that while a Hermitian superconductor gives a second-order phase transition, the non-Hermitian one produces a robust first-order phase transition. The corresponding thermodynamic properties and the Meissner effect are also modified accordingly. Finally, we discuss how such a PT -symmetric pairing can emerge from an antisymmetric potential, such as the Dzyloshinskii-Moriya interaction, but with an external bath, or complex potential, among others.

Modified Hermitian treatment of Dyson boson expansion theory

International Nuclear Information System (INIS)

Kajiyama, Atsushi

2009-01-01

The Hermitian treatment of the Dyson-type boson expansion theory is reinvestigated with the aid of small-parameter expansion. A naive application of the Hermitization formula sometimes yields an unrealistic phase that spoils the conventional treatment. The complementary use of another formula having the form of the arithmetic mean can avoid that problem. This modification will improve the accuracy of the Hermitian treatment. (author)

Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra

International Nuclear Information System (INIS)

Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah

2014-01-01

We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean–Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices. -- Highlights: •Different PT-symmetries lead to qualitatively different systems. •Construction of non-perturbative Dyson maps and isospectral Hermitian counterparts. •Numerical discussion of the eigenvalue spectra for one of the E(2)-systems. •Established link to systems studied in the context of optical lattices. •Setup for the E(3)-algebra is provided

Concrete minimal 3 × 3 Hermitian matrices and some general cases

Directory of Open Access Journals (Sweden)

Klobouk Abel H.

2017-12-01

Full Text Available Given a Hermitian matrix M ∈ M3(ℂ we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ, where ║ · ║ denotes the operator norm. Moreover, we generalize our techniques to some n × n cases.

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

International Nuclear Information System (INIS)

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene

2007-01-01

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P 2 . In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

Science.gov (United States)

Freund, Roland W.

1991-01-01

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Improved Power Decoding of One-Point Hermitian Codes

DEFF Research Database (Denmark)

Puchinger, Sven; Bouw, Irene; Rosenkilde, Johan Sebastian Heesemann

2017-01-01

We propose a new partial decoding algorithm for one-point Hermitian codes that can decode up to the same number of errors as the Guruswami–Sudan decoder. Simulations suggest that it has a similar failure probability as the latter one. The algorithm is based on a recent generalization of the power...... decoding algorithm for Reed–Solomon codes and does not require an expensive root-finding step. In addition, it promises improvements for decoding interleaved Hermitian codes....

Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra

Science.gov (United States)

Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah

2014-07-01

We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean-Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices.

Faster than Hermitian Quantum Mechanics

International Nuclear Information System (INIS)

Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.; Meister, Bernhard K.

2007-01-01

Given an initial quantum state vertical bar ψ I > and a final quantum state vertical bar ψ F >, there exist Hamiltonians H under which vertical bar ψ I > evolves into vertical bar ψ F >. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time τ? For Hermitian Hamiltonians τ has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, τ can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar ψ I > to vertical bar ψ F > can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing

Non-Hermitian Extensions of Wishart Random Matrix Ensembles

International Nuclear Information System (INIS)

Akemann, G.

2011-01-01

We briefly review the solution of three ensembles of non-Hermitian random matrices generalizing the Wishart-Laguerre (also called chiral) ensembles. These generalizations are realized as Gaussian two-matrix models, where the complex eigenvalues of the product of the two independent rectangular matrices are sought, with the matrix elements of both matrices being either real, complex or quaternion real. We also present the more general case depending on a non-Hermiticity parameter, that allows us to interpolate between the corresponding three Hermitian Wishart ensembles with real eigenvalues and the maximally non-Hermitian case. All three symmetry classes are explicitly solved for finite matrix size N x M for all complex eigenvalue correlations functions (and real or mixed correlations for real matrix elements). These are given in terms of the corresponding kernels built from orthogonal or skew-orthogonal Laguerre polynomials in the complex plane. We then present the corresponding three Bessel kernels in the complex plane in the microscopic large-N scaling limit at the origin, both at weak and strong non-Hermiticity with M - N ≥ 0 fixed. (author)

Geometry of quantal adiabatic evolution driven by a non-Hermitian Hamiltonian

International Nuclear Information System (INIS)

Wu Zhaoyan; Yu Ting; Zhou Hongwei

1994-01-01

It is shown by using a counter example, which is exactly solvable, that the quantal adiabatic theorem does not generally hold for a non-Hermitian driving Hamiltonian, even if it varies extremely slowly. The condition for the quantal adiabatic theorem to hold for non-Hermitian driving Hamiltonians is given. The adiabatic evolutions driven by a non-Hermitian Hamiltonian provide examples of a new geometric structure, that is the vector bundle in which the inner product of two parallelly transported vectors generally changes. A new geometric concept, the attenuation tensor, is naturally introduced to describe the decay or flourish of the open quantum system. It is constructed in terms of the spectral projector of the Hamiltonian. (orig.)

Supersymmetry and cotangent bundle over non-compact exceptional Hermitian symmetric space

International Nuclear Information System (INIS)

Arai, Masato; Baba, Kurando

2015-01-01

We construct N=2 supersymmetric nonlinear sigma models on the cotangent bundles over the non-compact exceptional Hermitian symmetric spaces M=E 6(−14) /SO(10)×U(1) and E 7(−25) /E 6 ×U(1). In order to construct them we use the projective superspace formalism which is an N=2 off-shell superfield formulation in four-dimensional space-time. This formalism allows us to obtain the explicit expression of N=2 supersymmetric nonlinear sigma models on the cotangent bundles over any Hermitian symmetric spaces in terms of the N=1 superfields, once the Kähler potentials of the base manifolds are obtained. We derive the N=1 supersymmetric nonlinear sigma models on the Kähler manifolds M. Then we extend them into the N=2 supersymmetric models with the use of the result in arXiv:1211.1537 developed in the projective superspace formalism. The resultant models are the N=2 supersymmetric nonlinear sigma models on the cotangent bundles over the Hermitian symmetric spaces M. In this work we complete constructing the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces.

Projective block Lanczos algorithm for dense, Hermitian eigensystems

International Nuclear Information System (INIS)

Webster, F.; Lo, G.C.

1996-01-01

Projection operators are used to effect open-quotes deflation by restrictionclose quotes and it is argued that this is an optimal Lanczos algorithm for memory minimization. Algorithmic optimization is constrained to dense, Hermitian eigensystems where a significant number of the extreme eigenvectors must be obtained reliably and completely. The defining constraints are operator algebra without a matrix representation and semi-orthogonalization without storage of Krylov vectors. other semi-orthogonalization strategies for Lanczos algorithms and conjugate gradient techniques are evaluated within these constraints. Large scale, sparse, complex numerical experiments are performed on clusters of magnetic dipoles, a quantum many-body system that is not block-diagonalizable. Plane-wave, density functional theory of beryllium clusters provides examples of dense complex eigensystems. Use of preconditioners and spectral transformations is evaluated in a preprocessor prior to a high accuracy self-consistent field calculation. 25 refs., 3 figs., 5 tabs

Higher genus correlators from the hermitian one-matrix model

International Nuclear Information System (INIS)

Ambjoern, J.; Chekhov, L.; Makeenko, Yu.

1992-01-01

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.)

Critical statistics for non-Hermitian matrices

International Nuclear Information System (INIS)

Garcia-Garcia, A.M.; Verbaarschot, J.J.M.; Nishigaki, S.M.

2002-01-01

We introduce a generalized ensemble of non-Hermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble, and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an extension of the Itzykson-Zuber formula to general complex matrices. Its correlation functions are studied both in the case of weak non-Hermiticity and in the case of strong non-Hermiticity. In the weak non-Hermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics: the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing. To lowest order, its slope does not depend on the degree of non-Hermiticity. Close the edge, the spectral correlations are similar to the Hermitian case. In the strong non-Hermiticity limit the crossover behavior from the Ginibre ensemble to the Poisson ensemble first appears close to the surface of the spectrum. Our model may be relevant for the description of the spectral correlations of an open disordered system close to an Anderson transition

Constant-intensity waves and their modulation instability in non-Hermitian potentials

Science.gov (United States)

Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2015-07-01

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

Frobenius–Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics

International Nuclear Information System (INIS)

Kullig, Julius; Wiersig, Jan

2016-01-01

In optical microdisk cavities with boundary deformations the backscattering between clockwise and counter-clockwise propagating waves is in general asymmetric. The striking consequence of this asymmetry is that these apparently weakly open systems show pronounced non-Hermitian phenomena. The optical modes appear in non-orthogonal pairs, where both modes copropagate in a preferred sense of rotation, i.e. the modes exhibit a finite chirality. Full asymmetry in the backscattering results in a non-Hermitian degeneracy (exceptional point) where the deviation from closed system evolution is strongest. We study the effects of asymmetric backscattering in ray dynamics. For this purpose, we construct a finite approximation of the Frobenius–Perron operator for deformed microdisk cavities, which describes the dynamics of intensities in phase space. Eigenstates of the Frobenius–Perron operator show nice analogies to optical modes: they come in non-orthogonal copropagating pairs and have a finite chirality. We introduce a new cavity system with a smooth asymmetric boundary deformation where we demonstrate our results and we illustrate the main aspects with the help of a simple analytically solvable 1D model. (paper)

Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification

Directory of Open Access Journals (Sweden)

Xiaofeng Xue

2016-01-01

Full Text Available A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF. It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI finite elements are used to reverse load identification in the Mindlin plate. The singular value decomposition (SVD method is adopted to solve the ill-posed inverse problem. Compared with ANSYS results, HCSWI Mindlin plate element can accurately identify the applied load. Numerical results show that the algorithm of HCSWI Mindlin plate element is effective. The accuracy of HCSWI can be verified by comparing the FRF of HCSWI and ANSYS elements with the experiment data. The experiment proves that the load identification of HCSWI Mindlin plate is effective and precise by using the FRF and response spectrums to calculate the loads.

Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories arXiv

CERN Document Server

Alexandre, Jean; Millington, Peter; Seynaeve, Dries

We demonstrate the extension to PT-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimisation of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantisation of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels.

Problem of the coexistence of several non-Hermitian observables in PT -symmetric quantum mechanics

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav; Semorádová, Iveta; Růžička, František; Moulla, H.; Leghrib, I.

2017-01-01

Roč. 95, č. 4 (2017), č. článku 042122. ISSN 2469-9926 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : operators * Hilbert space * non-Hermitian Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.925, year: 2016

Some spectral equivalences between Schroedinger operators

International Nuclear Information System (INIS)

Dunning, C; Hibberd, K E; Links, J

2008-01-01

Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schroedinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators

Resolutions of Identity for Some Non-Hermitian Hamiltonians. II. Proofs

Directory of Open Access Journals (Sweden)

Andrey V. Sokolov

2011-12-01

Full Text Available This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.

Various scattering properties of a new PT-symmetric non-Hermitian potential

International Nuclear Information System (INIS)

Ghatak, Ananya; Mandal, Raka Dona Ray; Mandal, Bhabani Prasad

2013-01-01

We complexify a 1-d potential V(x)=V 0 cosh 2 μ(tanh[(x−μd)/d]+tanh(μ)) 2 which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d) becomes imaginary. For the case of μ→iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d→id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: •Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. •Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. •Co-existence of MSS with deep energy minima of transitivity is obtained. •Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. •Penetrating states are shown to be reciprocal for all energies for PT-symmetric system

Astrophysical evidence for the non-Hermitian but PT-symmetric Hamiltonian of conformal gravity

International Nuclear Information System (INIS)

Mannheim, P.D.

2013-01-01

In this review we discuss the connection between two seemingly disparate topics, macroscopic gravity on astrophysical scales and Hamiltonians that are not Hermitian but PT symmetric on microscopic ones. In particular we show that the quantum-mechanical unitarity problem of the fourth-order derivative conformal gravity theory is resolved by recognizing that the scalar product appropriate to the theory is not the Dirac norm associated with a Hermitian Hamiltonian but is instead the norm associated with a non-Hermitian but PT-symmetric Hamiltonian. Moreover, the fourth-order theory Hamiltonian is not only not Hermitian, it is not even diagonalizable, being of Jordan-block form. With PT symmetry we establish that conformal gravity is consistent at the quantum-mechanical level. In consequence, we can apply the theory to data, to find that the theory is capable of naturally accounting for the systematics of the rotation curves of a large and varied sample of 138 spiral galaxies without any need for dark matter. The success of the fits provides evidence for the relevance of non-diagonalizable but PT-symmetric Hamiltonians to physics. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

A rule of the equilibrium of forces in the Hermitian theory of relativity

International Nuclear Information System (INIS)

Antoci, S.

1987-01-01

When the behaviour of the singularities, which are used to represent masses, charges or currents in exact solutions to the field equations of the Hermitian theory of relativity, is restricted by a no-jump rule, conditions are obtained, which determine the relative positions of masses, charges and currents. Due to these conditions the Hermitian theory of relativity appears to provide a unified description of gravitational, colour and electromagnetic forces. (author)

Various scattering properties of a new PT-symmetric non-Hermitian potential

Energy Technology Data Exchange (ETDEWEB)

Ghatak, Ananya, E-mail: gananya04@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India); Mandal, Raka Dona Ray, E-mail: rakad.ray@gmail.com [Department of Physics, Rajghat Besant School, Varanasi-221001 (India); Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com [Department of Physics, Banaras Hindu University, Varanasi-221005 (India)

2013-09-15

We complexify a 1-d potential V(x)=V{sub 0}cosh{sup 2}μ(tanh[(x−μd)/d]+tanh(μ)){sup 2} which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d) becomes imaginary. For the case of μ→iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from the left (or right) at certain discrete energies. The penetrating states in the other case (d→id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: •Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. •Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. •Co-existence of MSS with deep energy minima of transitivity is obtained. •Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. •Penetrating states are shown to be reciprocal for all energies for PT-symmetric system.

Parity-time symmetry meets photonics: A new twist in non-Hermitian optics

Science.gov (United States)

Longhi, Stefano

2017-12-01

In the past decade, the concept of parity-time (PT) symmetry, originally introduced in non-Hermitian extensions of quantum mechanical theories, has come into thinking of photonics, providing a fertile ground for studying, observing, and utilizing some of the peculiar aspects of PT symmetry in optics. Together with related concepts of non-Hermitian physics of open quantum systems, such as non-Hermitian degeneracies (exceptional points) and spectral singularities, PT symmetry represents one among the most fruitful ideas introduced in optics in the past few years. Judicious tailoring of optical gain and loss in integrated photonic structures has emerged as a new paradigm in shaping the flow of light in unprecedented ways, with major applications encompassing laser science and technology, optical sensing, and optical material engineering. In this perspective, I review some of the main achievements and emerging areas of PT -symmetric and non-Hermtian photonics, and provide an outline of challenges and directions for future research in one of the fastest growing research area of photonics.

Higher genus correlators for the hermitian matrix model with multiple cuts

International Nuclear Information System (INIS)

Akemann, G.

1996-01-01

An iterative scheme is set up for solving the loop equation of the hermitian one-matrix model with a multi-cut structure. Explicit results are presented for genus one for an arbitrary but finite number of cuts. Due to the complicated form of the boundary conditions, the loop correlators now contain elliptic integrals. This demonstrates the existence of new universality classes for the hermitian matrix model. The two-cut solution is investigated in more detail, including the double scaling limit. It is shown that in special cases it differs from the known continuum solution with one cut. (orig.)

On the subfield subcodes of Hermitian codes

DEFF Research Database (Denmark)

Pinero, Fernando; Janwa, Heeralal

2014-01-01

We present a fast algorithm using Gröbner basis to compute the dimensions of subfield subcodes of Hermitian codes. With these algorithms we are able to compute the exact values of the dimension of all subfield subcodes up to q ≤ 32 and length up to 215. We show that some of the subfield subcodes ...

Pseudo-Hermitian quantum dynamics of tachyonic spin-1/2 particles

International Nuclear Information System (INIS)

Jentschura, U D; Wundt, B J

2012-01-01

We investigate the spinor solutions, the spectrum and the symmetry properties of a matrix-valued wave equation whose plane-wave solutions satisfy the superluminal (tachyonic) dispersion relation E 2 = p-vector 2 - m 2 , where E is the energy, p-vector is the spatial momentum and m is the mass of the particle. The equation reads (iγ μ  ∂ μ − γ 5  m)ψ = 0, where γ 5 is the fifth current. The tachyonic equation is shown to be CP invariant and T invariant. The tachyonic Hamiltonian breaks parity and is non-Hermitian but fulfils the pseudo-Hermitian property H 5 ( r-vector ) = P H + 5 (- r-vector ) P -1 =P H + 5 ( r-vector ) P -1 , where P is the parity matrix and P is the full parity transformation. The energy eigenvalues and eigenvectors describe a continuous spectrum of plane-wave solutions (which correspond to real eigenvalues for | p-vector |≥m) and evanescent waves, which constitute resonances and anti-resonances with complex-conjugate pairs of resonance eigenvalues (for | p-vector | 5 . This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

Self-hybridization within non-Hermitian localized plasmonic systems

Science.gov (United States)

Lourenço-Martins, Hugo; Das, Pabitra; Tizei, Luiz H. G.; Weil, Raphaël; Kociak, Mathieu

2018-04-01

The orthogonal eigenmodes are well-defined solutions of Hermitian equations describing many physical situations from quantum mechanics to acoustics. However, a large variety of non-Hermitian problems, including gravitational waves close to black holes or leaky electromagnetic cavities, require the use of a bi-orthogonal eigenbasis with consequences challenging our physical understanding1-4. The need to compensate for energy losses made the few successful attempts5-8 to experimentally probe non-Hermiticity extremely complicated. We overcome this problem by considering localized plasmonic systems. As the non-Hermiticity in these systems does not stem from temporal invariance breaking but from spatial symmetry breaking, its consequences can be observed more easily. We report on the theoretical and experimental evidence for non-Hermiticity-induced strong coupling between surface plasmon modes of different orders within silver nanodaggers. The symmetry conditions for triggering this counter-intuitive self-hybridization phenomenon are provided. Similar observable effects are expected to exist in any system exhibiting bi-orthogonal eigenmodes.

2 × 2 random matrix ensembles with reduced symmetry: from Hermitian to PT -symmetric matrices

International Nuclear Information System (INIS)

Gong Jiangbin; Wang Qinghai

2012-01-01

A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or parity–time (PT)-symmetric matrices. To illustrate the main idea, we first study 2 × 2 complex Hermitian matrix ensembles with O(2)-invariant constraints, yielding novel level-spacing statistics such as singular distributions, the half-Gaussian distribution, distributions interpolating between the GOE (Gaussian orthogonal ensemble) distribution and half-Gaussian distributions, as well as the gapped-GOE distribution. Such a symmetry-reduction strategy is then used to explore 2 × 2 PT-symmetric matrix ensembles with real eigenvalues. In particular, PT-symmetric random matrix ensembles with U(2) invariance can be constructed, with the conventional complex Hermitian random matrix ensemble being a special case. In two examples of PT-symmetric random matrix ensembles, the level-spacing distributions are found to be the standard GUE (Gaussian unitary ensemble) statistics or the ‘truncated-GUE’ statistics. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

Hermitian relativity, chromodynamics and confinement

International Nuclear Information System (INIS)

Treder, H.J.

1983-01-01

The extension of the Riemann metrics of General Relativity to the complex domain (substitution of the symmetry conditions for the fundamental tensor, the affinity and the Ricci curvature by the conditions of hermicity) leads to a 'Generalized Theory of Gravity' (Einstein) describing the Newton-Einstein gravodynamics combined with the chromodynamics of quarks. The interaction of gravodynamics and chromodynamics implied by the Einstein-Schroedinger field equations of the hermitian relativity theory enforces the 'confinement'. The 'confinement' prevents the gravitational potential from divergence which would result in the lack of a Riemann space-time metric

A Boundary Value Problem for Hermitian Monogenic Functions

Directory of Open Access Journals (Sweden)

Ricardo Abreu Blaya

2008-02-01

Full Text Available We study the problem of finding a Hermitian monogenic function with a given jump on a given hypersurface in ℝm, m=2n. Necessary and sufficient conditions for the solvability of this problem are obtained.

Optical Lattice Design Assisted by Non-Hermitian Hamiltonians

International Nuclear Information System (INIS)

Rodríguez-Lara, B M

2016-01-01

A brief introduction to non-Hermitian arrays of coupled waveguides is presented. The PT-symmetric dimer is revisited for the sake of clarity. It belongs to the class of photonic lattices with underlying SO(2,1) symmetry that have been shown to provide all-optical conversion from phase to amplitude. (paper)

Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

Science.gov (United States)

Yin, Chuanhao; Jiang, Hui; Li, Linhu; Lü, Rong; Chen, Shu

2018-05-01

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems are integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number ν of a non-Hermitian system is equal to half of the summation of two winding numbers ν1 and ν2 associated with two exceptional points, respectively. The winding numbers ν1 and ν2 represent the times of the real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers. We further find that the difference of ν1 and ν2 is related to the second winding number or energy vorticity. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number ν1 and ν2.

Piecewise adiabatic following in non-Hermitian cycling

Science.gov (United States)

Gong, Jiangbin; Wang, Qing-hai

2018-05-01

The time evolution of periodically driven non-Hermitian systems is in general nonunitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be a genuine critical behavior and the precise phase boundary in the parameter space is located. Interestingly, the critical boundary for piecewise adiabatic following is found to be unrelated to the domain for exceptional points. To characterize the adiabatic following dynamics, we also advocate a simple definition of the Aharonov-Anandan (AA) phase for nonunitary cyclic dynamics, which always yields real AA phases. In the slow driving limit, the AA phase reduces to the Berry phase if adiabatic following persists throughout the driving without hopping, but oscillates violently and does not approach any limit in cases of piecewise adiabatic following. This work exposes the rich features of nonunitary dynamics in cases of slow cycling and should stimulate future applications of nonunitary dynamics.

Random matrix theory for pseudo-Hermitian systems: Cyclic blocks

Indian Academy of Sciences (India)

We discuss the relevance of random matrix theory for pseudo-Hermitian systems, and, for Hamiltonians that break parity and time-reversal invariance . In an attempt to understand the random Ising model, we present the treatment of cyclic asymmetric matrices with blocks and show that the nearest-neighbour spacing ...

Metric versus observable operator representation, higher spin models

Science.gov (United States)

Fring, Andreas; Frith, Thomas

2018-02-01

We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on how to employ the time-dependent Dyson relation and the quasi-Hermiticity relation to solve time-dependent Hermitian Hamiltonian systems. By solving both equations separately we argue here that it is in general easier to solve the former. We solve the mutually related time-dependent Schrödinger equation for a Hermitian and non-Hermitian spin 1/2, 1 and 3/2 model with time-independent and time-dependent metric, respectively. In all models the overdetermined coupled system of equations for the Dyson map can be decoupled algebraic manipulations and reduces to simple linear differential equations and an equation that can be converted into the non-linear Ermakov-Pinney equation.

Schwinger-Dyson loop equations as the w1+∞-like constraints for hermitian multi-matrix chain model at finite N

International Nuclear Information System (INIS)

Cheng, Yi-Xin

1992-01-01

The Schwinger-Dyson loop equations for the hermitian multi-matrix chain models at finite N, are derived from the Ward identities of the partition functional under the infinitesimal field transformations. The constraint operators W n (m) satisfy the w 1+∞ -like algebra up to a linear combination of the lower spin operators. We find that the all the higher spin constraints are reducible to the Virasoro-type constraints for all the matrix chain models. (author)

Non-Hermitian quantum mechanics and localization in physical systems

International Nuclear Information System (INIS)

Hatano, Naomichi

1998-01-01

Recent studies on a delocalization phenomenon of a non-Hermitian random system is reviewed. The complex spectrum of the system indicates delocalization transition of its eigenfunctions. It is emphasized that the delocalization is related to various physical phenomena such as flux-line pinning in superconductors and population biology of bacteria colony

Non-Hermitian Hamiltonians with a real spectrum and their physical ...

Indian Academy of Sciences (India)

We present an evaluation of some recent attempts to understand the role of pseudo-Hermitian and P T -symmetric Hamiltonians in modelling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in the study of complex scattering potentials.

Defect States Emerging from a Non-Hermitian Flatband of Photonic Zero Modes

Science.gov (United States)

Qi, Bingkun; Zhang, Lingxuan; Ge, Li

2018-03-01

We show the existence of a flatband consisting of photonic zero modes in a gain and loss modulated lattice system as a result of the underlying non-Hermitian particle-hole symmetry. This general finding explains the previous observation in parity-time symmetric systems where non-Hermitian particle-hole symmetry is hidden. We further discuss the defect states in these systems, whose emergence can be viewed as an unconventional alignment of a pseudospin under the influence of a complex-valued pseudomagnetic field. These defect states also behave as a chain with two types of links, one rigid in a unit cell and one soft between unit cells, as the defect states become increasingly localized with the gain and loss strength.

Random matrix theory for pseudo-Hermitian systems: Cyclic blocks

Indian Academy of Sciences (India)

Abstract. We discuss the relevance of random matrix theory for pseudo-Hermitian sys- tems, and, for Hamiltonians that break parity P and time-reversal invariance T. In an attempt to understand the random Ising model, we present the treatment of cyclic asym- metric matrices with blocks and show that the nearest-neighbour ...

Theory of non-hermitian localization in one dimension: Localization ...

Indian Academy of Sciences (India)

of the finite depinning field H . The degree of depinning is measured by the averaged .... system [2] shows a direct relationship between the localization length of the ... tight-binding model in a non-hermitian field h, where the discrete sites n, ..... shows that complex eigenvalues do not appear for field strengths less thanh2.

Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?

International Nuclear Information System (INIS)

Savin, Dmitry V.; Sokolov, Valentin V.; Sommers, Hans-Juergen

2003-01-01

We examine the notion and properties of the non-Hermitian effective Hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum. We present a consistent self-adjoint formulation of the problem of scattering on a finite-range potential, which is based on the separation of the configuration space into two segments, internal and external. The scattering amplitude is expressed in terms of the resolvent of a non-Hermitian operator H. The explicit form of this operator depends on both the radius of separation and the boundary conditions at this place, which can be chosen in many different ways. We discuss this freedom and show explicitly that the physical scattering amplitude is, nevertheless, unique, although not all choices are equally adequate from the physical point of view. The energy-dependent operator H should not be confused with the non-Hermitian effective Hamiltonian H eff which is usually exploited to describe interference of overlapping resonances. We note that the simple Breit-Wigner approximation is as a rule valid for any individual resonance in the case of few-channel scattering on a flat billiardlike cavity, leaving no room for nontrivial H eff to appear. The physics is appreciably richer in the case of an open chain of L connected similar cavities whose spectrum has a band structure. For a fixed band of L overlapping resonances, the smooth energy dependence of H can be ignored so that the constant LxL submatrix H eff approximately describes the time evolution of the chain in the energy domain of the band and the complex eigenvalues of H eff define the energies and widths of the resonances. We apply the developed formalism to the problem of a chain of L δ barriers, whose solution is also found independently in a closed form. We construct H eff for the two commonly considered types of boundary conditions (Neumann and Dirichlet) for the internal motion. Although the final results are in perfect

Hermitian-Einstein metrics on parabolic stable bundles

International Nuclear Information System (INIS)

Li Jiayu; Narasimhan, M.S.

1995-12-01

Let M-bar be a compact complex manifold of complex dimension two with a smooth Kaehler metric and D a smooth divisor on M-bar. If E is a rank 2 holomorphic vector bundle on M-bar with a stable parabolic structure along D, we prove the existence of a metric on E' = E module MbarD (compatible with the parabolic structure) which is Hermitian-Einstein with respect to the restriction of Kaehler metric of M-barD. A converse is also proved. (author). 24 refs

Bose-Operator Expansions of Tensor Operators in the Theory of Magnetism

DEFF Research Database (Denmark)

Lindgård, Per-Anker; Danielsen, O.

1974-01-01

Using a method of matching corresponding matrix elements, a hermitian Bose-operator expansion of tensor operators of arbitrary rank which transforms all kinematic effects into dynamical interactions between Bose particles is derived. It is shown that the method is a generalization of the Holstein...

Computing several eigenpairs of Hermitian problems by conjugate gradient iterations

International Nuclear Information System (INIS)

Ovtchinnikov, E.E.

2008-01-01

The paper is concerned with algorithms for computing several extreme eigenpairs of Hermitian problems based on the conjugate gradient method. We analyse computational strategies employed by various algorithms of this kind reported in the literature and identify their limitations. Our criticism is illustrated by numerical tests on a set of problems from electronic structure calculations and acoustics

Exact 2-point function in Hermitian matrix model

International Nuclear Information System (INIS)

Morozov, A.; Shakirov, Sh.

2009-01-01

J. Harer and D. Zagier have found a strikingly simple generating function [1,2] for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.

The complex Laguerre symplectic ensemble of non-Hermitian matrices

International Nuclear Information System (INIS)

Akemann, G.

2005-01-01

We solve the complex extension of the chiral Gaussian symplectic ensemble, defined as a Gaussian two-matrix model of chiral non-Hermitian quaternion real matrices. This leads to the appearance of Laguerre polynomials in the complex plane and we prove their orthogonality. Alternatively, a complex eigenvalue representation of this ensemble is given for general weight functions. All k-point correlation functions of complex eigenvalues are given in terms of the corresponding skew orthogonal polynomials in the complex plane for finite-N, where N is the matrix size or number of eigenvalues, respectively. We also allow for an arbitrary number of complex conjugate pairs of characteristic polynomials in the weight function, corresponding to massive quark flavours in applications to field theory. Explicit expressions are given in the large-N limit at both weak and strong non-Hermiticity for the weight of the Gaussian two-matrix model. This model can be mapped to the complex Dirac operator spectrum with non-vanishing chemical potential. It belongs to the symmetry class of either the adjoint representation or two colours in the fundamental representation using staggered lattice fermions

Sub-quadratic decoding of one-point hermitian codes

DEFF Research Database (Denmark)

Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter

2015-01-01

We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...... decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities....

Construction of a unique metric in quasi-Hermitian quantum mechanics: Nonexistence of the charge operator in a 2 x 2 matrix model (vol 640, pg 52, 2006)

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav; Geyer, HB.

2007-01-01

Roč. 649, 5-6 (2007), s. 494-494 ISSN 0370-2693 R&D Projects: GA ČR GA202/07/1307 Institutional research plan: CEZ:AV0Z10480505 Keywords : metrics * quasi-Hermitian * charge Subject RIV: BE - Theoretical Physics Impact factor: 4.189, year: 2007

Investigating and improving student understanding of quantum mechanical observables and their corresponding operators in Dirac notation

Science.gov (United States)

Marshman, Emily; Singh, Chandralekha

2018-01-01

In quantum mechanics, for every physical observable, there is a corresponding Hermitian operator. According to the most common interpretation of quantum mechanics, measurement of an observable collapses the quantum state into one of the possible eigenstates of the operator and the corresponding eigenvalue is measured. Since Dirac notation is an elegant notation that is commonly used in upper-level quantum mechanics, it is important that students learn to express quantum operators corresponding to observables in Dirac notation in order to apply the quantum formalism effectively in diverse situations. Here we focus on an investigation that suggests that, even though Dirac notation is used extensively, many advanced undergraduate and PhD students in physics have difficulty expressing the identity operator and other Hermitian operators corresponding to physical observables in Dirac notation. We first describe the difficulties students have with expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We then discuss how the difficulties found via written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of these concepts. The QuILT strives to help students become proficient in expressing the identity operator and a generic Hermitian operator corresponding to an observable in Dirac notation. We also discuss the effectiveness of the QuILT based on in-class evaluations.

Hermitian (ϵ,δ)-Freudenthal-Kantor Triple Systems and Certain Applications of *-Generalized Jordan Triple Systems to Field Theory

International Nuclear Information System (INIS)

Kamiya, Noriaki; Sato, Matsuo

2014-01-01

We define Hermitian (ϵ,δ)-Freudenthal-Kantor triple systems and prove a structure theorem. We also give some examples of triple systems that are generalizations of the u(N)⊕u(M) and sp(2N)⊕u(1) Hermitian 3-algebras. We apply a *-generalized Jordan triple system to a field theory and obtain a Chern-Simons gauge theory. We find that the novel Higgs mechanism works, where the Chern-Simons gauge theory reduces to a Yang-Mills theory in a certain limit

Duality property for a hermitian scalar field

International Nuclear Information System (INIS)

Bisognano, J.J.

1975-01-01

A general hermitian scalar Wightman field is considered. On the Hilbert space of physical states ''natural'' domains for certain complex Lorentz transformations are constructed, and a theorem relating these transformations to the TCP symmetry is stated and proved. Under the additional assumption that the field is ''locally'' essentially self-adjoint, duality is considered for the algebras generated by spectral projections of smeared fields. For a class of unbounded regions duality is proved, and for certain bounded regions ''local'' extensions of the algebras are constructed which satisfy duality. The relationship of the arguments presented to the Tomita--Takesaki theory of modular Hilbert algebras is discussed. A separate analysis for the free field is also given. (auth)

A note on Hermitian-Einstein metrics on parabolic stable bundles

International Nuclear Information System (INIS)

Li Jiayu; Narasimhan, M.S.

2000-01-01

Let M-bar be a compact complex manifold of complex dimension two with a smooth Kaehler metric and D a smooth divisor on M-bar. If E is a rank 2 holomorphic vector bundle on M-bar with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E' = E-vertical bar M-barbackslashD compatible with the parabolic structure, and whose curvature is square integrable. (author)

Non-hermitian symmetric N = 2 coset models, Poincare polynomials, and string compactification

International Nuclear Information System (INIS)

Fuchs, J.; Schweigert, C.

1994-01-01

The field identification problem, including fixed point resolution, is solved for the non-hermitian symmetric N = 2 superconformal coset theories. Thereby these models are finally identified as well-defined modular invariant conformal field theories. As an application, the theories are used as subtheories in N = 2 tensor products with c = 9, which in turn are taken as the inner sector of heterotic superstring compactifications. All string theories of this type are classified, and the chiral ring as well as the number of massless generations and anti-generations are computed with the help of the extended Poincare polynomial. Several equivalences between a priori different non-hermitian coset theories show up; in particular there is a level-rank duality for an infinite series of coset theories based on C-type Lie algebras. Further, some general results for generic N = 2 coset theories are proven: a simple formula for the number of identification currents is found, and it is shown that the set of Ramond ground states of any N = 2 coset model is invariant under charge conjugation. (orig.)

Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem

KAUST Repository

Raman, Aaswath

2010-02-26

We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.

Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem

KAUST Repository

Raman, Aaswath; Fan, Shanhui

2010-01-01

We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.

Correlation functions for Hermitian many-body systems: Necessary conditions

International Nuclear Information System (INIS)

Brown, E.B.

1994-01-01

Lee [Phys. Rev. B 47, 8293 (1993)] has shown that the odd-numbered derivatives of the Kubo autocorrelation function vanish at t=0. We show that this condition is based on a more general property of nondiagonal Kubo correlation functions. This general property provides that certain functional forms (e.g., simple exponential decay) are not admissible for any symmetric or antisymmetric Kubo correlation function in a Hermitian many-body system. Lee's result emerges as a special case of this result. Applications to translationally invariant systems and systems with rotational symmetries are also demonstrated

Superradiance, disorder, and the non-Hermitian Hamiltonian in open quantum systems

Energy Technology Data Exchange (ETDEWEB)

Celardo, G. L.; Biella, A.; Giusteri, G. G.; Mattiotti, F. [Dipartimento di Matematica e Fisica and Interdisciplinary Laboratories for Advanced Materials Physics, Università Cattolica, via Musei 41, 25121 Brescia (Italy); Zhang, Y.; Kaplan, L. [Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118 (United States)

2014-10-15

We first briefly review the non-Hermitian effective Hamiltonian approach to open quantum systems and the associated phenomenon of superradiance. We next discuss the superradiance crossover in the presence of disorder and the relationship between superradiance and the localization transition. Finally, we investigate the regime of validity of the energy-independent effective Hamiltonian approximation and show that the results obtained by these methods are applicable to realistic physical systems.

Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator

International Nuclear Information System (INIS)

Babich, R.; Brower, R. C.; Rebbi, C.; Brannick, J.; Clark, M. A.; Manteuffel, T. A.; McCormick, S. F.; Osborn, J. C.

2010-01-01

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ 5 -Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.

Large-N limit of the two-Hermitian-matrix model by the hidden BRST method

International Nuclear Information System (INIS)

Alfaro, J.

1993-01-01

This paper discusses the large-N limit of the two-Hermitian-matrix model in zero dimensions, using the hidden Becchi-Rouet-Stora-Tyutin method. A system of integral equations previously found is solved, showing that it contained the exact solution of the model in leading order of large N

Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

International Nuclear Information System (INIS)

Ndayiragije, F; Van Assche, W

2013-01-01

Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to r > 1 different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Following a recent construction of Miki, Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first kind), we construct r > 1 non-Hermitian oscillator Hamiltonians in r dimensions which are simultaneously diagonalizable and for which the common eigenstates are expressed in terms of multiple Meixner polynomials of the second kind. (paper)

Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups

DEFF Research Database (Denmark)

Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan

2012-01-01

For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g......_C=k_C+p_C is a complexified Cartan decomposition. In this realization the space of k-finite vectors consists of holomorphic polynomials on X. The reproducing kernel of the Fock space is calculated explicitly in terms of an I-Bessel function. We further find an explicit formula of a generalized Segal-Bargmann transform which...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....

Factorisations for partition functions of random Hermitian matrix models

International Nuclear Information System (INIS)

Jackson, D.M.; Visentin, T.I.

1996-01-01

The partition function Z N , for Hermitian-complex matrix models can be expressed as an explicit integral over R N , where N is a positive integer. Such an integral also occurs in connection with random surfaces and models of two dimensional quantum gravity. We show that Z N can be expressed as the product of two partition functions, evaluated at translated arguments, for another model, giving an explicit connection between the two models. We also give an alternative computation of the partition function for the φ 4 -model.The approach is an algebraic one and holds for the functions regarded as formal power series in the appropriate ring. (orig.)

Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

OpenAIRE

Hillar, Christopher; Johnson, Charles R.

2005-01-01

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a long-standing problem in theoretical physics, and it was previously approached by the authors for words in two real positive definite matrices with positive integral exponents. A large class of words that do guarantee positive eig...

Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices

Directory of Open Access Journals (Sweden)

Hjalmar Rosengren

2006-12-01

Full Text Available We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, for such kernels. In subsequent work, these results are applied in combinatorics (enumeration of marked shifted tableaux and number theory (representation of integers as sums of squares.

Digital coherent superposition of optical OFDM subcarrier pairs with Hermitian symmetry for phase noise mitigation.

Science.gov (United States)

Yi, Xingwen; Chen, Xuemei; Sharma, Dinesh; Li, Chao; Luo, Ming; Yang, Qi; Li, Zhaohui; Qiu, Kun

2014-06-02

Digital coherent superposition (DCS) provides an approach to combat fiber nonlinearities by trading off the spectrum efficiency. In analogy, we extend the concept of DCS to the optical OFDM subcarrier pairs with Hermitian symmetry to combat the linear and nonlinear phase noise. At the transmitter, we simply use a real-valued OFDM signal to drive a Mach-Zehnder (MZ) intensity modulator biased at the null point and the so-generated OFDM signal is Hermitian in the frequency domain. At receiver, after the conventional OFDM signal processing, we conduct DCS of the optical OFDM subcarrier pairs, which requires only conjugation and summation. We show that the inter-carrier-interference (ICI) due to phase noise can be reduced because of the Hermitain symmetry. In a simulation, this method improves the tolerance to the laser phase noise. In a nonlinear WDM transmission experiment, this method also achieves better performance under the influence of cross phase modulation (XPM).

Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles

International Nuclear Information System (INIS)

Akemann, G.; Bender, M.

2010-01-01

We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane. These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this. In the large n limit, the eigenvalue statistics at the spectral edge close to the real axis are described by the same family of kernels interpolating between Airy and Poisson that was recently found by one of the authors for the elliptic Ginibre ensemble. We conclude that this scaling limit is universal, appearing for two different non-Hermitian random matrix ensembles with unitary symmetry. As a second result we give an equivalent form for the interpolating Airy kernel in terms of a single real integral, similar to representations for the asymptotic kernel in the bulk and at the hard edge of the spectrum. This makes its structure as a one-parameter deformation of the Airy kernel more transparent.

Reality of Energy Spectra in Multi-dimensional Hamiltonians Having Pseudo Hermiticity with Respect to the Exchange Operator

International Nuclear Information System (INIS)

Nanayakkara, Asiri

2005-01-01

The pseudo Hermiticity with respect to the exchange operators of N-D complex Hamiltonians is investigated. It is shown that if an N-D Hamiltonian is pseudo Hermitian and any eigenfunction of it retains π α T symmetry then the corresponding eigen value is real, where π α is an exchange operator with respect to the permutation α of coordinates and T is the time reversal operator. We construct a special class of N-D pseudo Hermitian Hamiltonians with respect to exchange operators from both N/2-D and N-D general complex Hamiltonians. Examples are presented for Hamiltonians with πT symmetry (π:x↔y, p x ↔p y ) and the reality of these systems are investigated.

On a decomposition theorem for density operators of a pure quantum state

International Nuclear Information System (INIS)

Giannoni, M.J.

1979-03-01

Conditions for the existence of a decomposition of a hermitian projector rho into two hermitian and time reversal invariant operators r/rho 0 and chi under the form rho=esup(i,chi)rho 0 esup(-i,chi) are investigated. Sufficient conditions are given, and an explicit construction of a decomposition is performed when they are fulfilled. A stronger theorem of existence and unicity is studied. All the proofs are valid for any p-body reduced density operator of a pure state of a system of bosons as well as fermions. The decomposition studied in this work has already been used in Nuclear Physics, and may be of interest in other fields of Physics

Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

International Nuclear Information System (INIS)

Castro, P.G.; Kullock, R.; Toppan, F.

2011-01-01

Nonrelativistic quantum mechanics and conformal quantum mechanics are de- formed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles. (author)

20th International Workshop on Hermitian Symmetric Spaces and Submanifolds

CERN Document Server

Ohnita, Yoshihiro; Zhou, Jiazu; Kim, Byung; Lee, Hyunjin

2017-01-01

This book presents the proceedings of the 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds, which was held at the Kyungpook National University from June 21 to 25, 2016. The Workshop was supported by the Research Institute of Real and Complex Manifolds (RIRCM) and the National Research Foundation of Korea (NRF). The Organizing Committee invited 30 active geometers of differential geometry and related fields from all around the globe to discuss new developments for research in the area. These proceedings provide a detailed overview of recent topics in the field of real and complex submanifolds.

Non-Hermitian interaction representation and its use in relativistic quantum mechanics

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2017-01-01

Roč. 385, č. 10 (2017), s. 162-179 ISSN 0003-4916 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : unitary quantum systems * non-Hermitian version of Dirac's interaction picture * complete set of time-evolution equations * application in relativistic quantum mechanics * Klein-Gordon example with space-time-dependent mass Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.465, year: 2016

Investigating the Composite Step Biconjugate A-Orthogonal Residual Method for Non-Hermitian Dense Linear Systems in Electromagnetics

NARCIS (Netherlands)

Jing, Yan-Fei; Huang, Ting-Zhu; Carpentieri, Bruno; Duan, Yong

An interesting stabilizing variant of the biconjugate A-orthogonal residual (BiCOR) method is investigated for solving dense complex non-Hermitian systems of linear equations arising from the Galerlcin discretization of surface integral equations in electromagnetics. The novel variant is naturally

Diagonalization of Bounded Linear Operators on Separable Quaternionic Hilbert Space

International Nuclear Information System (INIS)

Feng Youling; Cao, Yang; Wang Haijun

2012-01-01

By using the representation of its complex-conjugate pairs, we have investigated the diagonalization of a bounded linear operator on separable infinite-dimensional right quaternionic Hilbert space. The sufficient condition for diagonalizability of quaternionic operators is derived. The result is applied to anti-Hermitian operators, which is essential for solving Schroedinger equation in quaternionic quantum mechanics.

Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

Energy Technology Data Exchange (ETDEWEB)

Castro, P.G., E-mail: pgcastro@cbpf.b [Universidade Federal de Juiz de Fora (DM/ICE/UFJF), Juiz de Fora, MG (Brazil). Inst. de Ciencias Exatas. Dept. de Matematica; Kullock, R.; Toppan, F., E-mail: ricardokl@cbpf.b, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (TEO/CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Fisica Teorica

2011-07-01

Nonrelativistic quantum mechanics and conformal quantum mechanics are de- formed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles. (author)

On the time evolution operator for time-dependent quadratic Hamiltonians

International Nuclear Information System (INIS)

Fernandez, F.M.

1989-01-01

The Schroedinger equation with a time-dependent quadratic Hamiltonian is investigated. The time-evolution operator is written as a product of exponential operators determined by the Heisenberg equations of motion. This product operator is shown to be global in the occupation number representation when the Hamiltonian is Hermitian. The success of some physical applications of the product-form representation is explained

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix

International Nuclear Information System (INIS)

Vecharynski, Eugene; Yang, Chao; Pask, John E.

2015-01-01

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer

Anti-Hermitian photodetector facilitating efficient subwavelength photon sorting.

Science.gov (United States)

Kim, Soo Jin; Kang, Ju-Hyung; Mutlu, Mehmet; Park, Joonsuk; Park, Woosung; Goodson, Kenneth E; Sinclair, Robert; Fan, Shanhui; Kik, Pieter G; Brongersma, Mark L

2018-01-22

The ability to split an incident light beam into separate wavelength bands is central to a diverse set of optical applications, including imaging, biosensing, communication, photocatalysis, and photovoltaics. Entirely new opportunities are currently emerging with the recently demonstrated possibility to spectrally split light at a subwavelength scale with optical antennas. Unfortunately, such small structures offer limited spectral control and are hard to exploit in optoelectronic devices. Here, we overcome both challenges and demonstrate how within a single-layer metafilm one can laterally sort photons of different wavelengths below the free-space diffraction limit and extract a useful photocurrent. This chipscale demonstration of anti-Hermitian coupling between resonant photodetector elements also facilitates near-unity photon-sorting efficiencies, near-unity absorption, and a narrow spectral response (∼ 30 nm) for the different wavelength channels. This work opens up entirely new design paradigms for image sensors and energy harvesting systems in which the active elements both sort and detect photons.

The Optimization on Ranks and Inertias of a Quadratic Hermitian Matrix Function and Its Applications

Directory of Open Access Journals (Sweden)

Yirong Yao

2013-01-01

Full Text Available We solve optimization problems on the ranks and inertias of the quadratic Hermitian matrix function subject to a consistent system of matrix equations and . As applications, we derive necessary and sufficient conditions for the solvability to the systems of matrix equations and matrix inequalities , and in the Löwner partial ordering to be feasible, respectively. The findings of this paper widely extend the known results in the literature.

Universal Superspace Unitary Operator and Nilpotent (Anti-)Dual-BRST Symmetries: Superfield Formalism

International Nuclear Information System (INIS)

Malik, R. P.; Srinivas, N.; Bhanja, T.

2016-01-01

We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator and its Hermitian conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor and modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of the dual unitary operators and corresponding (anti-)dual-BRST symmetries are completely novel results in our present investigation.

A method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix

International Nuclear Information System (INIS)

Godfrin, Elena

1990-01-01

This paper presents a method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix using adequate partitions of the complete matrix. This type of matrix is very usual in quantum mechanics and, more specifically, in solid state physics (e.g., interfaces and superlattices), when the tight-binding approximation is used. The efficiency of the method is analyzed comparing the required CPU time and work-area for different usual techniques. (Author)

E2-quasi-exact solvability for non-Hermitian models

International Nuclear Information System (INIS)

Fring, Andreas

2015-01-01

We propose the notion of E 2 -quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the complex Mathieu Hamiltonian in a double scaling limit, which enables us to compute the exceptional points in the energy spectrum of the latter as a limiting process of the zeros for some algebraic equations. The coefficient functions in the quasi-exact eigenfunctions are univariate polynomials in the energy obeying a three-term recurrence relation. The latter property guarantees the existence of a linear functional such that the polynomials become orthogonal. The polynomials are shown to factorize for all levels above the quantization condition leading to vanishing norms rendering them to be weakly orthogonal. In two concrete examples we compute the explicit expressions for the Stieltjes measure. (paper)

E2-quasi-exact solvability for non-Hermitian models

Science.gov (United States)

Fring, Andreas

2015-04-01

We propose the notion of E2-quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the complex Mathieu Hamiltonian in a double scaling limit, which enables us to compute the exceptional points in the energy spectrum of the latter as a limiting process of the zeros for some algebraic equations. The coefficient functions in the quasi-exact eigenfunctions are univariate polynomials in the energy obeying a three-term recurrence relation. The latter property guarantees the existence of a linear functional such that the polynomials become orthogonal. The polynomials are shown to factorize for all levels above the quantization condition leading to vanishing norms rendering them to be weakly orthogonal. In two concrete examples we compute the explicit expressions for the Stieltjes measure.

Wigner-Smith delay times and the non-Hermitian Hamiltonian for the HOCl molecule

International Nuclear Information System (INIS)

Barr, A.M.; Reichl, L.E.

2013-01-01

We construct the scattering matrix for a two-dimensional model of a Cl atom scattering from an OH dimer. We show that the scattering matrix can be written in terms of a non-Hermitian Hamiltonian whose complex energy eigenvalues can be used to compute Wigner-Smith delay times for the Cl-OH scattering process. We compute the delay times for a range of energies, and show that the scattering states with the longest delay times are strongly influenced by unstable periodic orbits in the classical dynamics. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

On the remarkable spectrum of a non-Hermitian random matrix model

International Nuclear Information System (INIS)

Holz, D E; Orland, H; Zee, A

2003-01-01

A non-Hermitian random matrix model proposed a few years ago has a remarkably intricate spectrum. Various attempts have been made to understand the spectrum, but even its dimension is not known. Using the Dyson-Schmidt equation, we show that the spectrum consists of a non-denumerable set of lines in the complex plane. Each line is the support of the spectrum of a periodic Hamiltonian, obtained by the infinite repetition of any finite sequence of the disorder variables. Our approach is based on the 'theory of words'. We make a complete study of all four-letter words. The spectrum is complicated because our matrix contains everything that will ever be written in the history of the universe, including this particular paper

Multiphoton ionization of H+2 at critical internuclear separations: non-Hermitian Floquet analysis

International Nuclear Information System (INIS)

Likhatov, P V; Telnov, D A

2009-01-01

We present ab initio time-dependent non-Hermitian Floquet calculations of multiphoton ionization (MPI) rates of hydrogen molecular ions subject to an intense linearly polarized monochromatic laser field with a wavelength of 800 nm. The orientation of the molecular axis is parallel to the polarization vector of the laser field. The MPI rates are computed for a wide range of internuclear separations R with high resolution in R and reproduce resonance and near-threshold structures. We show that enhancement of ionization at critical internuclear separations is related to resonance series with higher electronic states. The effect of two-centre interference on the MPI signal is discussed.

The BL-QMR algorithm for non-Hermitian linear systems with multiple right-hand sides

Energy Technology Data Exchange (ETDEWEB)

Freund, R.W. [AT& T Bell Labs., Murray Hill, NJ (United States)

1996-12-31

Many applications require the solution of multiple linear systems that have the same coefficient matrix, but differ in their right-hand sides. Instead of applying an iterative method to each of these systems individually, it is potentially much more efficient to employ a block version of the method that generates iterates for all the systems simultaneously. However, it is quite intricate to develop robust and efficient block iterative methods. In particular, a key issue in the design of block iterative methods is the need for deflation. The iterates for the different systems that are produced by a block method will, in general, converge at different stages of the block iteration. An efficient and robust block method needs to be able to detect and then deflate converged systems. Each such deflation reduces the block size, and thus the block method needs to be able to handle varying block sizes. For block Krylov-subspace methods, deflation is also crucial in order to delete linearly and almost linearly dependent vectors in the underlying block Krylov sequences. An added difficulty arises for Lanczos-type block methods for non-Hermitian systems, since they involve two different block Krylov sequences. In these methods, deflation can now occur independently in both sequences, and consequently, the block sizes in the two sequences may become different in the course of the iteration, even though they were identical at the beginning. We present a block version of Freund and Nachtigal`s quasi-minimal residual method for the solution of non-Hermitian linear systems with single right-hand sides.

Unidirectional reflectionless phenomena in a non-Hermitian quantum system of quantum dots coupled to a plasmonic waveguide.

Science.gov (United States)

Wu, Nan; Zhang, Cong; Jin, Xing Ri; Zhang, Ying Qiao; Lee, YoungPak

2018-02-19

Unidirectional reflectionless phenomena are investigated theoretically in a non-Hermitian quantum system composed of several quantum dots and a plasmonic waveguide. By adjusting the phase shifts between quantum dots, single- and dual-band unidirectional reflectionlessnesses are realized at exceptional points based on two and three quantum dots coupled to a plasmonic waveguide, respectively. In addition, single- and dual-band unidirectional perfect absorptions with high quality factors are obtained at the vicinity of exceptional points.

X-ray absorption in insulators with non-Hermitian real-time time-dependent density functional theory.

Science.gov (United States)

Fernando, Ranelka G; Balhoff, Mary C; Lopata, Kenneth

2015-02-10

Non-Hermitian real-time time-dependent density functional theory was used to compute the Si L-edge X-ray absorption spectrum of α-quartz using an embedded finite cluster model and atom-centered basis sets. Using tuned range-separated functionals and molecular orbital-based imaginary absorbing potentials, the excited states spanning the pre-edge to ∼20 eV above the ionization edge were obtained in good agreement with experimental data. This approach is generalizable to TDDFT studies of core-level spectroscopy and dynamics in a wide range of materials.

Sufficient conditions for positivity of non-Markovian master equations with Hermitian generators

International Nuclear Information System (INIS)

Wilkie, Joshua; Wong Yinmei

2009-01-01

We use basic physical motivations to develop sufficient conditions for positive semidefiniteness of the reduced density matrix for generalized non-Markovian integrodifferential Lindblad-Kossakowski master equations with Hermitian generators. We show that it is sufficient for the memory function to be the Fourier transform of a real positive symmetric frequency density function with certain properties. These requirements are physically motivated, and are more general and more easily checked than previously stated sufficient conditions. We also explore the decoherence dynamics numerically for some simple models using the Hadamard representation of the propagator. We show that the sufficient conditions are not necessary conditions. We also show that models exist in which the long time limit is in part determined by non-Markovian effects

Non-Hermitian multi-particle systems from complex root spaces

International Nuclear Information System (INIS)

Fring, Andreas; Smith, Monique

2012-01-01

We provide a general construction procedure for antilinearly invariant complex root spaces. The proposed method is generic and may be applied to any Weyl group allowing us to take any element of the group as a starting point for the construction. Worked-out examples for several specific Weyl groups are presented, focusing especially on those cases for which no solutions were found previously. When applied to the defining relations of models based on root systems, this usually leads to non-Hermitian models, which are nonetheless physically viable in a self-consistent sense as they are antilinearly invariant by construction. We discuss new types of Calogero models based on these complex roots. In addition, we propose an alternative construction leading to q-deformed roots. We employ the latter type of roots to formulate a new version of affine Toda field theories based on non-simply laced root systems. These models exhibit on the classical level a strong–weak duality in the coupling constant equivalent to a Lie algebraic duality, which is known for the quantum version of the undeformed case. (paper)

Seismic transmission operator reciprocity - II: impedance-operator symmetry via elastic lateral modes

Science.gov (United States)

Thomson, C. J.

2015-08-01

The properties of the overburden transmission response are of particular interest for the analysis of reflectivity illumination or blurring in seismic depth imaging. The first step to showing a transmission-operator reciprocity property is to identify the symmetry of the so-called displacement-to-traction operators. The latter are analogous to Dirichlet-to-Neumann operators and they may also be called impedance operators. Their symmetry is deduced here after development of a formal spectral or modal theory of lateral wavefunctions in a laterally heterogeneous generally anisotropic elastic medium. The elastic lateral modes are displacement-traction 6-vectors and they are built from two auxiliary 3-vector lateral-mode bases. These auxiliary modes arise from Hermitian and anti-Hermitian operators, so they have familiar properties such as orthogonality. There is no assumption of down/up symmetry of the elasticity tensor, but basic assumptions are made about the existence and completeness of the elastic modes. A point-symmetry property appears and plays a central role. The 6-vector elastic modes have a symplectic orthogonality property, which facilitates the development of modal expansions for 6-vector functions of the lateral coordinates when completeness is assumed. While the elastic modal theory is consistent with the laterally homogeneous case, numerical work would provide confidence that it is correct in general. An appendix contains an introductory overview of acoustic lateral modes that were studied by other authors, given from the perspective of this new work. A distinction is drawn between unit normalization of scalar auxiliary modes and a separate energy-flux normalization of 2-vector acoustic modes. Neither is crucial to the form of acoustic pressure-to-velocity or impedance operators. This statement carries over to the elastic case for the 3-vector auxiliary- and 6-vector elastic-mode normalizations. The modal theory is used to construct the kernel of the

The effect of a non-hermitian crystal potential on the scattering matrix in reflection electron diffraction

International Nuclear Information System (INIS)

Smith, A.E.; Josefsson, T.W.

1994-01-01

An extension to include general inelastic scattering effects is developed for the case of reflection electron diffraction scattering from surfaces. In this extension of work by Lynch and Moodie, it is shown how the resultant non-Hermitian matrix problem can be recast in a form that is suitable for computation. In particular, a computational method is outlined based on techniques developed by Eberlein for matrix diagonalisation using complex rotations and shears. The resultant methods are applied to the problem of Convergent Beam RHEED. 23 refs., 3 figs

Hybrid normed ideal perturbations of n-tuples of operators I

Science.gov (United States)

Voiculescu, Dan-Virgil

2018-06-01

In hybrid normed ideal perturbations of n-tuples of operators, the normed ideal is allowed to vary with the component operators. We begin extending to this setting the machinery we developed for normed ideal perturbations based on the modulus of quasicentral approximation and an adaptation of our non-commutative generalization of the Weyl-von Neumann theorem. For commuting n-tuples of hermitian operators, the modulus of quasicentral approximation remains essentially the same when Cn- is replaced by a hybrid n-tuple Cp1,…- , … , Cpn- , p1-1 + ⋯ + pn-1 = 1. The proof involves singular integrals of mixed homogeneity.

General operator form of the non-local three-nucleon force

Energy Technology Data Exchange (ETDEWEB)

Topolnicki, K. [Jagiellonian University, M. Smoluchowski Institute of Physics, Krakow (Poland)

2017-09-15

This paper describes a procedure to obtain the general form of the three-nucleon force. The result is an operator form where the momentum space matrix element of the three-nucleon potential is written as a linear combination of 320 isospin-spin-momentum operators and scalar functions of momenta. Any spatial and isospin rotation invariant three-nucleon force can be written in this way and in order for the potential to be Hermitian, symmetric under parity inversion, time reversal and particle exchange, the scalar functions must have definite transformation properties under these discrete operations. A complete list of the isospin-spin-momentum operators and scalar function transformation properties is given. (orig.)

Spectral correlations of the massive QCD Dirac operator at finite temperature

International Nuclear Information System (INIS)

Seif, Burkhard; Wettig, Tilo; Guhr, Thomas

1999-01-01

We use the graded eigenvalue method, a variant of the supersymmetry technique, to compute the universal spectral correlations of the QCD Dirac operator in the presence of massive dynamical quarks. The calculation is done for the chiral Gaussian unitary ensemble of random matrix theory with an arbitrary Hermitian matrix added to the Dirac matrix. This case is of interest for schematic models of OCD at finite temperature

Nonlinear transient heat transfer and thermoelastic analysis of thick-walled FGM cylinder with temperature-dependent material properties using Hermitian transfinite element

Energy Technology Data Exchange (ETDEWEB)

Azadi, Mohammad [Sharif University of Technology, Tehran (Iran, Islamic Republic of); Azadi, Mahboobeh [Shiraz University, Shiraz (Iran, Islamic Republic of)

2009-10-15

Nonlinear transient heat transfer and thermoelastic stress analyses of a thick-walled FGM cylinder with temperature dependent materials are performed by using the Hermitian transfinite element method. Temperature-dependency of the material properties has not been taken into account in transient thermoelastic analysis, so far. Due to the mentioned dependency, the resulting governing FEM equations of transient heat transfer are highly nonlinear. Furthermore, in all finite element analysis performed so far in the field, Lagrangian elements have been used. To avoid an artificial local heat source at the mutual boundaries of the elements, Hermitian elements are used instead in the present research. Another novelty of the present paper is simultaneous use of the transfinite element method and updating technique. Time variations of the temperature, displacements, and stresses are obtained through a numerical Laplace inversion. Finally, results obtained considering the temperature-dependency of the material properties are compared with those derived based on temperature independency assumption. Furthermore, the temperature distribution and the radial and circumferential stresses are investigated versus time, geometrical parameters and index of power law. Results reveal that the temperature-dependency effect is significant

Non-Hermitian localization in biological networks.

Science.gov (United States)

Amir, Ariel; Hatano, Naomichi; Nelson, David R

2016-04-01

We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90^{∘} rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's law" (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

Spectrum of the Wilson Dirac operator at finite lattice spacings

DEFF Research Database (Denmark)

Akemann, G.; Damgaard, Poul Henrik; Splittorff, Kim

2011-01-01

We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator...... as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral Random Matrix Theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral Perturbation Theory. All results are obtained for fixed index...... of the Wilson Dirac operator. The low-energy constants of Wilson chiral Perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator....

The area distribution of two-dimensional random walks and non-Hermitian Hofstadter quantum mechanics

International Nuclear Information System (INIS)

Matveenko, Sergey; Ouvry, Stéphane

2014-01-01

When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be obtained exactly (Mashkevich and Ouvry 2009 J. Stat. Phys. 137 71). We explicitly map this biased classical random system onto a non-Hermitian Hofstadter-like quantum model where a charged particle on a square lattice coupled to a perpendicular magnetic field hops only to the right. For the commensurate case, when the magnetic flux per unit cell is rational, an exact solution of the quantum model is obtained. The periodicity of the lattice allows one to relate traces of the Nth power of the Hamiltonian to probability distribution generating functions of biased walks of length N. (paper)

On the Similarity of Sturm-Liouville Operators with Non-Hermitian Boundary Conditions to Self-Adjoint and Normal Operators

Czech Academy of Sciences Publication Activity Database

Krejčiřík, David; Siegl, Petr; Železný, Jakub

2014-01-01

Roč. 8, č. 1 (2014), s. 255-281 ISSN 1661-8254 R&D Projects: GA MŠk LC06002; GA MŠk LC527; GA ČR GAP203/11/0701 Grant - others:GA ČR(CZ) GD202/08/H072 Institutional support: RVO:61389005 Keywords : Sturm-Liouville operators * non-symmetric Robin boundary conditions * similarity to normal or self-adjoint operators * discrete spectral operator * complex symmetric operator * PT-symmetry * metric operator * C operator * Hilbert- Schmidt operators Subject RIV: BE - Theoretical Physics Impact factor: 0.545, year: 2014

Non-Hermitian wave packet approximation for coupled two-level systems in weak and intense fields

Energy Technology Data Exchange (ETDEWEB)

Puthumpally-Joseph, Raiju; Charron, Eric [Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS, Univ. Paris-Sud, Université Paris-Saclay, F-91405 Orsay (France); Sukharev, Maxim [Science and Mathematics Faculty, College of Letters and Sciences, Arizona State University, Mesa, Arizona 85212 (United States)

2016-04-21

We introduce a non-Hermitian Schrödinger-type approximation of optical Bloch equations for two-level systems. This approximation provides a complete and accurate description of the coherence and decoherence dynamics in both weak and strong laser fields at the cost of losing accuracy in the description of populations. In this approach, it is sufficient to propagate the wave function of the quantum system instead of the density matrix, providing that relaxation and dephasing are taken into account via automatically adjusted time-dependent gain and decay rates. The developed formalism is applied to the problem of scattering and absorption of electromagnetic radiation by a thin layer comprised of interacting two-level emitters.

Crypto-Unitary Forms of Quantum Evolution Operators

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2013-01-01

Roč. 52, č. 6 (2013), s. 2038-2045 ISSN 0020-7748 R&D Projects: GA ČR GAP203/11/1433 Institutional support: RVO:61389005 Keywords : PT-symmetric quantum mechanics * time-dependent Schrödinger equation * manifestly time-dependent Hermitian Hamiltonians * Manifestly time-dependent Dyson maps * equivalent time-independent non-Hermitian Hamiltonians Subject RIV: BE - Theoretical Physics Impact factor: 1.188, year: 2013 http://link.springer.com/content/pdf/10.1007%2Fs10773-012-1451-9.pdf

Heat transfer operators associated with quantum operations

International Nuclear Information System (INIS)

Aksak, C; Turgut, S

2011-01-01

Any quantum operation applied on a physical system is performed as a unitary transformation on a larger extended system. If the extension used is a heat bath in thermal equilibrium, the concomitant change in the state of the bath necessarily implies a heat exchange with it. The dependence of the average heat transferred to the bath on the initial state of the system can then be found from the expectation value of a Hermitian operator, which is named as the heat transfer operator (HTO). The purpose of this paper is to investigate the relation between the HTOs and the associated quantum operations. Since any given quantum operation on a system can be realized by different baths and unitaries, many different HTOs are possible for each quantum operation. On the other hand, there are also strong restrictions on the HTOs which arise from the unitarity of the transformations. The most important of these is the Landauer erasure principle. This paper is concerned with the question of finding a complete set of restrictions on the HTOs that are associated with a given quantum operation. An answer to this question has been found only for a subset of quantum operations. For erasure operations, these characterizations are equivalent to the generalized Landauer erasure principle. For the case of generic quantum operations, however, it appears that the HTOs obey further restrictions which cannot be obtained from the entropic restrictions of the generalized Landauer erasure principle.

Complexified coherent states and quantum evolution with non-Hermitian Hamiltonians

International Nuclear Information System (INIS)

Graefe, Eva-Maria; Schubert, Roman

2012-01-01

The complex geometry underlying the Schrödinger dynamics of coherent states for non-Hermitian Hamiltonians is investigated. In particular, two seemingly contradictory approaches are compared: (i) a complex WKB formalism, for which the centres of coherent states naturally evolve along complex trajectories, which leads to a class of complexified coherent states; (ii) the investigation of the dynamical equations for the real expectation values of position and momentum, for which an Ehrenfest theorem has been derived in a previous paper, yielding real but non-Hamiltonian classical dynamics on phase space for the real centres of coherent states. Both approaches become exact for quadratic Hamiltonians. The apparent contradiction is resolved building on an observation by Huber, Heller and Littlejohn, that complexified coherent states are equivalent if their centres lie on a specific complex Lagrangian manifold. A rich underlying complex symplectic geometry is unravelled. In particular, a natural complex structure is identified that defines a projection from complex to real phase space, mapping complexified coherent states to their real equivalents. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Generalized space and linear momentum operators in quantum mechanics

International Nuclear Information System (INIS)

Costa, Bruno G. da; Borges, Ernesto P.

2014-01-01

We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p ^ q , and its canonically conjugate deformed position operator x ^ q . A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed

Euler polynomials and identities for non-commutative operators

Science.gov (United States)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

A comparative study of numerical methods for the overlap Dirac operator--a status report

International Nuclear Information System (INIS)

Eshof, J. van den; Frommer, A.; Lippert, Th.; Schilling, K.; Vorst, H. van der

2002-01-01

Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks show that this PFE together with removal of converged systems within a multi-shift CG appears to approximate the sign function times a vector most efficiently. A posteriori error bounds are given

Comment on 'New ansatz for metric operator calculation in pseudo-Hermitian field theory'

International Nuclear Information System (INIS)

Bender, Carl M.; Benincasa, Gregorio; Jones, H. F.

2009-01-01

In a recent Brief Report by Shalaby, a new first-order perturbative calculation of the metric operator for an iφ 3 scalar field theory is given. It is claimed that the incorporation of derivative terms in the ansatz for the metric operator results in a local solution, in contrast to the nonlocal solution previously obtained by Bender, Brody, and Jones. Unfortunately, Shalaby's calculation is not valid because of sign errors.

Singular Spectrum Near a Singular Point of Friedrichs Model Operators of Absolute Type

International Nuclear Information System (INIS)

Iakovlev, Serguei I.

2006-01-01

In L 2 (R) we consider a family of self adjoint operators of the Friedrichs model: A m =|t| m +V. Here |t| m is the operator of multiplication by the corresponding function of the independent variable t element of R, and (perturbation) is a trace-class integral operator with a continuous Hermitian kernel ν(t,x) satisfying some smoothness condition. These absolute type operators have one singular point of order m>0. Conditions on the kernel ν(t,x) are found guaranteeing the absence of the point spectrum and the singular continuous one of such operators near the origin. These conditions are actually necessary and sufficient. They depend on the finiteness of the rank of a perturbation operator and on the order of singularity. The sharpness of these conditions is confirmed by counterexamples

A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems. Ph.D. Thesis - Massachusetts Inst. of Technology, Aug. 1991

Science.gov (United States)

Nachtigal, Noel M.

1991-01-01

The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition, the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. Here, we present two new results. We propose an implementation of a look-ahead variant of the Lanczos algorithm which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur. The new algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products per step as the classical Lanczos algorithm without look-ahead. Based on the proposed look-ahead Lanczos algorithm, we then present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which avoids the second source of breakdowns in the BCG algorithm. We present details of the new method and discuss some of its properties. In particular, we discuss the relationship between QMR and BCG, showing how one can recover the BCG iterates, when they exist, from the QMR iterates. We also present convergence results for QMR, showing the connection between QMR and the generalized minimal residual (GMRES) algorithm, the optimal method in this class of methods. Finally, we give some numerical examples, both for eigenvalue computations and for non-Hermitian linear systems.

Calculating the C operator in PT-symmetric quantum mechanics

International Nuclear Information System (INIS)

Bender, C.M.

2004-01-01

It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT-symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition it is cumbersome to calculate C in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method can be used to calculate the C operator in quantum field theory. The C operator is a new time-independent observable in PT-symmetric quantum field theory. (author)

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

Science.gov (United States)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

BRST operator quantization of generally covariant gauge systems

International Nuclear Information System (INIS)

Ferraro, R.; Sforza, D.M.

1997-01-01

The BRST generator is realized as a Hermitian nilpotent operator for a finite-dimensional gauge system featuring a quadratic super-Hamiltonian and linear supermomentum constraints. As a result, the emerging ordering for the Hamiltonian constraint is not trivial, because the potential must enter the kinetic term in order to obtain a quantization invariant under scaling. Namely, BRST quantization does not lead to the curvature term used in the literature as a means to get that invariance. The inclusion of the potential in the kinetic term, far from being unnatural, is beautifully justified in light of the Jacobi's principle. copyright 1997 The American Physical Society

Low-lying eigenmodes of the Wilson-Dirac operator and correlations with topological objects

International Nuclear Information System (INIS)

Kusterer, Daniel-Jens; Hedditch, John; Kamleh, Waseem; Leinweber, D.B.; Williams, Anthony G.

2002-01-01

The probability density of low-lying eigenvectors of the hermitian Wilson-Dirac operator H(κ)=γ 5 D W (κ) is examined. Comparisons in position and size between eigenvectors, topological charge and action density are made. We do this for standard Monte-Carlo generated SU(3) background fields and for single instanton background fields. Both hot and cooled SU(3) background fields are considered. An instanton model is fitted to eigenmodes and topological charge density and the sizes and positions of these are compared

Unveiling the significance of eigenvectors in diffusing non-Hermitian matrices by identifying the underlying Burgers dynamics

Energy Technology Data Exchange (ETDEWEB)

Burda, Zdzislaw, E-mail: zdzislaw.burda@agh.edu.pl [AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, al. Mickiewicza 30, PL-30059 Kraków (Poland); Grela, Jacek, E-mail: jacekgrela@gmail.com [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Nowak, Maciej A., E-mail: nowak@th.if.uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Tarnowski, Wojciech, E-mail: wojciech.tarnowski@uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland); Warchoł, Piotr, E-mail: piotr.warchol@uj.edu.pl [M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Centre, Jagiellonian University, PL-30348 Kraków (Poland)

2015-08-15

Following our recent letter, we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size N and arbitrary initial conditions) for evolution of the averaged extended characteristic polynomial. The logarithm of this polynomial has an interpretation of a potential which generates a Burgers dynamics in quaternionic space. The dynamics of the ensemble in the large N limit is completely determined by the coevolution of the spectral density and a certain eigenvector correlation function. This coevolution is best visible in an electrostatic potential of a quaternionic argument built of two complex variables, the first of which governs standard spectral properties while the second unravels the hidden dynamics of eigenvector correlation function. We obtain general formulas for the spectral density and the eigenvector correlation function for large N and for any initial conditions. We exemplify our studies by solving three examples, and we verify the analytic form of our solutions with numerical simulations.

Product numerical range in a space with tensor product structure

OpenAIRE

Puchała, Zbigniew; Gawron, Piotr; Miszczak, Jarosław Adam; Skowronek, Łukasz; Choi, Man-Duen; Życzkowski, Karol

2010-01-01

We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product ...

Quantum Strategies and Local Operations

Science.gov (United States)

Gutoski, Gus

2010-02-01

This thesis is divided into two parts. In Part I we introduce a new formalism for quantum strategies, which specify the actions of one party in any multi-party interaction involving the exchange of multiple quantum messages among the parties. This formalism associates with each strategy a single positive semidefinite operator acting only upon the tensor product of the input and output message spaces for the strategy. We establish three fundamental properties of this new representation for quantum strategies and we list several applications, including a quantum version of von Neumann's celebrated 1928 Min-Max Theorem for zero-sum games and an efficient algorithm for computing the value of such a game. In Part II we establish several properties of a class of quantum operations that can be implemented locally with shared quantum entanglement or classical randomness. In particular, we establish the existence of a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. The existence of this ball is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. We also provide characterizations of local operations in terms of linear functionals that are positive and "completely" positive on a certain cone of Hermitian operators, under a natural notion of complete positivity appropriate to that cone. We end the thesis with a discussion of the properties of no-signaling quantum operations.

Hermitian symmetry free optical-single-carrier frequency division multiple access for visible light communication

Science.gov (United States)

Azim, Ali W.; Le Guennec, Yannis; Maury, Ghislaine

2018-05-01

Optical-orthogonal frequency division multiplexing (O-OFDM) is an effective scheme for visible light communications (VLC), offering a candid extension to multiple access (MA) scenarios, i.e., O-OFDMA. However, O-OFDMA exhibits high peak-to-average power ratio (PAPR), which exacerbates the non-linear distortions from the light emitting diode (LED). To overcome high PAPR while sustaining MA, optical-single-carrier frequency-division multiple access (O-SCFDMA) is used. For both O-OFDMA and O-SCFDMA, Hermitian symmetry (HS) constraint is imposed in frequency-domain (FD) to obtain a real-valued time-domain (TD) signal for intensity modulation-direct detection (IM-DD) implementation of VLC. Howbeit, HS results in an increase of PAPR for O-SCFDMA. In this regard, we propose HS free (HSF) O-SCFDMA (HSFO-SCFDMA). We compare HSFO-SCFDMA with several approaches in key parameters, such as, bit error rate (BER), optical power penalty, PAPR, quantization, electrical power efficiency and system complexity. BER performance and optical power penalty is evaluated considering multipath VLC channel and taking into account the bandwidth limitation of LED in combination with its optimized driver. It is illustrated that HSFO-SCFDMA outperforms other alternatives.

The brachistochrone problem in open quantum systems

International Nuclear Information System (INIS)

Rotter, Ingrid

2007-01-01

Recently, the quantum brachistochrone problem has been discussed in the literature by using non-Hermitian Hamilton operators of different types. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton operator. As an example, the numerical results obtained by Bulgakov et al for the transmission through microwave cavities of different shapes are analyzed from the point of view of the brachistochrone problem. The passage time is shortened in the crossover from the weak-coupling to the strong-coupling regime where the resonance states overlap and many branch points (exceptional points) in the complex plane exist. The effect can not be described in the framework of the standard quantum mechanics with the Hermitian Hamilton operator and consideration of S matrix poles

From a world-sheet supersymmetry to the Dirac equation

International Nuclear Information System (INIS)

Mankoc Borstnik, N.

1991-10-01

Starting from a classical action for a point particle with a local world-sheet supersymmetry, the Dirac equation follows with operators α-vector, β-vector γ-vector being defined in the Grassmann space as differential operators and having all the properties of the corresponding Dirac matrices except that α-vector and β-vector are anti-Hermitian rather than Hermitian. Such a particle interacts with an external field as expected. (author). 7 refs

The consequences of non-normality

International Nuclear Information System (INIS)

Hip, I.; Lippert, Th.; Neff, H.; Schilling, K.; Schroers, W.

2002-01-01

The non-normality of Wilson-type lattice Dirac operators has important consequences - the application of the usual concepts from the textbook (hermitian) quantum mechanics should be reconsidered. This includes an appropriate definition of observables and the refinement of computational tools. We show that the truncated singular value expansion is the optimal approximation to the inverse operator D -1 and we prove that due to the γ 5 -hermiticity it is equivalent to γ 5 times the truncated eigenmode expansion of the hermitian Wilson-Dirac operator

Gauge systems and functions, hermitian operators and clocks as conjugate functions for the constraints

International Nuclear Information System (INIS)

Cuesta, Vladimir; Vergara, Jose David; Montesinos, Merced

2011-01-01

We work with gauge systems and using gauge invariant functions we study its quantum counterpart and we find if all these operators are self adjoint or not. Our study is divided in two cases, when we choose clock or clocks that its Poisson brackets with the set of constraints is one or it is different to one. We show some transition amplitudes.

Conservation of connectivity of model-space effective interactions under a class of similarity transformation

International Nuclear Information System (INIS)

Duan Changkui; Gong Yungui; Dong Huining; Reid, Michael F.

2004-01-01

Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators, etc.) as those of the original operators between the corresponding true eigenstates. Various types of effective operators are possible. Those well defined effective operators have been shown to be related to each other by similarity transformation. Some of the effective operators have been shown to have connected-diagram expansions. It is shown in this paper that under a class of very general similarity transformations, the connectivity is conserved. The similarity transformation between Hermitian and non-Hermitian Rayleigh-Schroedinger perturbative effective operators is one of such transformations and hence the connectivity can be deducted from each other

Conservation of connectivity of model-space effective interactions under a class of similarity transformation.

Science.gov (United States)

Duan, Chang-Kui; Gong, Yungui; Dong, Hui-Ning; Reid, Michael F

2004-09-15

Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators, etc.) as those of the original operators between the corresponding true eigenstates. Various types of effective operators are possible. Those well defined effective operators have been shown to be related to each other by similarity transformation. Some of the effective operators have been shown to have connected-diagram expansions. It is shown in this paper that under a class of very general similarity transformations, the connectivity is conserved. The similarity transformation between Hermitian and non-Hermitian Rayleigh-Schrodinger perturbative effective operators is one of such transformations and hence the connectivity can be deducted from each other.

Hermitian Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds

International Nuclear Information System (INIS)

Popov, Alexander D.

2010-01-01

We consider the Hermitian Yang-Mills (HYM) equations for gauge potentials on a complex vector bundle E over an almost complex manifold X 6 which is the twistor space of an oriented Riemannian manifold M 4 . Each solution of the HYM equations on such X 6 defines a pseudo-holomorphic structure on the bundle E. It is shown that the pull-back to X 6 of any anti-self-dual gauge field on M 4 is a solution of the HYM equations on X 6 . This correspondence allows us to introduce new twistor actions for bosonic and supersymmetric Yang-Mills theories. As examples of X 6 we consider homogeneous nearly Kaehler and nearly Calabi-Yau manifolds which are twistor spaces of S 4 , CP 2 and B 4 , CB 2 (real 4-ball and complex 2-ball), respectively. Various explicit examples of solutions to the HYM equations on these spaces are provided. Applications in flux compactifications of heterotic strings are briefly discussed.

A note on the correspondence between qubit quantum operations and special relativity

Energy Technology Data Exchange (ETDEWEB)

Arrighi, Pablo [Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, Cambridge CB3 0FD (United Kingdom); Patricot, Christophe [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

2003-05-23

We exploit a well-known isomorphism between complex Hermitian 2 x 2 matrices and R{sup 4}, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in E{sup 1,3}, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences. (letter to the editor)

A note on the correspondence between qubit quantum operations and special relativity

International Nuclear Information System (INIS)

Arrighi, Pablo; Patricot, Christophe

2003-01-01

We exploit a well-known isomorphism between complex Hermitian 2 x 2 matrices and R 4 , which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in E 1,3 , whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences. (letter to the editor)

An integral conservative gridding--algorithm using Hermitian curve interpolation.

Science.gov (United States)

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K

2008-11-07

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to

An integral conservative gridding-algorithm using Hermitian curve interpolation

International Nuclear Information System (INIS)

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K

2008-01-01

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to

Hermitian versus holomorphic complex and quaternionic generalized supersymmetries of the M-theory. A classification

International Nuclear Information System (INIS)

Toppan, Francesco

2004-06-01

Relying upon the division-algebra classification of Clifford algebras and spinors, a classification of generalized supersymmetries (or, with a slight abuse of language, 'generalized super translations') is provided. In each given space-time the maximal, saturated, generalized supersymmetry, compatible with the division-algebra constraint that can be consistently imposed on spinors and on superalgebra generators, is furnished. Constraining the superalgebra generators in both the complex and the quaternionic cases gives rise to the two classes of constrained hermitian and holomorphic generalized supersymmetries. In the complex case these two classes of generalized supersymmetries can be regarded as complementary. The quaternionic holomorphic supersymmetry only exists in certain space-time dimensions and can admit at most a single bosonic scalar central charge. The results here presented pave the way for a better understanding of the various M algebra-type of structures which can be introduced in different space-time signatures and in association with different division algebras, as well as their mutual relations. In a previous work, e.g., the introduction of a complex holomorphic generalized supersymmetry was shown to be necessary in order to perform the analytic continuation of the standard M-theory to the 11-dimensional Euclidean space. As an application of the present results, it is shown that the above algebra also admits a 12-dimensional, Euclidean, F-algebra presentation. (author)

Analysis of unbounded operators and random motion

International Nuclear Information System (INIS)

Jorgensen, Palle E. T.

2009-01-01

We study infinite weighted graphs with view to 'limits at infinity' or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means 'very' large) networks of resistors or in statistical mechanics models for classical or quantum systems. However, more generally, our analysis includes reproducing kernel Hilbert spaces and associated operators on them. If X is some infinite set of vertices or nodes, in applications the essential ingredient going into the definition is a reproducing kernel Hilbert space; it measures the differences of functions on X evaluated on pairs of points in X. Moreover, the Hilbert norm-squared in H(X) will represent a suitable measure of energy. Associated unbounded operators will define a notion or dissipation, it can be a graph Laplacian or a more abstract unbounded Hermitian operator defined from the reproducing kernel Hilbert space under study. We prove that there are two closed subspaces in reproducing kernel Hilbert space H(X) that measure quantitative notions of limits at infinity in X: one generalizes finite-energy harmonic functions in H(X) and the other a deficiency index of a natural operator in H(X) associated directly with the diffusion. We establish these results in the abstract, and we offer examples and applications. Our results are related to, but different from, potential theoretic notions of 'boundaries' in more standard random walk models. Comparisons are made.

Quantum measurement with a positive operator-valued measure

International Nuclear Information System (INIS)

Brandt, Howard E

2003-01-01

In the quantum theory of measurement, the positive operator-valued measure (POVM) is an important concept, and its implementation can be useful. A POVM consists of a set of non-negative quantum-mechanical Hermitian operators that add up to the identity. The probability that a quantum system is in a particular state is given by the expectation value of the POVM operator corresponding to that state. Following a brief review of the mathematics and mention of the history of POVMs in quantum theory, a particular implementation of a POVM for use in the measurement of nonorthogonal photon polarization states is reviewed. The implementation consists simply of a Wollaston prism, a mirror, two beam splitters, a polarization rotator and three phototubes arranged in an interferometric configuration, and it is shown analytically that the device faithfully represents the POVM. Based on Neumark's extension theorem, the two-dimensional Hilbert space of the POVM implementation can be embedded in the three-dimensional Hilbert space of an ordinary projective-valued measure. Also, analytical expressions are given for the maximum Renyi information loss from the device to a disturbing probe, and for the error and inconclusive rates induced by the probe. Various aspects of the problem of probe optimization are elaborated

Quasilocal conservation laws in XXZ spin-1/2 chains: Open, periodic and twisted boundary conditions

Directory of Open Access Journals (Sweden)

Tomaž Prosen

2014-09-01

Full Text Available A continuous family of quasilocal exact conservation laws is constructed in the anisotropic Heisenberg (XXZ spin-1/2 chain for periodic (or twisted boundary conditions and for a set of commensurate anisotropies densely covering the entire easy plane interaction regime. All local conserved operators follow from the standard (Hermitian transfer operator in fundamental representation (with auxiliary spin s=1/2, and are all even with respect to a spin flip operation. However, the quasilocal family is generated by differentiation of a non-Hermitian highest weight transfer operator with respect to a complex auxiliary spin representation parameter s and includes also operators of odd parity. For a finite chain with open boundaries the time derivatives of quasilocal operators are not strictly vanishing but result in operators localized near the boundaries of the chain. We show that a simple modification of the non-Hermitian transfer operator results in exactly conserved, but still quasilocal operators for periodic or generally twisted boundary conditions. As an application, we demonstrate that implementing the new exactly conserved operator family for estimating the high-temperature spin Drude weight results, in the thermodynamic limit, in exactly the same lower bound as for almost conserved family and open boundaries. Under the assumption that the bound is saturating (suggested by agreement with previous thermodynamic Bethe ansatz calculations we propose a simple explicit construction of infinite time averages of local operators such as the spin current.

An accelerated conjugate gradient algorithm to compute low-lying eigenvalues - a study for the Dirac operator in SU(2) lattice QCD

International Nuclear Information System (INIS)

Kalkreuter, T.; Simma, H.

1995-07-01

The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalizations in the subspace spanned by the numerically computed eigenvectors. We study this combined algorithm in case of the Dirac operator with (dynamical) Wilson fermions in four-dimensional SU(2) gauge fields. The algorithm is numerically very stable and can be parallelized in an efficient way. On lattices of sizes 4 4 - 16 4 an acceleration of the pure CG method by a factor of 4 - 8 is found. (orig.)

Simple Closed-Form Expression for Penning Reaction Rate Coefficients for Cold Molecular Collisions by Non-Hermitian Time-Independent Adiabatic Scattering Theory.

Science.gov (United States)

Pawlak, Mariusz; Ben-Asher, Anael; Moiseyev, Nimrod

2018-01-09

We present a simple expression and its derivation for reaction rate coefficients for cold anisotropic collision experiments based on adiabatic variational theory and time-independent non-Hermitian scattering theory. We demonstrate that only the eigenenergies of the resulting one-dimensional Schrödinger equation for different complex adiabats are required. The expression is applied to calculate the Penning ionization rate coefficients of an excited metastable helium atom with molecular hydrogen in an energy range spanning from hundreds of kelvins down to the millikelvin regime. Except for trivial quantities like the masses of the nuclei and the bond length of the diatomic molecule participating in the collision, one needs as input data only the complex potential energy surface (CPES). In calculations, we used recently obtained ab initio CPES by D. Bhattacharya et al. ( J. Chem. Theory Comput. 2017 , 13 , 1682 - 1690 ) without fitting parameters. The results show good accord with current measurements ( Nat. Phys. 2017 , 13 , 35 - 38 ).

Emitter and absorber assembly for multiple self-dual operation and directional transparency

Science.gov (United States)

Kalozoumis, P. A.; Morfonios, C. V.; Kodaxis, G.; Diakonos, F. K.; Schmelcher, P.

2017-03-01

We demonstrate how to systematically design wave scattering systems with simultaneous coherent perfect absorbing and lasing operation at multiple and prescribed frequencies. The approach is based on the recursive assembly of non-Hermitian emitter and absorber units into self-dual emitter-absorber trimers at different composition levels, exploiting the simple structure of the corresponding transfer matrices. In particular, lifting the restriction to parity-time-symmetric setups enables the realization of emitter and absorber action at distinct frequencies and provides flexibility with respect to the choice of realistic parameters. We further show how the same assembled scatterers can be rearranged to produce unidirectional and bidirectional transparency at the selected frequencies. With the design procedure being generically applicable to wave scattering in single-channel settings, we demonstrate it with concrete examples of photonic multilayer setups.

Recovery of the matrix operators in the similarity and congruency transformations: Applications in polarimetry

International Nuclear Information System (INIS)

November, L.J.

1993-01-01

Formulas are presented for the recovery of the matrix operators in arbitrary-order similarity and congruency transformations. Two independent input and output matrix pairs exactly determine the similarity-transformation matrix operator, while three independent Hermitian-matrix pairs are required for the congruency-transformation operator. The congruency transformation is the natural form for the quantum observables of a multiple-element wave function, e.g., for polarized-light transfer: the recovery of the Jones matrix for a nondepolarizing device is demonstrated, given any three linearly independent partially polarized input Stokes states. The recovery formula gives a good solution even with large added noise in the test matrices. Combined with numerical least-squares methods, the formula can give an optimized solution for measures of observation error. A more general operator, which includes the effect of isotropic depolarization, is defined, and its recovery is demonstrated also. The recovery formulas have a three-dimensional geometric interpretation in the second-order case, e.g., in the Poincare sphere. It is pointed out that the geometric property is a purely mathematical property of quantum observables that arises without referring to spatial characteristics for the underlying wave function. 36 refs., 9 figs

FLIC-overlap fermions and topology

International Nuclear Information System (INIS)

Kamleh, W.; Kusterer, D.J.; Leinweber, D.B.; Williams, A.G.

2003-01-01

APE smearing the links in the irrelevant operators of clover fermions (Fat-Link Irrelevant Clover (FLIC) fermions) provides significant improvement in the condition number of the Hermitian-Dirac operator and gives rise to a factor of two savings in computing the overlap operator. This report investigates the effects of using a highly-improved definition of the lattice field-strength tensor F μν in the fermion action, made possible through the use of APE-smeared fat links in the construction of the irrelevant operators. Spurious double-zero crossings in the spectral flow of the Hermitian-Wilson Dirac operator associated with lattice artifacts at the scale of the lattice spacing are removed with FLIC fermions composed with an O(α 4 )-improved lattice field strength tensor. Hence, FLIC-Overlap fermions provide an additional benefit to the overlap formalism: a correct realization of topology in the fermion sector on the lattice

Perturbed beta-gamma systems and complex geometry

Energy Technology Data Exchange (ETDEWEB)

Zeitlin, Anton M. [Department of Mathematics, Yale University, 442 Dunham Lab, 10 Hillhouse Avenue, New Haven, CT 06511 (United States)], E-mail: anton.zeitlin@yale.edu

2008-05-11

We consider the equations, arising as the conformal invariance conditions of the perturbed curved beta-gamma system. These equations have the physical meaning of Einstein equations with a B-field and a dilaton on a Hermitian manifold, where the B-field 2-form is imaginary and proportional to the canonical form associated with Hermitian metric. We show that they decompose into linear and bilinear equations and lead to the vanishing of the first Chern class of the manifold where the system is defined. We discuss the relation of these equations to the generalized Maurer-Cartan structures related to BRST operator. Finally we describe the relations of the generalized Maurer-Cartan bilinear operation and the Courant/Dorfman brackets.

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

Science.gov (United States)

Chen, Yong; Yan, Zhenya

2016-03-22

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

To the confinement problem

International Nuclear Information System (INIS)

Savvidi, G.K.

1985-01-01

Such a viewpoint is proposed for separation of the physical quantities into observable and unobservable ones, when the latters are connected with the Hermitian operator for which the eigenvalue problem is unsolvable

Pseudospectra in non-Hermitian quantum mechanics

Czech Academy of Sciences Publication Activity Database

Krejčiřík, David; Siegl, Petr; Tater, Miloš; Viola, J.

2015-01-01

Roč. 56, č. 10 (2015), s. 103513 ISSN 0022-2488 R&D Projects: GA ČR(CZ) GA14-06818S; GA MŠk 7AMB12FR020 Institutional support: RVO:61389005 Keywords : quadratic differential operators * magnetic field Subject RIV: BE - Theoretical Physics Impact factor: 1.234, year: 2015

A microscopic derivation of stochastic differential equations

International Nuclear Information System (INIS)

Arimitsu, Toshihico

1996-01-01

With the help of the formulation of Non-Equilibrium Thermo Field Dynamics, a unified canonical operator formalism is constructed for the quantum stochastic differential equations. In the course of its construction, it is found that there are at least two formulations, i.e. one is non-hermitian and the other is hermitian. Having settled which framework should be satisfied by the quantum stochastic differential equations, a microscopic derivation is performed for these stochastic differential equations by extending the projector methods. This investigation may open a new field for quantum systems in order to understand the deeper meaning of dissipation

Topological matter, integrable models and fusion rings

International Nuclear Information System (INIS)

Nemeschansky, D.; Warner, N.P.

1992-01-01

We show how topological G k /G k models can be embedded into the topological matter models that are obtained by perturbing the twisted N = 2 supersymmetric, hermitian symmetric, coset models. In particular, this leads to an embedding of the fusion ring of G as a sub-ring of the perturbed, chiral primary ring. The perturbation of the twisted N = 2 model that leads to the fusion ring is also shown to lead to an integrable N = 2 supersymmetric field theory when the untwisted N = 2 superconformal field theory is perturbed by the same operator and its hermitian conjugate. (orig.)

Interpolation-Based Condensation Model Reduction Part 1: Frequency Window Reduction Method Application to Structural Acoustics

National Research Council Canada - National Science Library

Ingel, R

1999-01-01

.... Projection operators are employed for the model reduction or condensation process. Interpolation is then introduced over a user defined frequency window, which can have real and imaginary boundaries and be quite large. Hermitian...

POVMs: a small but important step beyond standard quantum mechanics

NARCIS (Netherlands)

Muynck, de W.M.; Nieuwenhuizen, T.M.; Spicka, V.; Mehmani, B.; et al., xx

2007-01-01

It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical oservable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a peripheral issue, allegedly to be understood in terms of a

Several complex variables

International Nuclear Information System (INIS)

Field, M.J.

1976-01-01

Topics discussed include the elementary of holomorphic functions of several complex variables; the Weierstrass preparation theorem; meromorphic functions, holomorphic line bundles and divisors; elliptic operators on compact manifolds; hermitian connections; the Hodge decomposition theorem. ( author)

Characterizing and quantifying quantum chaos with quantum ...

Indian Academy of Sciences (India)

We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal ...

Coordinate invariance, the differential force law, and the divergence of the stress-energy tensor

International Nuclear Information System (INIS)

Epstein, S.T.

1975-01-01

Hermitian operators linear in momenta generate coordinate transformations. The associated hypervirial theorems are written in the form of moments of a differential force law, and a connection is made with the stress-energy tensor of the Schrodinger field in configuration space

Nonequilibrium, steady-state electron transport with N-representable density matrices from the anti-Hermitian contracted Schrödinger equation

Science.gov (United States)

Rothman, Adam E.; Mazziotti, David A.

2010-03-01

We study molecular conductivity for a one-electron, bath-molecule-bath model Hamiltonian. The primary quantum-mechanical variable is the one-electron reduced density matrix (1-RDM). By identifying similarities between the steady-state Liouville equation and the anti-Hermitian contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. A 75, 022505 (2007)], we develop a way of enforcing nonequilibrium, steady-state behavior in a time-independent theory. Our results illustrate the relationship between current and voltage in molecular junctions assuming that the total number of electrons under consideration can be fixed across all driving potentials. The impetus for this work is a recent study by Subotnik et al. that also uses the 1-RDM to study molecular conductivity under different assumptions regarding the total number of electrons [J. E. Subotnik et al., J. Chem. Phys. 130, 144105 (2009)]. Unlike calculations in the previous study, our calculations result in 1-RDMs that are fully N-representable. The present work maintains N-representability through a bath-bath mixing that is related to a time-independent relaxation of the baths in the absence of the molecule, as governed by the ACSE. A lack of N-representability can be important since it corresponds to occupying energy states in the molecule or baths with more than one electron or hole (the absence of an electron) in violation of the Pauli principle. For this reason the present work may serve as an important, albeit preliminary, step in designing a 2-RDM/ACSE method for studying steady-state molecular conductivity with an explicit treatment of electron correlation.

Unified theory of fermion pair to boson mappings in full and truncated spaces

International Nuclear Information System (INIS)

Ginocchio, J.N.; Johnson, C.W.

1995-01-01

After a brief review of various mappings of fermion pairs to bosons, we rigorously derive a general approach. Following the methods of Marumori and Otsuka, Arima, and Iachello, our approach begins with mapping states and constructs boson representations that preserve fermion matrix elements. In several cases these representations factor into finite, Hermitian boson images times a projection or norm operator that embodies the Pauli principle. We pay particular attention to truncated boson spaces, and describe general methods for constructing Hermitian and approximately finite boson image Hamiltonians. This method is akin to that of Otsuka, Arima, and Iachello introduced in connection with the interacting boson model, but is more rigorous, general, and systematic

General-Covariant Quantum Mechanics of Dirac Particle in Curved Space-Times

International Nuclear Information System (INIS)

Tagirov, Eh.A.

1994-01-01

A general covariant analog of the standard non-relativistic Quantum Mechanics with relativistic corrections in normal geodesic frames in the general Riemannian space-time is constructed for the Dirac particle. Not only the Pauli equation with hermitian Hamiltonian and the pre-Hilbert structure of space of its solutions but also the matrix elements of hermitian operators of momentum, (curvilinear) spatial coordinates and spin of the particle are deduced as general-covariant asymptotic approximation in c -2 , c being the velocity of light, to their naturally determined general-relativistic pre images. It is shown that the Hamiltonian in the Pauli equation originated by the Dirac equation is unitary equivalent to the operator of energy, originated by the metric energy-momentum tensor of the spinor field. Commutation and other properties of the observables connected with the considered change of geometrical background of Quantum Mechanics are briefly discussed. 7 refs

A state space algorithm for the spectral factorization

NARCIS (Netherlands)

Kraffer, F.; Kraffer, F.; Kwakernaak, H.

1997-01-01

This paper presents an algorithm for the spectral factorization of a para-Hermitian polynomial matrix. The algorithm is based on polynomial matrix to state space and vice versa conversions, and avoids elementary polynomial operations in computations; It relies on well-proven methods of numerical

Hermitian-to-quasi-Hermitian quantum phase transitions

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

Roč. 97, č. 4 ( 2018 ), č. článku 042117. ISSN 2469-9926 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : quantum phase transition * PT-symmetric * Herimiticity Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.925, year: 2016

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators (±) is chosen antilinear. Secondly, both these components of a super-Hamiltonian H are defined along certain topologically non-trivial complex curves r(±)() which spread over ...

PT-symmetric models in curved manifolds

Czech Academy of Sciences Publication Activity Database

Krejčiřík, David; Siegl, Petr

2010-01-01

Roč. 43, č. 48 (2010), 485204/1-485204/30 ISSN 1751-8113 R&D Projects: GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : NON-HERMITIAN HAMILTONIANS * SCHRODINGER -TYPE OPERATORS * PSEUDO-HERMITICITY Subject RIV: BA - General Mathematics Impact factor: 1.641, year: 2010

A Givental-like formula and bilinear identities for tensor models

Energy Technology Data Exchange (ETDEWEB)

Dartois, Stéphane [LIPN, Institut Galilée, CNRS UMR 7030, Université Paris 13,F-93430, Villetaneuse (France); Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris 11,91405 Orsay Cedex (France)

2015-08-26

In this paper we express some simple random tensor models in a Givental-like fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models. Finally we derive Hirota’s equations for these tensor models. Our decomposition is a first step towards integrability of such models.

On solving the Schrödinger equation for a complex deictic potential ...

Indian Academy of Sciences (India)

The imaginary part of the energy eigenvalue exists only if the potential parameters are complex, whereas it reduces to zero for real coupling parameters and the result coincides with those derived from the invariance of Hamiltonian under PT operations. Thus, a non-Hermitian. Hamiltonian possesses real eigenvalue, if it is ...

Semiclassical evolution of dissipative Markovian systems

International Nuclear Information System (INIS)

Ozorio de Almeida, A M; Rios, P de M; Brodier, O

2009-01-01

A semiclassical approximation for an evolving density operator, driven by a 'closed' Hamiltonian operator and 'open' Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra 'open' term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further 'small-chord' approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions

Toward a Strongly Interacting Scalar Higgs Particle

International Nuclear Information System (INIS)

Shalaby, Abouzeid M.; El-Houssieny, M.

2008-01-01

We calculate the vacuum energy of the non-Hermitian and PT symmetric (-gφ 4 ) 2+1 scalar field theory. Rather than the corresponding Hermitian theory and due to the asymptotic freedom property of the theory, the vacuum energy does not blow up for large energy scales which is a good sign to solve the hierarchy problem when using this model to break the U(1)xSU(2) symmetry in the standard model. The theory is strongly interacting and in fact, all the dimensionful parameters in the theory like mass and energy are finite even for very high energy scales. Moreover, relative to the vacuum energy for the Hermitian φ 4 theory, the vacuum energy of the non-Hermitian and PT symmetric (-gφ 4 ) 2+1 theory is tiny, which is a good sign toward the solution of the cosmological constant problem. Remarkably, these features of the non-Hermitian and PT symmetric (-gφ 4 ) 2+1 scalar field theory make it very plausible to be employed as a Higgs mechanism in the standard model instead of the problematic Hermitian Higgs mechanism

Chequered surfaces and complex matrices

International Nuclear Information System (INIS)

Morris, T.R.; Southampton Univ.

1991-01-01

We investigate a large-N matrix model involving general complex matrices. It can be reinterpreted as a model of two hermitian matrices with specific couplings, and as a model of positive definite hermitian matrices. Large-N perturbation theory generates dynamical triangulations in which the triangles can be chequered (i.e. coloured so that neighbours are opposite colours). On a sphere there is a simple relation between such triangulations and those generated by the single hermitian matrix model. For the torus (and a quartic potential) we solve the counting problem for the number of triangulations that cannot be quechered. The critical physics of chequered triangulations is the same as that of the hermitian matrix model. We show this explicitly by solving non-perturbatively pure two-dimensional ''chequered'' gravity. The interpretative framework given here applies to a number of other generalisations of the hermitian matrix model. (orig.)

Four-state solution of the Yang-Baxter equation

International Nuclear Information System (INIS)

Kashaev, R.M.; Mangazeev, V.V.

1990-01-01

A new four-state solution of the Yang-Baxter equation is constructed with the help of the lowest dimensional cyclic L-operator related to a 3-state R-matrix. Some special choice of parameters which this solution depends on, leads to the exactly solvable spin model on the chain with Hermitian Hamiltonian. 8 refs

On calculation of the Laplace transformation of the Heisenberg operators in finite-dimensional spaces

International Nuclear Information System (INIS)

Dzheparov, F.S.

1977-01-01

The integral H tilde (lambda) = ∫sub(0)sup(infinity) dt exp[-(lambda-iF)t]Xexp(-iHt) and the solution of the matrix equation iX tilde (lambda)H+(lambda-iF)Xtilde (lambda)=X, where F and H are hermitian matrices with dimensions M and N, respectively, are represented as a polynomial of the (M-1) degree in F and of the (N-1) degree in H whose coefficients are found from the characteristic polynomials of the F and H matrices

Comparison of different lattice definitions of the topological charge

International Nuclear Information System (INIS)

Cichy, Krzysztof; Ottnad, Konstantin; Bonn Univ.; Bonn Univ.; Urbach, Carsten; Zimmermann, Falk; Bonn Univ.; Wenger, Urs

2014-11-01

We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac operator, spectral projectors, spectral flow of the Hermitian Wilson-Dirac operator and field theoretic with different kinds of smoothing of gauge fields (HYP and APE smearings, gradient flow, cooling). We also show some results on the topological susceptibility.

Random matrix ensembles for PT-symmetric systems

International Nuclear Information System (INIS)

Graefe, Eva-Maria; Mudute-Ndumbe, Steve; Taylor, Matthew

2015-01-01

Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting PT-symmetry. Here we show that there is a one-to-one correspondence between complex PT-symmetric matrices and split-complex and split-quaternionic versions of Hermitian matrices. We introduce two new random matrix ensembles of (a) Gaussian split-complex Hermitian; and (b) Gaussian split-quaternionic Hermitian matrices, of arbitrary sizes. We conjecture that these ensembles represent universality classes for PT-symmetric matrices. For the case of 2 × 2 matrices we derive analytic expressions for the joint probability distributions of the eigenvalues, the one-level densities and the level spacings in the case of real eigenvalues. (fast track communication)

EISPACK, Subroutines for Eigenvalues, Eigenvectors, Matrix Operations

International Nuclear Information System (INIS)

Garbow, Burton S.; Cline, A.K.; Meyering, J.

1993-01-01

1 - Description of problem or function: EISPACK3 is a collection of 75 FORTRAN subroutines, both single- and double-precision, that compute the eigenvalues and eigenvectors of nine classes of matrices. The package can determine the Eigen-system of complex general, complex Hermitian, real general, real symmetric, real symmetric band, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matrices. In addition, there are two routines which use the singular value decomposition to solve certain least squares problem. The individual subroutines are - Identification/Description: BAKVEC: Back transform vectors of matrix formed by FIGI; BALANC: Balance a real general matrix; BALBAK: Back transform vectors of matrix formed by BALANC; BANDR: Reduce sym. band matrix to sym. tridiag. matrix; BANDV: Find some vectors of sym. band matrix; BISECT: Find some values of sym. tridiag. matrix; BQR: Find some values of sym. band matrix; CBABK2: Back transform vectors of matrix formed by CBAL; CBAL: Balance a complex general matrix; CDIV: Perform division of two complex quantities; CG: Driver subroutine for a complex general matrix; CH: Driver subroutine for a complex Hermitian matrix; CINVIT: Find some vectors of complex Hess. matrix; COMBAK: Back transform vectors of matrix formed by COMHES; COMHES: Reduce complex matrix to complex Hess. (elementary); COMLR: Find all values of complex Hess. matrix (LR); COMLR2: Find all values/vectors of cmplx Hess. matrix (LR); CCMQR: Find all values of complex Hessenberg matrix (QR); COMQR2: Find all values/vectors of cmplx Hess. matrix (QR); CORTB: Back transform vectors of matrix formed by CORTH; CORTH: Reduce complex matrix to complex Hess. (unitary); CSROOT: Find square root of complex quantity; ELMBAK: Back transform vectors of matrix formed by ELMHES; ELMHES: Reduce real matrix to real Hess. (elementary); ELTRAN: Accumulate transformations from ELMHES (for HQR2); EPSLON: Estimate unit roundoff

Boundary conditions for open quantum systems driven far from equilibrium

Science.gov (United States)

Frensley, William R.

1990-07-01

This is a study of simple kinetic models of open systems, in the sense of systems that can exchange conserved particles with their environment. The system is assumed to be one dimensional and situated between two particle reservoirs. Such a system is readily driven far from equilibrium if the chemical potentials of the reservoirs differ appreciably. The openness of the system modifies the spatial boundary conditions on the single-particle Liouville-von Neumann equation, leading to a non-Hermitian Liouville operator. If the open-system boundary conditions are time reversible, exponentially growing (unphysical) solutions are introduced into the time dependence of the density matrix. This problem is avoided by applying time-irreversible boundary conditions to the Wigner distribution function. These boundary conditions model the external environment as ideal particle reservoirs with properties analogous to those of a blackbody. This time-irreversible model may be numerically evaluated in a discrete approximation and has been applied to the study of a resonant-tunneling semiconductor diode. The physical and mathematical properties of the irreversible kinetic model, in both its discrete and its continuum formulations, are examined in detail. The model demonstrates the distinction in kinetic theory between commutator superoperators, which may become non-Hermitian to describe irreversible behavior, and anticommutator superoperators, which remain Hermitian and are used to evaluate physical observables.

State vector labelling problem: a review of structural principles

International Nuclear Information System (INIS)

Louck, J.D.

1976-01-01

The technique of labeling state vectors by use of the simultaneous eigenvalues of a complete set of commuting Hermitian operators stems from the early days of quantum theory. In sharp contrast to the classical method, there stands the nonorthogonal bases methods of Moshinsky and Bargmann and the null space methods of Biedenharn and Louck. The structural principles underlying these various methods are presented and discussed. 2 figures

Conformal symmetry in quantum finance

International Nuclear Information System (INIS)

Romero, Juan M; Lavana, Ulises; Miranda, Elio Martínez

2014-01-01

The quantum finance symmetries are studied. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited and the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schrödinger algebra representation is constructed. In addition, it is shown that the operators of this last representation are not hermitian and not conserved.

A fast, preconditioned conjugate gradient Toeplitz solver

Science.gov (United States)

Pan, Victor; Schrieber, Robert

1989-01-01

A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.

Strings from position-dependent noncommutativity

International Nuclear Information System (INIS)

Fring, Andreas; Gouba, Laure; Scholtz, Frederik G

2010-01-01

We introduce a new set of noncommutative spacetime commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative spacetime relations taken here to have position-dependent structure constants. Some of the new variables are non-Hermitian in the most natural choice. We construct their Hermitian counterparts by means of a Dyson map, which also serves to introduce a new metric operator. We propose PT-like symmetries, i.e. antilinear involutory maps, respected by these deformations. We compute minimal lengths and momenta arising in this space from generalized versions of Heisenberg's uncertainty relations and find that any object in this two-dimensional space is string like, i.e. having a fundamental length in one direction beyond which a resolution is impossible. Subsequently, we formulate and partly solve some simple models in these new variables, the free particle, its PT-symmetric deformations and the harmonic oscillator.

From the shell model to the interacting boson model

International Nuclear Information System (INIS)

Ginocchio, J.N.; Johnson, C.W.

1994-01-01

Starting from a general, microscopic fermion-pair-to-boson mapping of a complete fermion space that preserves Hermitian conjugation, we show that the resulting infinite and non-convergent boson Hamilitonian can be factored into a finite (e.g., a 1 + 2-body fermion Hamiltonian is mapped to a 1 + 2-body boson Hamiltonian) image Hamilitonian times the norm operator, and it is the norm operator that is infinite and non-convergent. We then truncate to a collective boson space and we give conditions under which the exact boson images of finite fermion operators are also finite in the truncated basis

Separability in Distant Jauch-Type Hybrid Macrostates of a Quantum and a Classical System

Science.gov (United States)

Herbut, Fedor

1986-12-01

It is assumed that for a quantum system ( Q) plus a classical one ( C) that are in a distant state the actually measurable Hermitian operators are of the form A⊗∑ k⌆K b k Q k ( A is any Hermitian operator for Q, and the decomposition ∑ k Q k =1 of the identity is, after von Neumann, characteristic for C). This leads to Jauch-type macrostates (classes of microstates or statistical operators) for Q+C. On the other hand, it is shown that in the Q+Q case the essence of quantum correlations are the conditional states (or statistical operators) of subsystem I and the reduced state ρ II. Along these lines, the correlation entities (as a complete set of invariants) for the macrostates of the Q+C system are derived, and it is shown that one can make an isomorphic transition from the σ-convex set of the latter to that of the hybrid macrostates ( ρ k , p k ) Here ρ k is the conditional state of Q under the condition that Q k occurs on C, and p k is a classical discrete probability distribution on K, taking the place of ρ II as the macrostate of C. This study indirectly throws new light on the nonseparability in the Q+Q case by contrasting it with a well-understood separability in the C+C and Q+C cases.

Separability in distant Jauch-type hybrid macrostates of a quantum and classical system

International Nuclear Information System (INIS)

Herbut, F.

1986-01-01

It is assumed that for a quantum system (Q) plus a classical one (C) that are in a distant state the actually measurable Hermitian operators are of the form A circle cross Sigma/sub k epsilon K/ b/sub k/Q/sub k/ (A is any Hermitian operator for Q, and the decomposition Sigma/sub k/Q/sub k/ = 1 of the identity is, after von Neumann, characteristic for C). This leads to Jauch-type macrostates (classes of microstates or statistical operators) for Q + C. On the other hand, it is shown that in the Q + Q case the essence of quantum correlations are the conditional states (or statistical operators) of subsystem I and the reduced state rho/sub II/. Along these lines, the correlation entities (as a complete set of invariants) for the macrostates of the Q + C system are derived, and it is shown that one can make an isomorphic transition from the σ-convex set of the latter to that of the hybrid macrostates (rho/sub k/, p/sub k/). Here rho/sub k/ is the conditional state of Q under the condition that Q/sub k/ occurs on C, and p/sub k/ is a classical discrete probability distribution on K, taking the place of rho/sub II/ as the macrostate of C. This study indirectly throws new light on the nonseparability in the Q + Q case by contrasting it with a well-understood separability in the C + C and Q + C cases

Comment on 'Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential' [J. Math. Phys. 48, 073515 (2007)

International Nuclear Information System (INIS)

Castro, L. B.; Castro, A. S. de

2010-01-01

It is shown that the paper 'Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential' by Merad and Bensaid [J. Math. Phys. 48, 073515 (2007)] is not correct in using inadvertently a non-Hermitian Hamiltonian in a formalism that does require Hermitian Hamiltonians.

Generalized Lie superalgebras and superqravity with a positive cosmological constant

International Nuclear Information System (INIS)

Vasil'ev, M.A.

1984-01-01

A modified law of Hermitian conjugation has been suggested, which permits to plot the Hermitian effect for supergravitation with a positive cosmological constant Λ. The modified conjugation is shown to result in generalized (Z 2 xZ 2 - graded) Lie superalgebras, corresconding to supergravitation With Λ > 0

Generalized Lie superalgebras and a supergravity with a positive cosmological constant

International Nuclear Information System (INIS)

Vasil'ev, M.A.

1984-01-01

A new law for forming the Hermitian conjugation makes it possible to construct a Hermitian action for a supergravity with a positive cosmological constant Λ. This modified conjugation leads to generalized (Z 2 x Z 2 -gauge) Lie superalgebras that correspond to a supergravity with Λ>0

Quantized Dirac field interacting with a classical Maxwell field

International Nuclear Information System (INIS)

Kolsrud, M.

1987-10-01

The S operator for the quantized and the s matrix for the unquantized Dirac field, both fields interacting with an unquantized Maxwell field, are shown to be related in the following way: S=exp(-ic†kc) and s=exp(-ik). Here c is the column matrix of the particle operators, and k is a Hermitian matrix. With splitting of c into an electron and a positron part, a corresponding factorization of S is performed. Exact expressions for the probability amplitude for various electron and/or positron processes are then obtained

The Dynamical Invariant of Open Quantum System

OpenAIRE

Wu, S. L.; Zhang, X. Y.; Yi, X. X.

2015-01-01

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...

Polynômes orthogonaux avec argument matriciel et les semigroupes associés

OpenAIRE

Balderrama , Cristina

2009-01-01

In this work we construct and study families of generalized orthogonal polynomials with hermitian matrix argument associated to a family of orthogonal polynomials on R. Different normalizations for these polynomials are considered and we obtain some classical formulas for orthogonal polynomials from the corresponding formulas for the one–dimensional polynomials. We also construct semigroups of operators associated to the generalized orthogonal polynomials and we give an expression of the infi...

Weyl tensors for asymmetric complex curvatures

International Nuclear Information System (INIS)

Oliveira, C.G.

Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

September 2009, pages 215-626a. Non-Hermitian Hamiltonians in Quantum Physics - Part II ... Entanglement in non-Hermitian quantum theory · Arun K Pati · More Details Abstract ... Minimal classical communication and measurement complexity for quantum information splitting of a two-qubit state · Prasanta K Panigrahi ...

Alternative structures and bi-Hamiltonian systems on a Hilbert space

International Nuclear Information System (INIS)

Marmo, G; Scolarici, G; Simoni, A; Ventriglia, F

2005-01-01

We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide a few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and the non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems

Crossing rule for a PT-symmetric two-level time-periodic system

International Nuclear Information System (INIS)

Moiseyev, Nimrod

2011-01-01

For a two-level system in a time-periodic field we show that in the non-Hermitian PT case the level crossing is of two quasistationary states that have the same dynamical symmetry property. At the field's parameters where the two levels which have the same dynamical symmetry cross, the corresponding quasienergy states coalesce and a self-orthogonal state is obtained. This situation is very different from the Hermitian case where a crossing of two quasienergy levels happens only when the corresponding two quasistationary states have different dynamical symmetry properties and, unlike the situation in the non-Hermitian case, the spectrum remains complete also when the two levels cross.

Hermiticity and gauge invariance

International Nuclear Information System (INIS)

Treder, H.J.

1987-01-01

In the Theory of Hermitian Relativity (HRT) the postulates of hermiticity and gauge invariance are formulated in different ways, due to a different understanding of the idea of hermiticity. However all hermitian systems of equations have to satisfy Einstein's weak system of equations being equivalent to Einstein-Schroedinger equations. (author)

The quantum hydrodynamics of the Sutherland model

International Nuclear Information System (INIS)

Stone, Michael; Gutman, Dmitry

2008-01-01

We show that the form of the chiral condition found by Abanov et al in the quantum hydrodynamics of the Sutherland model arises because there are two distinct inner products with respect to which the chiral Hamiltonian is Hermitian, but only one with respect to which the full, non-chiral, Hamiltonian is Hermitian

Chiral anomaly, bosonization, and fractional charge

International Nuclear Information System (INIS)

Mignaco, J.A.; Monteiro, M.A.R.

1985-01-01

We present a method to evaluate the Jacobian of chiral rotations, regulating determinants through the proper-time method and using Seeley's asymptotic expansion. With this method we compute easily the chiral anomaly for ν = 4,6 dimensions, discuss bosonization of some massless two-dimensional models, and handle the problem of charge fractionization. In addition, we comment on the general validity of Fujikawa's approach to regulate the Jacobian of chiral rotations with non-Hermitian operators

Methods of applied mathematics

CERN Document Server

Hildebrand, Francis B

1992-01-01

This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.

Harnessing molecular excited states with Lanczos chains

Science.gov (United States)

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O.; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-01

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Harnessing molecular excited states with Lanczos chains

Energy Technology Data Exchange (ETDEWEB)

Baroni, Stefano; Baris Malcioglu, O; Xian Jiawei [SISSA-Scuola Internazionale Superiore di Studi Avanzati, I-34151 Trieste (Italy); Gebauer, Ralph; Umari, Paolo [CNR DEMOCRITOS Theory-Elettra Group, c/o Sincrotrone Trieste, Area Science Park, I-34012 Basovizza, Trieste (Italy); Saad, Yousef [Department of Computer Science and Engineering, University of Minnesota, and Minnesota Supercomputing Institute, Minneapolis, MN 55455 (United States)

2010-02-24

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Harnessing molecular excited states with Lanczos chains.

Science.gov (United States)

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-24

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Harnessing molecular excited states with Lanczos chains

International Nuclear Information System (INIS)

Baroni, Stefano; Baris Malcioglu, O; Xian Jiawei; Gebauer, Ralph; Umari, Paolo; Saad, Yousef

2010-01-01

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Direct estimation of elements of quantum states algebra and entanglement detection via linear contractions

International Nuclear Information System (INIS)

Horodecki, Pawel

2003-01-01

Possibility of some nonlinear-like operations in quantum mechanics are studied. Some general formula for real linear maps are derived. With the results we show how to perform physically separability tests based on any linear contraction (on product states) that either is real or Hermitian. We also show how to estimate either product or linear combinations of quantum states without knowledge about the states themselves. This can be viewed as a sort of quantum computing on quantum states algebra

Quantum principles and particles

CERN Document Server

Wilcox, Walter

2012-01-01

QUANTUM PRINCIPLESPerspective and PrinciplesPrelude to Quantum MechanicsStern-Gerlach Experiment Idealized Stern-Gerlach ResultsClassical Model AttemptsWave Functions for Two Physical-Outcome CaseProcess Diagrams, Operators, and Completeness Further Properties of Operators/ModulationOperator ReformulationOperator RotationBra-Ket Notation/Basis StatesTransition AmplitudesThree-Magnet Setup Example-CoherenceHermitian ConjugationUnitary OperatorsA Very Special OperatorMatrix RepresentationsMatrix Wave Function RecoveryExpectation ValuesWrap Up ProblemsFree Particles in One DimensionPhotoelectric EffectCompton EffectUncertainty Relation for PhotonsStability of Ground StatesBohr ModelFourier Transform and Uncertainty RelationsSchrödinger EquationSchrödinger Equation ExampleDirac Delta FunctionsWave Functions and ProbabilityProbability CurrentTime Separable SolutionsCompleteness for Particle StatesParticle Operator PropertiesOperator RulesTime Evolution and Expectation ValuesWrap-UpProblemsSome One-Dimensional So...

On the extreme value statistics of normal random matrices and 2D Coulomb gases: Universality and finite N corrections

Science.gov (United States)

Ebrahimi, R.; Zohren, S.

2018-03-01

In this paper we extend the orthogonal polynomials approach for extreme value calculations of Hermitian random matrices, developed by Nadal and Majumdar (J. Stat. Mech. P04001 arXiv:1102.0738), to normal random matrices and 2D Coulomb gases in general. Firstly, we show that this approach provides an alternative derivation of results in the literature. More precisely, we show convergence of the rescaled eigenvalue with largest modulus of a normal Gaussian ensemble to a Gumbel distribution, as well as universality for an arbitrary radially symmetric potential. Secondly, it is shown that this approach can be generalised to obtain convergence of the eigenvalue with smallest modulus and its universality for ring distributions. Most interestingly, the here presented techniques are used to compute all slowly varying finite N correction of the above distributions, which is important for practical applications, given the slow convergence. Another interesting aspect of this work is the fact that we can use standard techniques from Hermitian random matrices to obtain the extreme value statistics of non-Hermitian random matrices resembling the large N expansion used in context of the double scaling limit of Hermitian matrix models in string theory.

Boson representations of the real symplectic group and their applications to the nuclear collective model

International Nuclear Information System (INIS)

Deenen, J.; Quesne, C.

1985-01-01

Both non-Hermitian Dyson and Hermitian Holstein--Primakoff representations of the Sp(2d,R) algebra are obtained when the latter is restricted to a positive discrete series irreducible representation 1 +n/2>. For such purposes, some results for boson representations, recently deduced from a study of the Sp(2d,R) partially coherent states, are combined with some standard techniques of boson expansion theories. The introduction of Usui operators enables the establishment of useful relations between the various boson representations. Two Dyson representations of the Sp(2d,R) algebra are obtained in compact form in terms of ν = d(d+1)/2 pairs of boson creation and annihilation operators, and of an extra U(d) spin, characterized by the irreducible representation [lambda 1 xxxlambda/sub d/]. In contrast to what happens when lambda 1 = xxx = lambda/sub d/ = lambda, it is shown that the Holstein--Primakoff representation of the Sp(2d,R) algebra cannot be written in such a compact form for a generic irreducible representation. Explicit expansions are, however, obtained by extending the Marumori, Yamamura, and Tokunaga method of boson expansion theories. The Holstein--Primakoff representation is then used to prove that, when restricted to the Sp(2d,R) irreducible representation 1 +n/2>, the dn-dimensional harmonic oscillator Hamiltonian has a U(ν) x SU(d) symmetry group

A geometric form of the canonical commutation

International Nuclear Information System (INIS)

Guz, W.

1987-01-01

Some aspects of a geometric approach to quantum theory, in which the quantum-mechanical position and momentum operators are represented by covariant derivatives, are here developed. Here, the previously estabilished formalism of Caianiello and his co-workers is extended to the case of an integrable almost complex Hermitian manifold. The general theory is then applied to the two-dimensional case, where the structure of the 'quantum geometry' induced in the manifold by the quantum-mechanical CCR can be explicitly determined

Seniority mappings for probing phenomenological nuclear boson models

International Nuclear Information System (INIS)

De Kock, E.A.

1988-12-01

The interacting boson model (IBM) and interacting boson-fermion model (IBFM) are discussed. The main ideas of boson mapping of fermion systems are introduced using Holstein-Primakoff and Dyson-Maleev mappings of angular momentum operators. Generalized Dyson-Maleev (GDM) and Holstein-Primakoff (GHP) mappings are included. In fermoin problems, the degrees of freedom of collective motion are described by a collective subalgebra of the complete bifermion subalgebra. GDM mapping of Sp(6) generators, the transformation to collect bosons and truncation to these bosons led to collective sd-boson realization of Sp(6) algebra. This resulted in an IBM-like description of the collective subspace. Non-hermitian and existing hermitian forms are indicated in the assumed structure of an IBM Hamiltonian Boson mapping based on seniority considerations and involving single-j shell approximations of the shell model are examined. One method utilized truncation of a shell model space to a space spanned by monopole (S) and quadrupole (D) pairs. The association between states in truncated fermion and sd-boson spaces constructs boson images of fermion operators by equating boson and fermion matrix elements. To obtain boson images with IBM-like structures, a zero-order approximation was adopted. This approximation retains only N-body terms in the images of N-body fermion operators. A similarity transformation re-expressing GDM images of single-j shell fermion operators in seniority bosons was applied to the GDM image of a general shell model Hamiltonian. Numerical results for the surface-delta interaction show that truncation to s- and d-bosons in the seniority image of a two-body operator is not allowed if N≥2. This transformation was extended to odd fermion systems and applied to the image of the quadrupole pairing interaction. 79 refs., 3 figs., 4 tabs

PT symmetry and a dynamical realization of the SU(1, 1) algebra

Science.gov (United States)

Banerjee, Rabin; Mukherjee, Pradip

2016-01-01

We show that the elementary modes of the planar harmonic oscillator can be quantized in the framework of quantum mechanics based on pseudo-hermitian Hamiltonians. These quantized modes are demonstrated to act as dynamical structures behind a new Jordan-Schwinger realization of the SU(1, 1) algebra. This analysis complements the conventional Jordan-Schwinger construction of the SU(2) algebra based on hermitian Hamiltonians of a doublet of oscillators.

Phase integral approximation for coupled ordinary differential equations of the Schroedinger type

International Nuclear Information System (INIS)

Skorupski, Andrzej A.

2008-01-01

Four generalizations of the phase integral approximation (PIA) to sets of ordinary differential equations of Schroedinger type [u j '' (x)+Σ k=1 N R jk (x)u k (x)=0, j=1,2,...,N] are described. The recurrence relations for higher order corrections are given in a form valid to arbitrary order and for the matrix R(x)[≡(R jk (x))] either Hermitian or non-Hermitian. For Hermitian and negative definite R(x) matrices, a Wronskian conserving PIA theory is formulated, which generalizes Fulling's current conserving theory pertinent to positive definite R(x) matrices. The idea of a modification of the PIA, which is well known for one equation [u '' (x)+R(x)u(x)=0], is generalized to sets. A simplification of Wronskian or current conserving theories is proposed which in each order eliminates one integration from the formulas for higher order corrections. If the PIA is generated by a nondegenerate eigenvalue of the R(x) matrix, the eliminated integration is the only one present. In that case, the simplified theory becomes fully algorithmic and is generalized to non-Hermitian R(x) matrices. The general theory is illustrated by a few examples automatically generated by using the author's program in MATHEMATICA published in e-print arXiv:0710.5406 [math-ph

Parity-Time Symmetric Photonics

KAUST Repository

Zhao, Han

2018-01-17

The establishment of non-Hermitian quantum mechanics (such as parity-time (PT) symmetry) stimulates a paradigmatic shift for studying symmetries of complex potentials. Owing to the convenient manipulation of optical gain and loss in analogy to the complex quantum potentials, photonics provides an ideal platform for visualization of many conceptually striking predictions from the non-Hermitian quantum theory. A rapidly developing field has emerged, namely, PT symmetric photonics, demonstrating intriguing optical phenomena including eigenstate coalescence and spontaneous PT symmetry breaking. The advance of quantum physics, as the feedback, provides photonics with brand-new paradigms to explore the entire complex permittivity plane for novel optical functionalities. Here, we review recent exciting breakthroughs in PT symmetric photonics while systematically presenting their underlying principles guided by non-Hermitian symmetries. The potential device applications for optical communication and computing, bio-chemical sensing, and healthcare are also discussed.

The chiral Gaussian two-matrix ensemble of real asymmetric matrices

International Nuclear Information System (INIS)

Akemann, G; Phillips, M J; Sommers, H-J

2010-01-01

We solve a family of Gaussian two-matrix models with rectangular N x (N + ν) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter μ. Our model can be thought of as the chiral extension of the real Ginibre ensemble, relevant for Dirac operators in the same symmetry class. It has the property that its eigenvalues are either real, purely imaginary or come in complex conjugate eigenvalue pairs. The eigenvalue joint probability distribution for our model is explicitly computed, leading to a non-Gaussian distribution including K-Bessel functions. All n-point density correlation functions are expressed for finite N in terms of a Pfaffian form. This contains a kernel involving Laguerre polynomials in the complex plane as a building block which was previously computed by the authors. This kernel can be expressed in terms of the kernel for complex non-Hermitian matrices, generalizing the known relation among ensembles of Hermitian random matrices. Compact expressions are given for the density at finite N as an example, as well as its microscopic large-N limits at the origin for fixed ν at strong and weak non-Hermiticity.

Loop equations and topological recursion for the arbitrary-$\\beta$ two-matrix model

CERN Document Server

Bergère, Michel; Marchal, Olivier; Prats-Ferrer, Aleix

2012-01-01

We write the loop equations for the $\\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.

On Gupta-Bleuler quantization of systems with second-class constraints

International Nuclear Information System (INIS)

Kalau, Wolfgang.

1992-01-01

In this paper Hamiltonian systems with mixed first and second-class constraints are discussed. The authors prove that in a neighborhood of the constraint surface the complexified constraints can always be split into a holomorphic and an anti-holomorphic set, such that the holomorphic set can be implemented consistently on the ket-states of the corresponding quantum theory. The quantization is performed with BRSY-methods using a non-hermitian BRST-operator. As an example this method is used to quantize the 4-dimensional superparticle. (author). 25 refs

Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops

OpenAIRE

Tanaka, Atushi; Kim, Sang Wook; Cheon, Taksu

2014-01-01

The correspondence between exotic quantum holonomy that occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expressions of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, are obtained. It is also shown that the quantum kicked tops with the complexified adiabatic parameter have a higher order EP, which is broken i...

Pseudo-supersymmetry and the domain-wall/cosmology correspondence

International Nuclear Information System (INIS)

Skenderis, Kostas; Townsend, Paul K

2007-01-01

The correspondence between domain-wall and cosmological solutions of gravity coupled to scalar fields is explained. Any domain-wall solutions that admit a Killing spinor are shown to correspond to a cosmology that admits a pseudo-Killing spinor; whereas the Killing spinor obeys a Dirac-type equation with Hermitian 'mass'-matrix, the corresponding pseudo-Killing spinor obeys a Dirac-type equation with a anti-Hermitian 'mass'-matrix. We comment on some implications of (pseudo)supersymmetry

Possible identification of quarks with leptons in Lie-isotopic SU(3) theory

International Nuclear Information System (INIS)

Animalu, A.O.E.

1984-01-01

A possible identification of the six quarks (d,s,c;u,t,b) with the corresponding leptons (e - ,μ - ,tau - ;v/sub e/,v/sub μ/,v/sub tau/) is attempted via the corrspondence principle, dapprox.(uv-bar/sub e/)e - , sapprox.(tv-bar/sub μ/)μ - , c(bv-bar/sub t/)t - ,uapprox.(uv/sub e/) v/sub e/,..., and its inverse, which are formally represented by a non-unitary integral transformation (with kernel P) and its inverse or dual (with kernel Q), connecting the quark and lepton fields. It is shown that PQ and QP may be interpreted as hadronic and leptonic density matrix operators which obey the quantum mechanical analog of the Liouville equation of conservation from which a Lie-isotopic generalization of Heisenberg's equation of motion is abstracted. P and Q form iso-canonically conjugate dynamical veriables, i.e., Q is the isotpic element for the isoassociative product H*Q = HPQ in the equation of motion for Q. It is also shown that PQ and QP, being idempotent operators, have eigenvalues 0 or 1, which imply that both P and Q can be singular, leading to a further differentiation of ''hadronic mechanics'' into the conventional ''isotopic'' theory in which the isotopic element (g) in the isoassociative product A*B = AgB is non-singular and Hermitian, and a new ''homotopic'' theory in which g is singular and non-Hermitian A Lie-admissible generalization is also obained, and SU(2)-spin realizations are indicated

From a particle in a box to the uncertainty relation in a quantum dot and to reflecting walls for relativistic fermions

International Nuclear Information System (INIS)

Al-Hashimi, M.H.; Wiese, U.-J.

2012-01-01

We consider a 1-parameter family of self-adjoint extensions of the Hamiltonian for a particle confined to a finite interval with perfectly reflecting boundary conditions. In some cases, one obtains negative energy states which seem to violate the Heisenberg uncertainty relation. We use this as a motivation to derive a generalized uncertainty relation valid for an arbitrarily shaped quantum dot with general perfectly reflecting walls in d dimensions. In addition, a general uncertainty relation for non-Hermitian operators is derived and applied to the non-Hermitian momentum operator in a quantum dot. We also consider minimal uncertainty wave packets in this situation, and we prove that the spectrum depends monotonically on the self-adjoint extension parameter. In addition, we construct the most general boundary conditions for semiconductor heterostructures such as quantum dots, quantum wires, and quantum wells, which are characterized by a 4-parameter family of self-adjoint extensions. Finally, we consider perfectly reflecting boundary conditions for relativistic fermions confined to a finite volume or localized on a domain wall, which are characterized by a 1-parameter family of self-adjoint extensions in the (1+1)-d and (2+1)-d cases, and by a 4-parameter family in the (3+1)-d and (4+1)-d cases. - Highlights: ► Finite volume Heisenberg uncertainty relation. ► General self-adjoint extensions for relativistic fermions. ► New prospective for the problem of particle in a box.

Boson mappings for elementary excitations in fermion systems

International Nuclear Information System (INIS)

Geyer, H.B.

1981-07-01

The boson mapping formalism is presented with a dual purpose in mind. It is first demonstrated to constitute a microscopic formalism leading to the introduction of collective variables into the many-fermion problem in an exact and consistent manner. Secondly it is shown to present ideal exploring ground with a view to the reconciliation of phenomenological collective nuclear models and microscopic considerations. Of the various existing possibilities for the construction of a boson mapping, we single out the finite, non-unitary Dyson-Maleev mapping, emphasising the convenience of its finiteness, especially in investigations concerning formal aspects of the boson mapping formalism. A contribution to the theory of Dyson-Maleev mappinigs for fermion operators is made by introducing the construction of a consistent mapping for single fermion operators which is free of limitations previously imposed on such a mapping. In various fermion models studies it is shown how the Dyson-Maleev mapping can be utilized to obtain equivalent boson models which, however, can be restricted to yield information about the collective subspace only. As far as phenomenological models are concerned, some new light from a microscopic viewpiont is shed on the assumption underlying the interacting boson model as well as on the calculational procedures usually adopted in this model. The most important observation concerns the assumed structure of the IBM hamiltonian where a non-hermitian form, rather than the existing hermitian form, is indicated

Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Facchi, Paolo [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Kulkarni, Ravi [Vivekananda Yoga Research Foundation, Bangalore 560 080 (India); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, Giuseppe [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Sudarshan, E.C.G. [Department of Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, Franco [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy)

2010-11-01

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

International Nuclear Information System (INIS)

Facchi, Paolo; Kulkarni, Ravi; Man'ko, V.I.; Marmo, Giuseppe; Sudarshan, E.C.G.; Ventriglia, Franco

2010-01-01

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

Observation of the exceptional point in cavity magnon-polaritons.

Science.gov (United States)

Zhang, Dengke; Luo, Xiao-Qing; Wang, Yi-Pu; Li, Tie-Fu; You, J Q

2017-11-08

Magnon-polaritons are hybrid light-matter quasiparticles originating from the strong coupling between magnons and photons. They have emerged as a potential candidate for implementing quantum transducers and memories. Owing to the dampings of both photons and magnons, the polaritons have limited lifetimes. However, stationary magnon-polariton states can be reached by a dynamical balance between pumping and losses, so the intrinsically nonequilibrium system may be described by a non-Hermitian Hamiltonian. Here we design a tunable cavity quantum electrodynamics system with a small ferromagnetic sphere in a microwave cavity and engineer the dissipations of photons and magnons to create cavity magnon-polaritons which have non-Hermitian spectral degeneracies. By tuning the magnon-photon coupling strength, we observe the polaritonic coherent perfect absorption and demonstrate the phase transition at the exceptional point. Our experiment offers a novel macroscopic quantum platform to explore the non-Hermitian physics of the cavity magnon-polaritons.

Semiclassical Loop Quantum Gravity and Black Hole Thermodynamics

Directory of Open Access Journals (Sweden)

Arundhati Dasgupta

2013-02-01

Full Text Available In this article we explore the origin of black hole thermodynamics using semiclassical states in loop quantum gravity. We re-examine the case of entropy using a density matrix for a coherent state and describe correlations across the horizon due to SU(2 intertwiners. We further show that Hawking radiation is a consequence of a non-Hermitian term in the evolution operator, which is necessary for entropy production or depletion at the horizon. This non-unitary evolution is also rooted in formulations of irreversible physics.

Reply to 'Comment on 'Almost-periodic time observables for bound quantum systems''

International Nuclear Information System (INIS)

Hall, Michael J W

2009-01-01

In a recent paper (Hall 2008 J. Phys. A: Math. Gen. 41 255301), I made several critical remarks on a 'Hermitian time operator' proposed by Galapon (2002 Proc. R. Soc. A 458 2671). Galapon has correctly pointed out that remarks pertaining to 'denseness' of the commutator domain are wrong (Galapon 2008 J. Phys. A: Math. Theor. 42 018001). However, the other remarks still apply, and it is further noted that a given quantum system can be a member of this domain only at a set of times of total measure zero. (reply)

Noncommutative spaces and matrix embeddings on flat ℝ{sup 2n+1}

Energy Technology Data Exchange (ETDEWEB)

Karczmarek, Joanna L.; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

2015-11-23

We conjecture an embedding operator which assigns, to any 2n+1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n+1)-dimensional Euclidean space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding to N D0-branes. Points on the emergent hypersurface correspond to zero eigenstates of the embedding operator, which have an interpretation as coherent states underlying the emergent noncommutative geometry. Using this correspondence, all physical properties of the emergent D(2n)-brane can be computed. We apply our conjecture to noncommutative flat and spherical spaces. As a by-product, we obtain a construction of a rotationally symmetric flat noncommutative space in 4 dimensions.

Electromagnetic field and the theory of conformal and biholomorphic invariants

International Nuclear Information System (INIS)

Lawrynowicz, J.

1976-01-01

This paper contains sections on: 1. Conformal invariance and variational principles in electrodynamics. 2. The principles of Dirichlet and Thomson as a physical motivation for the methods of conformal capacities and extremal lengths. 3. Extension to pseudoriemannian manifolds. 4. Extension to hermitian manifolds. 5. An extension of Schwarz's lemma for hermitian manifolds and its physical significance. 6. Variation of ''complex'' capacities within the admissible class of plurisubharmonic functions. The author concentrates on motivations and interpretations connected with the electromagnetic field. (author)

Dynamical correlations for circular ensembles of random matrices

International Nuclear Information System (INIS)

Nagao, Taro; Forrester, Peter

2003-01-01

Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of antisymmetric Hermitian matrix initial conditions, Brownian dynamics toward the unitary symmetry is analyzed. The dynamical correlation functions of arbitrary number of Brownian particles at arbitrary number of times are shown to be written in the forms of quaternion determinants, similarly as in the case of Hermitian random matrix models

Reciprocity relation for multichannel coupling kernels

International Nuclear Information System (INIS)

Cotanch, S.R.; Satchler, G.R.

1981-01-01

Assuming time-reversal invariance of the many-body Hamiltonian, it is proven that the kernels in a general coupled-channels formulation are symmetric, to within a specified spin-dependent phase, under the interchange of channel labels and coordinates. The theorem is valid for both Hermitian and suitably chosen non-Hermitian Hamiltonians which contain complex effective interactions. While of direct practical consequence for nuclear rearrangement reactions, the reciprocity relation is also appropriate for other areas of physics which involve coupled-channels analysis

Integrals of motion in the many-body localized phase

Directory of Open Access Journals (Sweden)

V. Ros

2015-02-01

Full Text Available We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum {0,1}, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization–delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.

Chiral Modes at Exceptional Points in Exciton-Polariton Quantum Fluids

Science.gov (United States)

Gao, T.; Li, G.; Estrecho, E.; Liew, T. C. H.; Comber-Todd, D.; Nalitov, A.; Steger, M.; West, K.; Pfeiffer, L.; Snoke, D. W.; Kavokin, A. V.; Truscott, A. G.; Ostrovskaya, E. A.

2018-02-01

We demonstrate the generation of chiral modes-vortex flows with fixed handedness in exciton-polariton quantum fluids. The chiral modes arise in the vicinity of exceptional points (non-Hermitian spectral degeneracies) in an optically induced resonator for exciton polaritons. In particular, a vortex is generated by driving two dipole modes of the non-Hermitian ring resonator into degeneracy. Transition through the exceptional point in the space of the system's parameters is enabled by precise manipulation of real and imaginary parts of the closed-wall potential forming the resonator. As the system is driven to the vicinity of the exceptional point, we observe the formation of a vortex state with a fixed orbital angular momentum (topological charge). This method can be extended to generate higher-order orbital angular momentum states through coalescence of multiple non-Hermitian spectral degeneracies. Our Letter demonstrates the possibility of exploiting nontrivial and counterintuitive properties of waves near exceptional points in macroscopic quantum systems.

Chiral Modes at Exceptional Points in Exciton-Polariton Quantum Fluids.

Science.gov (United States)

Gao, T; Li, G; Estrecho, E; Liew, T C H; Comber-Todd, D; Nalitov, A; Steger, M; West, K; Pfeiffer, L; Snoke, D W; Kavokin, A V; Truscott, A G; Ostrovskaya, E A

2018-02-09

We demonstrate the generation of chiral modes-vortex flows with fixed handedness in exciton-polariton quantum fluids. The chiral modes arise in the vicinity of exceptional points (non-Hermitian spectral degeneracies) in an optically induced resonator for exciton polaritons. In particular, a vortex is generated by driving two dipole modes of the non-Hermitian ring resonator into degeneracy. Transition through the exceptional point in the space of the system's parameters is enabled by precise manipulation of real and imaginary parts of the closed-wall potential forming the resonator. As the system is driven to the vicinity of the exceptional point, we observe the formation of a vortex state with a fixed orbital angular momentum (topological charge). This method can be extended to generate higher-order orbital angular momentum states through coalescence of multiple non-Hermitian spectral degeneracies. Our Letter demonstrates the possibility of exploiting nontrivial and counterintuitive properties of waves near exceptional points in macroscopic quantum systems.

How the geometric calculus resolves the ordering ambiguity of quantum theory in curved space

International Nuclear Information System (INIS)

Pavsic, Matej

2003-01-01

The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford algebra. The momentum operator is defined to be the vector derivative (the gradient) multiplied by -i; it can be expanded in terms of basis vectors γ μ as p = -iγ μ ∂ μ . The product of two such operators is unambiguous, and such is the Hamiltonian which is just the d'Alembert operator in curved space; the curvature scalar term is not present in the Hamiltonian if we confine our consideration to scalar wavefunctions only. It is also shown that p is Hermitian and a self-adjoint operator: the presence of the basis vectors γ μ compensates the presence of √|g| in the matrix elements and in the scalar product. The expectation value of such an operator follows the classical geodetic line

Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles

International Nuclear Information System (INIS)

Forrester, P.J.; Witte, N.S.

2000-01-01

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s) e-b(s) for a simply related to a Painleve transcendent and b its anti-derivative. A formula consisting of the sum of two such terms is given for the symplectic case (Hermitian matrices with real quaternion elements)

Generalized Eigenvalues for pairs on heritian matrices

Science.gov (United States)

Rublein, George

1988-01-01

A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.

Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops.

Science.gov (United States)

Tanaka, Atushi; Kim, Sang Wook; Cheon, Taksu

2014-04-01

The correspondence between exotic quantum holonomy, which occurs in families of Hermitian cycles, and exceptional points (EPs) for non-Hermitian quantum theory is examined in quantum kicked tops. Under a suitable condition, an explicit expression of the adiabatic parameter dependencies of quasienergies and stationary states, which exhibit anholonomies, is obtained. It is also shown that the quantum kicked tops with the complexified adiabatic parameter have a higher-order EP, which is broken into lower-order EPs with the application of small perturbations. The stability of exotic holonomy against such bifurcation is demonstrated.

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.

Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction

International Nuclear Information System (INIS)

Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.

2004-01-01

It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition to calculate C is cumbersome in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method is used to calculate the C operator in quantum field theory. The C operator is a time-independent observable in PT-symmetric quantum field theory

Code Samples Used for Complexity and Control

Science.gov (United States)

Ivancevic, Vladimir G.; Reid, Darryn J.

2015-11-01

The following sections are included: * MathematicaⓇ Code * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ Code * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# Code * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * Lagrangian Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran Code * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-Code: Levenberg-Marquardt Optimizer * Free Basic Code: 2D Crowd Dynamics with 3000 Agents

Lattice QCD study of the $H$ dibaryon using hexaquark and two-baryon interpolators arXiv

CERN Document Server

Francis, A.; Junnarkar, P.M.; Miao, Ch.; Rae, T.D.; Wittig, H.

We present a lattice QCD spectroscopy study in the isospin singlet, strangeness $-2$ sectors relevant for the conjectured $H$ dibaryon. We employ both hexaquark and two-baryon interpolating operators to isolate the ground state in the rest frame and in moving frames. Calculations are performed using two flavors of O($a$)-improved Wilson fermions and a quenched strange quark. Our initial point-source method for constructing correlators does not allow for two-baryon operators at the source; nevertheless, results from using these operators at the sink indicate that they provide an improved overlap onto the ground state in comparison with the hexaquark operators. We also present results, in the rest frame, using a second method based on distillation to compute a hermitian matrix of correlators with two-baryon operators at both the source and the sink. This method yields a much more precise and reliable determination of the ground-state energy. In the flavor-SU(3) symmetric case, we apply L\\"uscher's finite-volume...

Non-unitary boson mapping and its application to nuclear collective motions

International Nuclear Information System (INIS)

Takada, Kenjiro

2001-01-01

First, the general theory of boson mapping for even-number many-fermion systems is surveyed. In order to overcome the confusion concerning the so-called unphysical or spurious states in the boson mapping, the correct concept of the unphysical states is precisely given in a clear-cut way. Next, a method to apply the boson mapping to a truncated many-fermion Hilbert space consisting of collective phonons is proposed, by putting special emphasis on the Dyson-type non-unitary boson mapping. On the basis of this method, it becomes possible for the first time to apply the Dyson-type boson mapping to analyses of collective motions in realistic nuclei. This method is also extended to be applicable to odd-number-fermion systems. As known well, the Dyson-type boson mapping is a non-unitary transformation and it gives a non-Hermitian boson Hamiltonian. It is not easy (but not impossible) to solve the eigenstates of the non-Hermitian Hamiltonian. A Hermitian treatment of this non-Hermitian eigenvalue problem is discussed and it is shown that this treatment is a very good approximation. using this Hermitian treatment, we can obtain the normal-ordered Holstein-Primakoff-type boson expansion in the multi-collective-phonon subspace. Thereby the convergence of the boson expansion can be tested. Some examples of application of the Dyson-type non-unitary boson mapping to simplified models and realistic nuclei are also shown, and we can see that it is quite useful for analysis of the collective motions in realistic nuclei. In contrast to the above-mentioned ordinary type of boson mapping, which may be called a a 'static' boson mapping, the Dyson-type non-unitary self-consistent-collective-coordinate method is discussed. The latter is, so to speak, a 'dynamical' boson mapping, which is a dynamical extension of the ordinary boson mapping to be capable to include the coupling effects from the non-collective degrees of freedom self-consistently.Thus all of the Dyson-type non-unitary boson

Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering

Science.gov (United States)

Weatherford, Charles A.

1993-01-01

One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.

On the exact spectra of two electrons confined by two-dimensional quantum dots

International Nuclear Information System (INIS)

Soldatov, A.V.; Bogolubov Jr, N.N.

2005-12-01

Applicability of the method of intermediate problems to investigation of the energy spectrum and eigenstates of a two- electron two-dimensional quantum dot (QD) formed by a parabolic confining potential is discussed. It is argued that the method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic variational method thus providing an efficient tool of verification of the results obtained so far by various analytical and numerical methods being of current usage for studies of quantum dot models. (author)

Deformed two-photon squeezed states in noncommutative space

International Nuclear Information System (INIS)

Zhang Jianzu

2004-01-01

Recent studies on nonperturbation aspects of noncommutative quantum mechanics explored a new type of boson commutation relations at the deformed level, described by deformed annihilation-creation operators in noncommutative space. This correlated boson commutator correlates different degrees of freedom, and shows an essential influence on dynamics. This Letter devotes to the development of formalism of deformed two-photon squeezed states in noncommutative space. General representations of deformed annihilation-creation operators and the consistency condition for the electromagnetic wave with a single mode of frequency in noncommunicative space are obtained. Two-photon squeezed states are studied. One finds that variances of the dimensionless Hermitian quadratures of the annihilation operator in one degree of freedom include variances in the other degree of freedom. Such correlations show the new feature of spatial noncommutativity and allow a deeper understanding of the correlated boson commutator

Pseudo-Hermitian random matrix theory

International Nuclear Information System (INIS)

Srivastava, S.C.L.; Jain, S.R.

2013-01-01

Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

A diagrammatic construction of formal E-independent model hamiltonian

International Nuclear Information System (INIS)

Kvasnicka, V.

1977-01-01

A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian

Twisted supersymmetry: Twisted symmetry versus renormalizability

International Nuclear Information System (INIS)

Dimitrijevic, Marija; Nikolic, Biljana; Radovanovic, Voja

2011-01-01

We discuss a deformation of superspace based on a Hermitian twist. The twist implies a *-product that is noncommutative, Hermitian and finite when expanded in a power series of the deformation parameter. The Leibniz rule for the twisted supersymmetry transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model. We discuss different possibilities to render a renormalizable model.

Dynamical polarizability of atoms

International Nuclear Information System (INIS)

Mukhopadhyay, G.; Lundqvist, S.

1980-07-01

The frequency-dependent polarizability of a closed-shell atom is considered in an RPA type approximation. This is usually done using many-body perturbation theory but can also be recast into the form of equations for the density oscillations as previously shown by the authors. The latter approach is known to lead to a non-hermitian problem because of the structure of the interaction kernel. This note shows that this is also true if using the reaction matrix method. The main result is to derive the expression for the polarizability function taking into account the non-hermitian nature of the problem. (author)

Time as a Quantum Observable, Canonically Conjugated to Energy, and Foundations of Self-Consistent Time Analysis of Quantum Processes

Directory of Open Access Journals (Sweden)

V. S. Olkhovsky

2009-01-01

Full Text Available Recent developments are reviewed and some new results are presented in the study of time in quantum mechanics and quantum electrodynamics as an observable, canonically conjugate to energy. This paper deals with the maximal Hermitian (but nonself-adjoint operator for time which appears in nonrelativistic quantum mechanics and in quantum electrodynamics for systems with continuous energy spectra and also, briefly, with the four-momentum and four-position operators, for relativistic spin-zero particles. Two measures of averaging over time and connection between them are analyzed. The results of the study of time as a quantum observable in the cases of the discrete energy spectra are also presented, and in this case the quasi-self-adjoint time operator appears. Then, the general foundations of time analysis of quantum processes (collisions and decays are developed on the base of time operator with the proper measures of averaging over time. Finally, some applications of time analysis of quantum processes (concretely, tunneling phenomena and nuclear processes are reviewed.

Covariant and consistent anomalies in two dimensions in path-integral formulation

International Nuclear Information System (INIS)

Joglekar, S.D.; Saini, G.

1993-01-01

We give a definition of a one-parameter family of regularized chiral currents in a chiral non-Abelian gauge theory in two dimensions in path-integral formulation. We show that covariant and consistent currents are obtained from this family by selecting two specific values of the free parameter, and thus our regularization interpolates between these two. Our procedure uses chiral bases constructed from eigenfunctions of the same operator for ψ L and anti ψ L . Definition of integration measure and regularization is done in terms of the same Hermitian operator D α =∂+iαA. Covariant and consistent currents (and indeed the entire family) are classically conserved. Difference with previous works are explained, in particular, that an anomaly in the general basis does differ from the Jacobian contribution. (orig.)

Restricted numerical range: A versatile tool in the theory of quantum information

Science.gov (United States)

Gawron, Piotr; Puchała, Zbigniew; Miszczak, Jarosław Adam; Skowronek, Łukasz; Życzkowski, Karol

2010-10-01

Numerical range of a Hermitian operator X is defined as the set of all possible expectation values of this observable among a normalized quantum state. We analyze a modification of this definition in which the expectation value is taken among a certain subset of the set of all quantum states. One considers, for instance, the set of real states, the set of product states, separable states, or the set of maximally entangled states. We show exemplary applications of these algebraic tools in the theory of quantum information: analysis of k-positive maps and entanglement witnesses, as well as study of the minimal output entropy of a quantum channel. Product numerical range of a unitary operator is used to solve the problem of local distinguishability of a family of two unitary gates.

On the pseudo-norm in some PT-symmetric potentials

International Nuclear Information System (INIS)

Levai, G.

2005-01-01

Complete text of publication follows. PT-symmetric quantum mechanical systems possess non-hermitian Hamiltonian, still they have some characteristics similar to hermitian problems. The most notable of these is their discrete energy spectrum, which can be partly or completely real. These systems are invariant under the simultaneous action of the P space and T time inversion operations. Perhaps the simplest PT-symmetric Hamiltonian contains a one-dimensional Schroedinger operator with a complex potential satisfying the V*(-x) = V (x) relation. Another typical feature PT-symmetric systems have in common with hermitian problems is that their basis states form an orthogonal set provided that the inner product is redefined as (ψ φ)PT ≡ (ψ Pφ). However, the norm defined by this inner product, the pseudo-norm turned out to possess indefinite sign, and this raised the question of the probabilistic interpretation of PT-symmetric systems. This problem was later put into a more general context when it was found that PT symmetry is a special case of pseudo-hermiticity, and this explains most of the peculiar features of PT-symmetric systems. There have been several attempts to link PT-symmetric, and in general, pseudo- hermitian systems with equivalent hermitian ones, and the sign of the pseudo-norm was found to play an important role in this respect. It is thus essential to evaluate the pseudo- norm for various potentials, especially considering the fact that there are some inconsistencies in the available results. Numerical studies indicated that the sign of the pseudo-norm typically alternates according to the n principal quantum number as (-1) n , and this was later proven for a class of potentials that are written in a polynomial form of ix. However, some potentials of other type did not fit into this line: this was the case for the Scarf II potential, the most well-known exactly solvable PT-symmetric potential. In contrast with the other examples, this potential is

Complex matrix model duality

International Nuclear Information System (INIS)

Brown, T.W.

2010-11-01

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.)

Complex matrix model duality

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.)

Multigrid for Staggered Lattice Fermions

Energy Technology Data Exchange (ETDEWEB)

Brower, Richard C. [Boston U.; Clark, M. A. [Unlisted, US; Strelchenko, Alexei [Fermilab; Weinberg, Evan [Boston U.

2018-01-23

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

Data depth and rank-based tests for covariance and spectral density matrices

KAUST Repository

Chau, Joris

2017-06-26

In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.

Data depth and rank-based tests for covariance and spectral density matrices

KAUST Repository

Chau, Joris; Ombao, Hernando; Sachs, Rainer von

2017-01-01

In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.

On complexified mechanics and coquaternions

International Nuclear Information System (INIS)

Brody, Dorje C; Graefe, Eva-Maria

2011-01-01

While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalizations have hitherto remained tangential. In this communication, quaternionic and coquaternionic (split-signature analogue of quaternions) extensions of Hamiltonian mechanics are introduced and are shown to offer a unifying framework for complexified classical and quantum mechanics. In particular, quantum theories characterized by complex Hamiltonians invariant under spacetime reflection are shown to be equivalent to certain coquaternionic extensions of Hermitian quantum theories. One of the interesting consequences is that the spacetime dimension of these systems is six, not four, on account of the structures of coquaternionic quantum mechanics. (fast track communication)

Kurt Symanzik-a stable fixed point beyond triviality

International Nuclear Information System (INIS)

Kleefeld, Frieder

2006-01-01

In 1970 Kurt Symanzik proposed a 'precarious' Φ 4 -theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight into the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short-certainly controversial-communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non-)triviality and asymptotic freedom. (letter to the editor)

A user's manual of Tools for Error Estimation of Complex Number Matrix Computation (Ver.1.0)

International Nuclear Information System (INIS)

Ichihara, Kiyoshi.

1997-03-01

'Tools for Error Estimation of Complex Number Matrix Computation' is a subroutine library which aids the users in obtaining the error ranges of the complex number linear system's solutions or the Hermitian matrices' eigen values. This library contains routines for both sequential computers and parallel computers. The subroutines for linear system error estimation calulate norms of residual vectors, matrices's condition numbers, error bounds of solutions and so on. The error estimation subroutines for Hermitian matrix eigen values' derive the error ranges of the eigen values according to the Korn-Kato's formula. This user's manual contains a brief mathematical background of error analysis on linear algebra and usage of the subroutines. (author)

Factorising the 3D topologically twisted index

Science.gov (United States)

Cabo-Bizet, Alejandro

2017-04-01

We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on {S}_2 times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on {S}_2 times halves of {S}_1 , second as TTCSM on {S}_2 times {S}_1 — with a puncture, — and third as TTCSM on {S}_2× {S}_1 . In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.

Generalized continuity equations from two-field Schrödinger Lagrangians

Science.gov (United States)

Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

2016-11-01

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.

Balanced metrics for vector bundles and polarised manifolds

DEFF Research Database (Denmark)

Garcia Fernandez, Mario; Ross, Julius

2012-01-01

leads to a Hermitian-Einstein metric on E and a constant scalar curvature Kähler metric in c_1(L). For special values of α, limits of balanced metrics are solutions of a system of coupled equations relating a Hermitian-Einstein metric on E and a Kähler metric in c1(L). For this, we compute the top two......We consider a notion of balanced metrics for triples (X, L, E) which depend on a parameter α, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of α, we prove that the limit of a convergent sequence of balanced metrics...

Constacyclic codes over the ring F_q+v{F}_q+v2F_q and their applications of constructing new non-binary quantum codes

Science.gov (United States)

Ma, Fanghui; Gao, Jian; Fu, Fang-Wei

2018-06-01

Let R={F}_q+v{F}_q+v2{F}_q be a finite non-chain ring, where q is an odd prime power and v^3=v. In this paper, we propose two methods of constructing quantum codes from (α +β v+γ v2)-constacyclic codes over R. The first one is obtained via the Gray map and the Calderbank-Shor-Steane construction from Euclidean dual-containing (α +β v+γ v2)-constacyclic codes over R. The second one is obtained via the Gray map and the Hermitian construction from Hermitian dual-containing (α +β v+γ v2)-constacyclic codes over R. As an application, some new non-binary quantum codes are obtained.

Factorising the 3D topologically twisted index

Energy Technology Data Exchange (ETDEWEB)

Cabo-Bizet, Alejandro [Instituto de Astronomía y Física del Espacio (CONICET-UBA),Ciudad Universitaria, C.P. 1428, Buenos Aires (Argentina)

2017-04-20

We explore the path integration — upon the contour of hermitian (non-auxliary) field configurations — of topologically twisted N=2 Chern-Simons-matter theory (TTCSM) on S{sub 2} times a segment. In this way, we obtain the formula for the 3D topologically twisted index, first as a convolution of TTCSM on S{sub 2} times halves of S{sub 1}, second as TTCSM on S{sub 2} times S{sub 1} — with a puncture, — and third as TTCSM on S{sub 2}×S{sub 1}. In contradistinction to the first two cases, in the third case, the vector multiplet auxiliary field D is constrained to be anti-hermitian.

Matrix model calculations beyond the spherical limit

International Nuclear Information System (INIS)

Ambjoern, J.; Chekhov, L.; Kristjansen, C.F.; Makeenko, Yu.

1993-01-01

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.)

The relationship between the Johnson-Baranger time-dependent folded diagram expansion and the time-independent methods of perturbation theory

International Nuclear Information System (INIS)

Passos, E.M.J. de

1976-01-01

The relationship between the Johnson-Baranger time-dependent folded diagram (JBFD) expansion, and the time independent methods of perturbation theory, are investigated. In the nondegenerate case, the JBFD expansion and the Rayleigh-Schroedinger perturbation expansion, for the ground state energy, are identical. On the other hand, in the degenerate case, for the nonhermitian effective interaction considered, the JBFD expansion, of the effective interaction, is equal to the perturbative expansion of the effective interaction of the nonhermitian eigenvalue problem of Bloch and Brandow-Des Cloizeaux. For the two hermitian effective interactions, the JBFD expansion of the effective interaction differs from the perturbation expansion of the effective interaction of the hermitian eigenvalue problem of Des Cloizeaux [pt

Gyroscopic stabilization and indefimite damped systems

DEFF Research Database (Denmark)

Pommer, Christian

a class of feasibel skew-Hermitian matrices A depending on the choise of M. The theory can be applied to dynamical systems of the form x''(t) + ( dD + g G) x'(t) + K x(t) = 0 where G is a skew symmetric gyrocopic matrix, D is a symmetric indefinite damping matrix and K > 0 is a positive definite stiffness......An important issue is how to modify a given unstable matrix in such a way that the resulting matrix is stable. We investigate in general under which condition a matrix M+A is stable,where M is an arbitrary matrix and A is skew-Hermitian. We show that if trace(M) > 0 it is always possible to find...

A game with geometry and quantum mechanics

International Nuclear Information System (INIS)

Caianiello, E.R.

1981-01-01

An attempt is made to geometrize quantum mechanics. A hermitian metric has been taken as a dogma. The Heisenberg commutation relations in cartesian coordinates were taken for the single particle. Position and momentum operators become covariant derivatives, whose commutator is the curvature tensor. The Bohz-Sommerfeld rules are derived both for rotation and vibration degrees of freedom. The Klein-Gordon equation is determined by the first Beltrami parameters. The Dirac equation splits into two sets coupling 8-component semispinors of first and second kind. The only invariance allowed is found to be CPT. A study of the solutions of the Klein-Gordon equation shows that the free particle described by this formalism has inner degrees of freedom [ru

Pseudo-Hermitian Representation of Quantum Mechanics

International Nuclear Information System (INIS)

Mustafazade, A.

2008-01-01

I will outline a formulation of quantum mechanics in which the inner product on the Hilbert space of a quantum system is treated as a degree of freedom. I will outline some of the basic mathematical and conceptual features of the resulting theory and discuss some of its applications. In particular, I will present a quantum mechanical analogue of Einstein's field equations that links the inner product of the Hilbert space and the Hamiltonian of the system and discuss how the resulting theory can be used to address a variety of problems in classical electrodynamics, relativistic quantum mechanics, and quantum computation

Entanglement in non-Hermitian quantum theory

Indian Academy of Sciences (India)

hope that the entanglement in PT -symmetric quantum theory may provide new ways of processing information in the quantum world. We conclude our .... Similarly, if we have a two-level atom, then an arbitrary superposition of the ground state ...

Pure connection formulation, twistors, and the chase for a twistor action for general relativity

Science.gov (United States)

Herfray, Yannick

2017-11-01

This paper establishes the relation between traditional results from the (Euclidean) twistor theory and chiral formulations of general relativity (GR), especially the pure connection formulation. Starting from an SU(2)-connection only, we show how to construct natural complex data on twistor space, mainly an almost Hermitian structure and a connection on some complex line bundle. Only when this almost Hermitian structure is integrable is the connection related to an anti-self-dual-Einstein metric and makes contact with the usual results. This leads to a new proof of the non-linear graviton theorem. Finally, we discuss what new strategies this "connection approach" to twistors suggests for constructing a twistor action for gravity. In Appendix A, we also review all known chiral Lagrangians for GR.

Instantons on Calabi-Yau and hyper-Kähler cones

Science.gov (United States)

Geipel, Jakob C.; Sperling, Marcus

2017-10-01

The instanton equations on vector bundles over Calabi-Yau and hyper-Kähler cones can be reduced to matrix equations resembling Nahm's equations. We complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau cones, based on regular semi-simple elements, by a new set of (singular) boundary conditions which have a known instanton solution in one direction. This approach extends the classic results of Kronheimer by probing a relation between generalised Nahm's equations and nilpotent pairs/tuples. Moreover, we consider quaternionic instantons on hyper-Kähler cones over generic 3-Sasakian manifolds and study the HYM moduli spaces arising in this set-up, using the fact that their analysis can be traced back to the intersection of three Hermitian Yang-Mills conditions.

On Born's deformed reciprocal complex gravitational theory and noncommutative gravity

International Nuclear Information System (INIS)

Castro, Carlos

2008-01-01

Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U(1,3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative generators [Z a ,Z b ]≠0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors R μν ,S μν . The deformed Born's reciprocal gravitational action linear in the Ricci scalars R,S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Z μ =E μ a Z a as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where E μ a is the complex vielbein associated with the Hermitian metric G μν =g (μν) +ig [μν] =E μ a E-bar ν b η ab . This could be one of the underlying reasons why string-theory involves gravity

Analogies between random matrix ensembles and the one-component plasma in two-dimensions

Directory of Open Access Journals (Sweden)

Peter J. Forrester

2016-03-01

Full Text Available The eigenvalue PDF for some well known classes of non-Hermitian random matrices — the complex Ginibre ensemble for example — can be interpreted as the Boltzmann factor for one-component plasma systems in two-dimensional domains. We address this theme in a systematic fashion, identifying the plasma system for the Ginibre ensemble of non-Hermitian Gaussian random matrices G, the spherical ensemble of the product of an inverse Ginibre matrix and a Ginibre matrix G1−1G2, and the ensemble formed by truncating unitary matrices, as well as for products of such matrices. We do this when each has either real, complex or real quaternion elements. One consequence of this analogy is that the leading form of the eigenvalue density follows as a corollary. Another is that the eigenvalue correlations must obey sum rules known to characterise the plasma system, and this leads us to an exhibit of an integral identity satisfied by the two-particle correlation for real quaternion matrices in the neighbourhood of the real axis. Further random matrix ensembles investigated from this viewpoint are self dual non-Hermitian matrices, in which a previous study has related to the one-component plasma system in a disk at inverse temperature β=4, and the ensemble formed by the single row and column of quaternion elements from a member of the circular symplectic ensemble.

Relativistic model for statevector reduction

International Nuclear Information System (INIS)

Pearle, P.

1991-04-01

A relativistic quantum field model describing statevector reduction for fermion states is presented. The time evolution of the states is governed by a Schroedinger equation with a Hamiltonian that has a Hermitian and a non-Hermitian part. In addition to the fermions, the Hermitian part describes positive and negative energy mesons of equal mass, analogous to the longitudinal and timelike photons of electromagnetism. The meson-field-sum is coupled to the fermion field. This ''dresses'' each fermion so that, in the extreme nonrelativistic limit (non-moving fermions), a fermion in a position eigenstate is also in an eigenstate of the meson-field-difference with the Yukawa-potential as eigenvalue. However, the fermions do not interact: this is a theory of free dressed fermions. It is possible to obtain a stationary normalized ''vacuum'' state which satisfies two conditions analogous to the gauge conditions of electromagnetism (i.e., that the meson-field-difference, as well as its time derivative, give zero when applied to the vacuum state), to any desired degree of accuracy. The non-Hermitian part of the Hamiltonian contains the coupling of the meson-field-difference to an externally imposed c-number fluctuating white noise field, of the CSL (Continuous Spontaneous Localization) form. This causes statevector reduction, as is shown in the extreme nonrelativistic limit. For example, a superposition of spatially separated wavepackets of a fermion will eventually be reduced to a single wavepacket: the meson-field-difference discriminates among the Yukawa-potential ''handles'' attached to each wavepacket, thereby selecting one wavepacket to survive by the CSL mechanism. Analysis beyond that given in this paper is required to see what happens when the fermions are allowed to move. (It is possible that the ''vacuum'' state becomes involved in the dynamics so that the ''gauge'' conditions can no longer be maintained.) It is shown how to incorporate these ideas into quantum

A first-order spectral phase transition in a class of periodically modulated Hermitian Jacobi matrices

Directory of Open Access Journals (Sweden)

Irina Pchelintseva

2008-01-01

Full Text Available We consider self-adjoint unbounded Jacobi matrices with diagonal \\(q_n = b_{n}n\\ and off-diagonal entries \\(\\lambda_n = n\\, where \\(b_{n}\\ is a \\(2\\-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum of the operator is either purely absolutely continuous or discrete. We study the situation where the spectral phase transition occurs, namely the case of \\(b_{1}b_{2} = 4\\. The main motive of the paper is the investigation of asymptotics of generalized eigenvectors of the Jacobi matrix. The pure point part of the spectrum is analyzed in detail.

On stability of Kummer surfaces' tangent bundle

International Nuclear Information System (INIS)

Bozhkov, Y.D.

1988-10-01

In this paper we propose an explicit approximation of the Kaehler-Einstein-Calabi-Yau metric on the Kummer surfaces, which are manifolds of type K3. It is constructed by gluing 16 pieces of the Eguchi-Hanson metric and 16 pieces of the Euclidean metric. Two estimates on its curvature are proved. Then we prove an estimate on the first eigenvalue of a covariant differential operator of second order. This enables us to apply Taubes' iteration procedure to obtain that there exists an anti-self-dual connection on the considered Kummer surface. In fact, it is a Hermitian-Einstein connection from which we conclude that Kummer surfaces' co-tangent bundle is stable and therefore their tangent bundle is stable too. (author). 40 refs

Localization and chiral symmetry in 2+1 flavor domain wall QCD

Energy Technology Data Exchange (ETDEWEB)

David J. Antonio; Kenneth C. Bowler; Peter A. Boyle; Norman H. Christ; Michael A. Clark; Saul D. Cohen; Chris Dawson; Alistair Hart; Balint Joó; Chulwoo Jung; Richard D. Kenway; Shu Li; Meifeng Lin; Robert D. Mawhinney; Christopher M. Maynard; Shigemi Ohta; Robert J. Tweedie; Azusa Yamaguchi

2008-01-01

We present results for the dependence of the residual mass of domain wall fermions (DWF) on the size of the fifth dimension and its relation to the density and localization properties of low-lying eigenvectors of the corresponding hermitian Wilson Dirac operator relevant to simulations of 2+1 flavor domain wall QCD. Using the DBW2 and Iwasaki gauge actions, we generate ensembles of configurations with a $16^3\\times 32$ space-time volume and an extent of 8 in the fifth dimension for the sea quarks. We demonstrate the existence of a regime where the degree of locality, the size of chiral symmetry breaking and the rate of topology change can be acceptable for inverse lattice spacings $a^{-1} \\ge 1.6$ GeV.

Matrix model as a mirror of Chern-Simons theory

International Nuclear Information System (INIS)

Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun

2004-01-01

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological amplitudes on toric Calabi-Yau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators. (author)

Relativistic quantum mechanics of bosons

International Nuclear Information System (INIS)

Ghose, P.; Home, D.; Sinha Roy, M.N.

1993-01-01

We show that it is possible to use the Klein-Gordon, Proca and Maxwell formulations to construct multi-component relativistic configuration space wavefunctions of spin-0 and spin-1 bosons in an external field. These wavefunctions satisfy the first-order Kemmer-Duffin equation. The crucial ingredient is the use of the future-causal normal n μ (n μ n μ =1, n 0 >0) to the space-like hypersurfaces foliating space-time, inherent in the concept of a relativistic wavefunction, to construct a conserved future-causal probability current four-vector from the second-rank energy-momentum tensor, following Holland's prescription. The existence of a Hermitian position operator, localized solutions, compatibility with the second quantized theories and the question of interpretation are discussed. (orig.)

Unquenched Complex Dirac Spectra at Nonzero Chemical Potential: Two-Color QCD Lattice Data versus Matrix Model

International Nuclear Information System (INIS)

Akemann, Gernot; Bittner, Elmar

2006-01-01

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses

Boson representations of fermion systems: Proton-neutron systems

International Nuclear Information System (INIS)

Sambataro, M.

1988-01-01

Applications of a procedure recently proposed to construct boson images of fermion Hamiltonians are shown for proton-neutron systems. First the mapping from SD fermion onto sd boson spaces is discussed and a Q/sub π/xQ/sub ν/ interaction investigated. A Hermitian one-body Q boson operator is derived and analytical expressions for its coefficients are obtained. A (Q/sub π/+Q/sub ν/)x(Q/sub π/+Q/sub ν/) interaction is, then, studied for particle-hole systems and the connections with the SU/sup */(3) dynamical symmetry of the neutron-proton interacting boson model are discussed. Finally, an example of mapping from SDG onto sdg spaces is analyzed. Fermion spectra and E2 matrix elements are well reproduced in the boson spaces

Exceptional points in open quantum systems

International Nuclear Information System (INIS)

Mueller, Markus; Rotter, Ingrid

2008-01-01

Open quantum systems are embedded in the continuum of scattering wavefunctions and are naturally described by non-Hermitian Hamilton operators. In the complex energy plane, exceptional points appear at which two (or more) eigenvalues of the Hamilton operator coalesce. Although they are a countable set of single points in the complex energy plane and therefore of measure zero, they determine decisively the dynamics of open quantum systems. A powerful method for the description of open quantum systems is the Feshbach projection operator formalism. It is used in the present paper as a basic tool for the study of exceptional points and of the role they play for the dynamics of open quantum systems. Among others, the topological structure of the exceptional points, the rigidity of the phases of the eigenfunctions in their vicinity, the enhancement of observable values due to the reduced phase rigidity and the appearance of phase transitions are considered. The results are compared with existing experimental data on microwave cavities. In the last section, some questions being still unsolved, are considered

Optimization of entanglement witnesses

Science.gov (United States)

Lewenstein, M.; Kraus, B.; Cirac, J. I.; Horodecki, P.

2000-11-01

An entanglement witness (EW) is an operator that allows the detection of entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e., to detect entangled states in an optimal way. We show how to optimize general EW, and then we particularize our results to the nondecomposable ones; the latter are those that can detect positive partial transpose entangled states (PPTES's). We also present a method to systematically construct and optimize this last class of operators based on the existence of ``edge'' PPTES's, i.e., states that violate the range separability criterion [Phys. Lett. A 232, 333 (1997)] in an extreme manner. This method also permits a systematic construction of nondecomposable positive maps (PM's). Our results lead to a sufficient condition for entanglement in terms of nondecomposable EW's and PM's. Finally, we illustrate our results by constructing optimal EW acting on H=C2⊗C4. The corresponding PM's constitute examples of PM's with minimal ``qubit'' domains, or-equivalently-minimal Hermitian conjugate codomains.

Subroutine library for error estimation of matrix computation (Ver. 1.0)

International Nuclear Information System (INIS)

Ichihara, Kiyoshi; Shizawa, Yoshihisa; Kishida, Norio

1999-03-01

'Subroutine Library for Error Estimation of Matrix Computation' is a subroutine library which aids the users in obtaining the error ranges of the linear system's solutions or the Hermitian matrices' eigenvalues. This library contains routines for both sequential computers and parallel computers. The subroutines for linear system error estimation calculate norms of residual vectors, matrices's condition numbers, error bounds of solutions and so on. The subroutines for error estimation of Hermitian matrix eigenvalues derive the error ranges of the eigenvalues according to the Korn-Kato's formula. The test matrix generators supply the matrices appeared in the mathematical research, the ones randomly generated and the ones appeared in the application programs. This user's manual contains a brief mathematical background of error analysis on linear algebra and usage of the subroutines. (author)

Implications of maximal Jarlskog invariant and maximal CP violation

International Nuclear Information System (INIS)

Rodriguez-Jauregui, E.; Universidad Nacional Autonoma de Mexico

2001-04-01

We argue here why CP violating phase Φ in the quark mixing matrix is maximal, that is, Φ=90 . In the Standard Model CP violation is related to the Jarlskog invariant J, which can be obtained from non commuting Hermitian mass matrices. In this article we derive the conditions to have Hermitian mass matrices which give maximal Jarlskog invariant J and maximal CP violating phase Φ. We find that all squared moduli of the quark mixing elements have a singular point when the CP violation phase Φ takes the value Φ=90 . This special feature of the Jarlskog invariant J and the quark mixing matrix is a clear and precise indication that CP violating Phase Φ is maximal in order to let nature treat democratically all of the quark mixing matrix moduli. (orig.)

State-independent uncertainty relations and entanglement detection

Science.gov (United States)

Qian, Chen; Li, Jun-Li; Qiao, Cong-Feng

2018-04-01

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of N-dimensional observables. The uncertainty relation for the incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn's conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations.

Parity-Time Symmetric Photonics

KAUST Repository

Zhao, Han; Feng, Liang

2018-01-01

The establishment of non-Hermitian quantum mechanics (such as parity-time (PT) symmetry) stimulates a paradigmatic shift for studying symmetries of complex potentials. Owing to the convenient manipulation of optical gain and loss in analogy

Virial expansion for almost diagonal random matrices

Science.gov (United States)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\

Finite boson mappings of fermion systems

International Nuclear Information System (INIS)

Johnson, C.W.; Ginocchio, J.N.

1994-01-01

We discuss a general mapping of fermion pairs to bosons that preserves Hermitian conjugation, with an eye towards producing finite and usable boson Hamiltonians that approximate well the low-energy dynamics of a fermion Hamiltonian

to view fulltext PDF

Indian Academy of Sciences (India)

effects for Lyman and Balmer lines with a 'moderate' principal quantum number ... a non-Hermitian part accounting for natural broadening) and the Zeeman effect .... The authors would like to acknowledge the financial support from the Agence.

A Survey on Operator Monotonicity, Operator Convexity, and Operator Means

Directory of Open Access Journals (Sweden)

Pattrawut Chansangiam

2015-01-01

Full Text Available This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means.

Operator theory, operator algebras and applications

CERN Document Server

Lebre, Amarino; Samko, Stefan; Spitkovsky, Ilya

2014-01-01

This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geo...

Open-system Kohn-Sham density functional theory.

Science.gov (United States)

Zhou, Yongxi; Ernzerhof, Matthias

2012-03-07

A simple model for electron transport through molecules is provided by the source-sink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys. 134, 174101 (2011)] to the Hubbard model. Here we present a step towards its generalization for first-principles electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex non-Hermitian Hamiltonians. This theory enables us to combine SSP and Kohn-Sham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the Hartree-Fock method is extended to the realm of non-Hermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complex-density functional theory (CODFT) as well as non-Hermitian Hartree-Fock theory to electron transport through molecules. © 2012 American Institute of Physics

Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers

Science.gov (United States)

Abdukhalikov, Kanat; Scharlau, Rudolf

2009-03-01

All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in mathbb{Q}(sqrt{-3}) are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3.

Quantum jumps on Anderson attractors

Science.gov (United States)

Yusipov, I. I.; Laptyeva, T. V.; Ivanchenko, M. V.

2018-01-01

In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence that is believed to restore normal diffusion. We demonstrate that for a class of experimentally feasible non-Hermitian dissipators, which admit signatures of localization in asymptotic states, quantum particle opts between diffusive and ballistic regimes, depending on the phase parameter of dissipators, with sticking about localization centers. In a diffusive regime, statistics of quantum jumps is non-Poissonian and has a power-law interval, a footprint of intermittent locking in Anderson modes. Ballistic propagation reflects dispersion of an ordered lattice and introduces the second timescale for jumps, resulting in non-nonmonotonous probability distribution. Hermitian dephasing dissipation makes localization features vanish, and Poissonian jump statistics along with normal diffusion are recovered.

Topologically protected bound states in photonic parity-time-symmetric crystals.

Science.gov (United States)

Weimann, S; Kremer, M; Plotnik, Y; Lumer, Y; Nolte, S; Makris, K G; Segev, M; Rechtsman, M C; Szameit, A

2017-04-01

Parity-time (PT)-symmetric crystals are a class of non-Hermitian systems that allow, for example, the existence of modes with real propagation constants, for self-orthogonality of propagating modes, and for uni-directional invisibility at defects. Photonic PT-symmetric systems that also support topological states could be useful for shaping and routing light waves. However, it is currently debated whether topological interface states can exist at all in PT-symmetric systems. Here, we show theoretically and demonstrate experimentally the existence of such states: states that are localized at the interface between two topologically distinct PT-symmetric photonic lattices. We find analytical closed form solutions of topological PT-symmetric interface states, and observe them through fluorescence microscopy in a passive PT-symmetric dimerized photonic lattice. Our results are relevant towards approaches to localize light on the interface between non-Hermitian crystals.

Scattering theory using smeared non-Hermitian potentials

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2009-01-01

Roč. 80, č. 4 (2009), 045009/1-045009/12 ISSN 1550-7998 R&D Projects: GA MŠk LC06002; GA ČR GA202/07/1307 Institutional research plan: CEZ:AV0Z10480505 Keywords : symmetric quantum-mechanics * pseudo-hermiticity * real spectrum Subject RIV: BE - Theoretical Physics Impact factor: 4.922, year: 2009

Sparse symmetric preconditioners for dense linear systems in electromagnetism

NARCIS (Netherlands)

Carpentieri, Bruno; Duff, Iain S.; Giraud, Luc; Monga Made, M. Magolu

2004-01-01

We consider symmetric preconditioning strategies for the iterative solution of dense complex symmetric non-Hermitian systems arising in computational electromagnetics. In particular, we report on the numerical behaviour of the classical incomplete Cholesky factorization as well as some of its recent

Matrix models with Penner interaction inspired by interacting ...

Indian Academy of Sciences (India)

distribution of structure with temperature calculated from the NL model .... where φi are the random Hermitian matrices of size (N × N) placed at each base position ..... PB thanks UGC for research fellowships and ND thanks CSIR Project No.

On the energy flux of stationary electromagnetic waves in anisotropic dissipative media with spatial dispersion

NARCIS (Netherlands)

Tokman, M. D.; Westerhof, E.; Gavrilova, M. A.

2000-01-01

The special features of the propagation of electromagnetic waves in gyrotropic medium with dispersion and resonant dissipation (specifically, in a magnetoactive plasma) are studied. Even though the anti-Hermitian components of the permittivity tensor are substantial in magnitude, weakly damped waves

Stability and special metrics for complex vector bundles with global sections

International Nuclear Information System (INIS)

Xi Zhang

2004-07-01

In this paper, we study one kind of vortex equations on complex vector bundles over almost Hermitian manifolds and prove a Hitchin-Kobayashi type correspondence relating the existence of solutions of these vortex equations to a certain stability condition. (author)

PT-symmetric model with an interplay between kinematical and dynamical non-localities

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2015-01-01

Roč. 48, č. 19 (2015), s. 195303 ISSN 1751-8113 Institutional support: RVO:61389005 Keywords : non-Hermitian long-range interactions * closed-form constructions of bound states * physical inner products Subject RIV: BE - Theoretical Physics Impact factor: 1.933, year: 2015

Emergent geometry of membranes

Energy Technology Data Exchange (ETDEWEB)

Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

2015-11-13

In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.

A generalized resonating group method with absorptive interaction

International Nuclear Information System (INIS)

Hernandez, E.; Mondragon, A.; Instituto Nacional de Investigaciones Nucleares, Mexico City)

1981-01-01

A generalized Hill-Wheeler equation for the elastic collision at two composite nuclei is obtained projecting the complete many-body Schroedinger equation on the subspace of model internal wave functions and on its orthogonal complement. We get a new, non hermitian (absorptive) interaction term W which takes into account the flux loss in the elastic channel, besides the usual RGM effective Hamiltonian and normalization kernels. A perturbation series expansion for W containing only linked diagrams is given. Finally, the antisymmetrized product of internal wave functions of the fragments that appear in the projection operator is expressed in terms of complex generator coordinates, then the terms appearing in effective interaction can be written as matrix elements of the microscopic interactions and/or the antisymmetrizer between two center shell model states. (author)

Your Lung Operation: After Your Operation

Medline Plus

Full Text Available ... Lung Operation After Your Operation Your Discharge and Recovery Complete Video After Your Operation Guidance for after ... Your Lung Operation Read Next Your Discharge and Recovery Back to Top Find A Surgeon Find A ...

Combining the CORS and BiCORSTAB Iterative Methods with MLFMA and SAI Preconditioning for Solving Large Linear Systems in Electromagnetics

NARCIS (Netherlands)

Carpentieri, Bruno; Jing, Yan-Fei; Huang, Ting-Zhu; Pi, Wei-Chao; Sheng, Xin-Qing

We report on experiments with a novel family of Krylov subspace methods for solving dense, complex, non-Hermitian systems of linear equations arising from the Galerkin discretization of surface integral equation models in Electromagnetics. By some experiments on realistic radar-cross-section

Fast inverse nonlinear Fourier transformation using exponential one-step methods : Darboux transformation

NARCIS (Netherlands)

Vaibhav, V.K.

2017-01-01

This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU(2) nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the

Universal correlators for multi-arc complex matrix models

International Nuclear Information System (INIS)

Akemann, G.

1997-01-01

The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the Hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result for one arc. The basic tool is the iterative solution of the loop equation for the complex matrix model with multiple arcs, which provides all multi-loop correlators up to an arbitrary genus. Explicit results for genus one are given for any number of arcs. The two-arc solution is investigated in detail, including the double-scaling limit. In addition universal expressions for the string susceptibility are given for both the complex and Hermitian model. (orig.)

Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)

2011-02-11

The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)

Linear algebra and analytic geometry for physical sciences

CERN Document Server

Landi, Giovanni

2018-01-01

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises. Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers m...

Critical Investigation of Jauch's Approach to the Quantum Theory of Measurement

Science.gov (United States)

Herbut, Fedor

1986-08-01

To make Jauch's approach more realistic, his assumptions are modified in two ways: (1) On the quantum system plus the measuring apparatus (S+MA) after the measuring interaction has ceased, one can actually measure only operators of the form A⊗∑ k b k Q k ,where A is any Hermitian operator for S, the resolution of the identity ∑kQk=1 defines MA as a classical system (following von Neumann), and the b k are real numbers (S and MA are distant). (2) Measurement is defined in the most general way (including, besides first-kind, also second-kind and third-kind or indirect measurements). It is shown that Jauch's basic result that the microstates (statistical operators) of S+MA before and after the collapse correspond to the same macrostate (belong to the same equivalence class of microstates) remains valid under the above modifications, and that the significance of this result goes beyond measurement theory. On the other hand, it is argued that taking the orthodox (i.e. uncompromisingly quantum) view of quantum mechanics, it is not the collapse, but the Jauch-type macrostates that are spurious in a Jauch-type theory.

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

Further, employing random matrix theory developed for pseudo-Hermitian systems, time correlation functions are studied in the framework of linear response theory. The results given here provide a quantum brachistochrone problem where the system will evolve in a thermodynamic environment with spectral complexity that ...

Lorentzian 3d gravity with wormholes via matrix models

NARCIS (Netherlands)

Ambjørn, J.; Jurkiewicz, J.; Loll, R.; Vernizzi, G.

2001-01-01

We uncover a surprising correspondence between a non-perturbative formulation of three-dimensional Lorentzian quantum gravity and a hermitian two-matrix model with ABAB-interaction. The gravitational transfer matrix can be expressed as the logarithm of a two-matrix integral, and we deduce from

Advantages of complex scaling only the most diffuse basis functions in simultaneous description of both resonances and bound states

Czech Academy of Sciences Publication Activity Database

Landau, A.; Haritan, I.; Kaprálová-Žďánská, Petra Ruth; Moiseyev, N.

2015-01-01

Roč. 113, 19-20 (2015), s. 3141-3146 ISSN 0026-8976 R&D Projects: GA MŠk(CZ) LG13029 Institutional support: RVO:68378271 Keywords : resonance * complex scaling * non-Hermitian * ab-initio Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.837, year: 2015

Spectral calculations in magnetohydrodynamics using the Jacobi-Davidson method

NARCIS (Netherlands)

Belien, A. J. C.; van der Holst, B.; Nool, M.; van der Ploeg, A.; Goedbloed, J. P.

2001-01-01

For the solution of the generalized complex non-Hermitian eigenvalue problems Ax = lambda Bx occurring in the spectral study of linearized resistive magnetohydrodynamics (MHD) a new parallel solver based on the recently developed Jacobi-Davidson [SIAM J. Matrix Anal. Appl. 17 (1996) 401] method has

Representations of locally symmetric spaces

International Nuclear Information System (INIS)

Rahman, M.S.

1995-09-01

Locally symmetric spaces in reference to globally and Hermitian symmetric Riemannian spaces are studied. Some relations between locally and globally symmetric spaces are exhibited. A lucid account of results on relevant spaces, motivated by fundamental problems, are formulated as theorems and propositions. (author). 10 refs

Some properties of the representation of the quasilocal observables in statistical mechanics and quantum field theory

International Nuclear Information System (INIS)

Testard, D.; Centre National de la Recherche Scientifique, 13 - Marseille

1977-09-01

For a finite non zero temperature state in Statistical Mechanics it is proved that the factor obtained in the corresponding representation of the quasilocal algebra has the property of Araki. The same result also holds for the 'wedge-algebras' of a hermitian scalar Wightman field

Conduct of operations: establishing operational focus and setting operational standards

International Nuclear Information System (INIS)

Lane, L.; McGuigan, K.

1998-01-01

Due to the nature of our business, we have often tended to focus on the technological aspects of the nuclear industry. The focus of this paper is directed towards the importance of addressing the people skills, attitudes, and 'culture' within, and surrounding, our facilities as key areas of improvement. Within Ontario Hydro Nuclear (OLIN) we have developed the terminology 'event free' operation and 'event free' culture. 'Event Free' recognizes errors as a part of human performance. 'Event Free' takes into account human weaknesses, and provides tools (such as standards) to manage, control, and mitigate errors. In essence, 'Event Free' encompasses two concepts: 1. Prevent errors from occurring; 2. If an error is made, catch it before it can affect safe operation of the facility, learn from the error, and ensure that it does not happen again. In addressing these business realities, Ontario Hydro has identified a number of key support mechanisms and corresponding performance standards that are essential for achieving operating excellence and an 'event free' business culture. This paper will discuss two operational aspects of an 'event free' culture, the first being a set of expectations to enhance the culture, and the second an example of cultural change: 1. Operating Standards - establishing clear expectations for human performance in operating staff; 2. Operational Focus - the understanding that, as a nuclear worker, you should consider every task, activity, in fact everything you do in this business, for the potential to affect safe and reliable operation of a nuclear facility. Note that although the term 'Operational' appears in the title, this concept applies to every individual in the nuclear business, from the cleaner, to the Board of Directors, to the external supplier. (author)

Your Lung Operation: After Your Operation

Medline Plus

Full Text Available ... Overview ACS-AEI Consortium Quarterly ACS Chapter News Cancer ... American College of Surgeons Education Patients and Family Skills Programs Your Lung Operation Your Lung Operation DVD After Your Operation ...

Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case

Science.gov (United States)

Springborg, Michael; Molayem, Mohammad; Kirtman, Bernard

2017-09-01

A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.

A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation

Science.gov (United States)

Somma, Rolando D.

2016-06-01

We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm with respect to the dimension of the Lie algebra, or when the norm of the effective operator resulting from nested commutators is less than the product of the norms, the number of terms in the product is significantly less than that obtained from well-known results. We apply our results to construct product formulas useful for the quantum simulation of some continuous-variable and bosonic physical systems, including systems whose potential is not quadratic. For many of these systems, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is usually determined by the energy scale of the problem. Our results emphasize the power of quantum computers for the simulation of various quantum systems.

Your Lung Operation: After Your Operation

Medline Plus

Full Text Available ... Medical Student Core Curriculum ACS/ASE Medical Student Simulation-Based Surgical Skills Curriculum Cancer Education Cancer Education ... Surgeons Education Patients and Family Skills Programs Your Lung Operation Your Lung Operation DVD After Your Operation ...

Your Lung Operation: After Your Operation

Medline Plus

Full Text Available ... You Want to Be a Surgeon Resident Resources Teaching Resources Online Guide to Choosing a Surgical Residency ... After Your Operation Your Discharge and Recovery Complete Video After Your Operation Guidance for after the operation ...

Your Lung Operation: After Your Operation

Medline Plus

Full Text Available ... Liability Surgeons as Advocates Surgeons and Bundled Payment Models Surgeons as Institutional Employees Our Changing Health Care ... Lung Operation After Your Operation Your Discharge and Recovery Complete Video After Your Operation Guidance for after ...

Your Lung Operation: After Your Operation

Medline Plus

Full Text Available ... Safety Resources About the Patient Education Program The Recovery Room Choosing Wisely Educational Programs Educational Programs Educational ... Lung Operation After Your Operation Your Discharge and Recovery Complete Video After Your Operation Guidance for after ...

On the completeness of the natural modes for quantum mechanical potential scattering

NARCIS (Netherlands)

Hoenders, B.J.

1979-01-01

The set of natural modes, associated with quantum mechanical scattering from a central potential of finite-range is shown to be complete. The natural modes satisfy a non-Hermitian homogeneous integral equation, or alternatively, are solutions of the time independent Schrödinger equation subject to a

Solvable PT-symmetric model with a tunable interspersion of nonmerging levels

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2005-01-01

Roč. 46, č. 6 (2005), 062109 ISSN 0022-2488 R&D Projects: GA AV ČR(CZ) IAA1048302 Institutional research plan: CEZ:AV0Z10480505 Keywords : non-Hermitian Hamiltonians * quantum-mechanics * square-well Subject RIV: BE - Theoretical Physics Impact factor: 1.192, year: 2005

PT symmetric models in more dimensions and solvable square-well versions of their angular Schrodinger equations

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2003-01-01

Roč. 36, č. 28 (2003), s. 7825-7838 ISSN 0305-4470 R&D Projects: GA AV ČR IAA1048302 Institutional research plan: CEZ:AV0Z1048901 Keywords : non-Hermitian Hamiltonians * quantum-mechanics Subject RIV: BE - Theoretical Physics Impact factor: 1.357, year: 2003

Estimating the two-particle $K$-matrix for multiple partial waves and decay channels from finite-volume energies

DEFF Research Database (Denmark)

Morningstar, Colin; Bulava, John; Singha, Bijit

2017-01-01

An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\\"uscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating...

Jacobi-Davidson methods for generalized MHD-eigenvalue problems

NARCIS (Netherlands)

J.G.L. Booten; D.R. Fokkema; G.L.G. Sleijpen; H.A. van der Vorst (Henk)

1995-01-01

textabstractA Jacobi-Davidson algorithm for computing selected eigenvalues and associated eigenvectors of the generalized eigenvalue problem $Ax = lambda Bx$ is presented. In this paper the emphasis is put on the case where one of the matrices, say the B-matrix, is Hermitian positive definite. The

On the rate of convergence of the alternating projection method in finite dimensional spaces

Science.gov (United States)

Galántai, A.

2005-10-01

Using the results of Smith, Solmon, and Wagner [K. Smith, D. Solomon, S. Wagner, Practical and mathematical aspects of the problem of reconstructing objects from radiographs, Bull. Amer. Math. Soc. 83 (1977) 1227-1270] and Nelson and Neumann [S. Nelson, M. Neumann, Generalizations of the projection method with application to SOR theory for Hermitian positive semidefinite linear systems, Numer. Math. 51 (1987) 123-141] we derive new estimates for the speed of the alternating projection method and its relaxed version in . These estimates can be computed in at most O(m3) arithmetic operations unlike the estimates in papers mentioned above that require spectral information. The new and old estimates are equivalent in many practical cases. In cases when the new estimates are weaker, the numerical testing indicates that they approximate the original bounds in papers mentioned above quite well.

Unidirectional reflectionless light propagation at exceptional points

Directory of Open Access Journals (Sweden)

Huang Yin

2017-05-01

Full Text Available In this paper, we provide a comprehensive review of unidirectional reflectionless light propagation in photonic devices at exceptional points (EPs. EPs, which are branch point singularities of the spectrum, associated with the coalescence of both eigenvalues and corresponding eigenstates, lead to interesting phenomena, such as level repulsion and crossing, bifurcation, chaos, and phase transitions in open quantum systems described by non-Hermitian Hamiltonians. Recently, it was shown that judiciously designed photonic synthetic matters could mimic the complex non-Hermitian Hamiltonians in quantum mechanics and realize unidirectional reflection at optical EPs. Unidirectional reflectionlessness is of great interest for optical invisibility. Achieving unidirectional reflectionless light propagation could also be potentially important for developing optical devices, such as optical network analyzers. Here, we discuss unidirectional reflectionlessness at EPs in both parity-time (PT-symmetric and non-PT-symmetric optical systems. We also provide an outlook on possible future directions in this field.

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts

Science.gov (United States)

Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.

2017-12-01

We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.

New quantum codes derived from a family of antiprimitive BCH codes

Science.gov (United States)

Liu, Yang; Li, Ruihu; Lü, Liangdong; Guo, Luobin

The Bose-Chaudhuri-Hocquenghem (BCH) codes have been studied for more than 57 years and have found wide application in classical communication system and quantum information theory. In this paper, we study the construction of quantum codes from a family of q2-ary BCH codes with length n=q2m+1 (also called antiprimitive BCH codes in the literature), where q≥4 is a power of 2 and m≥2. By a detailed analysis of some useful properties about q2-ary cyclotomic cosets modulo n, Hermitian dual-containing conditions for a family of non-narrow-sense antiprimitive BCH codes are presented, which are similar to those of q2-ary primitive BCH codes. Consequently, via Hermitian Construction, a family of new quantum codes can be derived from these dual-containing BCH codes. Some of these new antiprimitive quantum BCH codes are comparable with those derived from primitive BCH codes.

Revisiting the Optical PT-Symmetric Dimer

Directory of Open Access Journals (Sweden)

José Delfino Huerta Morales

2016-08-01

Full Text Available Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of PT -symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical PT -symmetric dimer, a two-waveguide coupler where the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry-based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar N-waveguide couplers that are the optical realization of the Lorentz group in 2 + 1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of the Ehrenfest theorem.

Complex Algebraic Varieties

CERN Document Server

Peternell, Thomas; Schneider, Michael; Schreyer, Frank-Olaf

1992-01-01

The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory.- G. Bohnhorst, H. Spindler: The stability of certain vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on positive line bundles.- T. Fujita: On adjoint bundles of ample vector bundles.- Y. Kawamata: Moderate degenerations of algebraic surfaces.- U. Persson: Genus two fibra...

Giving up the ghost

International Nuclear Information System (INIS)

Bender, Carl M; Mannheim, Philip D

2008-01-01

The Pais-Uhlenbeck model is a quantum theory described by a higher-derivative field equation. It has been believed for many years that this model possesses ghost states (quantum states of negative norm) and therefore that this model is a physically unacceptable quantum theory. The existence of such ghost states was believed to be attributable to the field equation having more than two derivatives. This paper shows that the Pais-Uhlenbeck model does not possess any ghost states at all and that it is a perfectly acceptable quantum theory. The supposed ghost states in this model arise if the Hamiltonian of the model is (incorrectly) treated as being Dirac Hermitian (invariant under combined matrix transposition and complex conjugation). However, the Hamiltonian is not Dirac Hermitian, but rather it is PT symmetric. When it is quantized correctly according to the rules of PT quantum mechanics, the energy spectrum is real and bounded below and all of the quantum states have positive norm

Use of a preconditioned Bi-conjugate gradient method for hybrid plasma stability analysis

International Nuclear Information System (INIS)

Mikic, Z.; Morse, E.C.

1985-01-01

The numerical stability analysis of compact toroidal plasmas using implicit time differencing requires the solution of a set of coupled, 2-dimensional, elliptic partial differential equations for the field quantities at every timestep. When the equations are spatially finite-differenced and written in matrix form, the resulting matrix is large, sparse, complex, non-Hermitian, and indefinite. The use of the preconditioned bi-conjugate gradient method for solving these equations is discussed. The effect of block-diagonal preconditioning and incomplete block-LU preconditionig on the convergence of the method is investigated. For typical matrices arising in our studies, the eigenvalue spectra of the original and preconditioned matrices are calculated as an illustration of the effectiveness of the preconditioning. We show that the preconditioned bi-conjugate gradient method coverages more rapidly than the conjugate gradient method applied to the normal equations, and that it is an effective iterative method for the class of non-Hermitian, indefinite problems of interest

Claims of operators, non-operators and third parties arising from oil and gas operations

International Nuclear Information System (INIS)

Block, R.W.; Semadeni, T.

1999-01-01

There has come a resurgence in the number of companies involved in the oil and gas industry seeking protection from their creditors because of the recent weakness in commodity prices. Because most operations in this industry are conducted jointly, a single insolvency can lead to a toppling of other participants in the joint venture and beyond. The problem is to minimize one's losses if other members of the joint venture become insolvent. An examination is included of some remedies which may be available to operators, non-operators and third parties when faced with an insolvent oil and gas participant. The remedies which may be available to the non-operator that is owed moneys by its operator are discussed. The remedies that the operator has against its non-operators, with an emphasis on the nature of the operator's lien and the right of set-off, are described. A brief review is included of some of the remedies that might be available to a third party as against the operators and non-operators. Some s uggestions are included for directors, bankers, third parties, non-operators and operators

Operator-assisted planning and execution of proximity operations subject to operational constraints

Science.gov (United States)

Grunwald, Arthur J.; Ellis, Stephen R.

1991-01-01

Future multi-vehicle operations will involve multiple scenarios that will require a planning tool for the rapid, interactive creation of fuel-efficient trajectories. The planning process must deal with higher-order, non-linear processes involving dynamics that are often counter-intuitive. The optimization of resulting trajectories can be difficult to envision. An interaction proximity operations planning system is being developed to provide the operator with easily interpreted visual feedback of trajectories and constraints. This system is hosted on an IRIS 4D graphics platform and utilizes the Clohessy-Wiltshire equations. An inverse dynamics algorithm is used to remove non-linearities while the trajectory maneuvers are decoupled and separated in a geometric spreadsheet. The operator has direct control of the position and time of trajectory waypoints to achieve the desired end conditions. Graphics provide the operator with visualization of satisfying operational constraints such as structural clearance, plume impingement, approach velocity limits, and arrival or departure corridors. Primer vector theory is combined with graphical presentation to improve operator understanding of suggested automated system solutions and to allow the operator to review, edit, or provide corrective action to the trajectory plan.

Applied Operations Research: Operator's Assistant

Science.gov (United States)

Cole, Stuart K.

2015-01-01

NASA operates high value critical equipment (HVCE) that requires trouble shooting, periodic maintenance and continued monitoring by Operations staff. The complexity HVCE and information required to maintain and trouble shoot HVCE to assure continued mission success as paper is voluminous. Training on new HVCE is commensurate with the need for equipment maintenance. LaRC Research Directorate has undertaken a proactive research to support Operations staff by initiation of the development and prototyping an electronic computer based portable maintenance aid (Operator's Assistant). This research established a goal with multiple objectives and a working prototype was developed. The research identified affordable solutions; constraints; demonstrated use of commercial off the shelf software; use of the US Coast Guard maintenance solution; NASA Procedure Representation Language; and the identification of computer system strategies; where these demonstrations and capabilities support the Operator, and maintenance. The results revealed validation against measures of effectiveness and overall proved a substantial training and capability sustainment tool. The research indicated that the OA could be deployed operationally at the LaRC Compressor Station with an expectation of satisfactorily results and to obtain additional lessons learned prior to deployment at other LaRC Research Directorate Facilities. The research revealed projected cost and time savings.

Using fractional order method to generalize strengthening generating operator buffer operator and weakening buffer operator

OpenAIRE

Wu, L.; Liu, S.; Yang, Yingjie

2016-01-01

Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases.

Decays of degeneracies in PT-symmetric ring-shaped lattices

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2011-01-01

Roč. 375, č. 39 (2011), s. 3435-3441 ISSN 0375-9601 R&D Projects: GA ČR GAP203/11/1433 Institutional research plan: CEZ:AV0Z10480505 Keywords : NON-HERMITIAN HAMILTONIANS * quantum -mechanics * OBSERVABILITY Subject RIV: BE - Theoretical Physics Impact factor: 1.632, year: 2011

On the Chern Yamabe Problem

DEFF Research Database (Denmark)

Angella, Daniele; Calamai, Simone; Spotti, Cristiano

2017-01-01

We undertake the study of an analogue of the Yamabe problem for complex manifolds. More precisely, for any conformal Hermitian structure on a compact complex manifold, we are concerned in the existence of metrics with constant Chern scalar curvature. In this note, we set the problem and we provid...

AUTHOR INDEX

Indian Academy of Sciences (India)

Uniqueness of solutions to Schrödinger equations on complex semi-simple Lie groups. 325. Chen Lili. On the compactly locally uniformly rotund points of Orlicz spaces. 471. Chu Jifeng. Positive solutions and eigenvalue intervals for nonlinear systems. 85. Clozel L. Equivariant embeddings of Hermitian sym- metric spaces.

Three Solvable Matrix Models of a Quantum Catastrophe

Czech Academy of Sciences Publication Activity Database

Levai, G.; Růžička, František; Znojil, Miloslav

2014-01-01

Roč. 53, č. 9 (2014), s. 2875-2890 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : quantum theory * PT symmetry * Finite-dimensional non-Hermitian Hamiltonians * exceptional-point localization * quantum theory of catastrophes * methods of computer algebra Subject RIV: BE - Theoretical Physics Impact factor: 1.184, year: 2014

A mini review on CP-violating minimal supersymmetric Standard ...

Indian Academy of Sciences (India)

2016-08-24

Aug 24, 2016 ... invariant local quantum field theory with a Hermitian. Hamiltonian .... butions to the Higgs mass introducing scalar partners of the SM .... troweak symmetry breaking. Name. Spin. Gauge eigenstates ..... icant amount of higher-order loop corrections in the ..... Krasnoshekova, A V Vasiliev, A O Polyushkin, M S.

Experiments in PT-symmetric quantum mechanics

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2004-01-01

Roč. 54, č. 1 (2004), s. 151-156 ISSN 0011-4626 R&D Projects: GA AV ČR IAA1048302 Institutional research plan: CEZ:AV0Z1048901 Keywords : quantum mechanics * relativistic kinematics * non-Hermitian observables Subject RIV: BE - Theoretical Physics Impact factor: 0.292, year: 2004

Prevalence of operator fatigue in winter maintenance operations.

Science.gov (United States)

Camden, Matthew C; Medina-Flintsch, Alejandra; Hickman, Jeffrey S; Bryce, James; Flintsch, Gerardo; Hanowski, Richard J

2018-02-02

Similar to commercial motor vehicle drivers, winter maintenance operators are likely to be at an increased risk of becoming fatigued while driving due to long, inconsistent shifts, environmental stressors, and limited opportunities for sleep. Despite this risk, there is little research concerning the prevalence of winter maintenance operator fatigue during winter emergencies. The purpose of this research was to investigate the prevalence, sources, and countermeasures of fatigue in winter maintenance operations. Questionnaires from 1043 winter maintenance operators and 453 managers were received from 29 Clear Road member states. Results confirmed that fatigue was prevalent in winter maintenance operations. Over 70% of the operators and managers believed that fatigue has a moderate to significant impact on winter maintenance operations. Approximately 75% of winter maintenance operators reported to at least sometimes drive while fatigued, and 96% of managers believed their winter maintenance operators drove while fatigued at least some of the time. Furthermore, winter maintenance operators and managers identified fatigue countermeasures and sources of fatigue related to winter maintenance equipment. However, the countermeasures believed to be the most effective at reducing fatigue during winter emergencies (i.e., naps) were underutilized. For example, winter maintenance operators reported to never use naps to eliminate fatigue. These results indicated winter maintenance operations are impacted by operator fatigue. These results support the increased need for research and effective countermeasures targeting winter maintenance operator fatigue. Copyright © 2018 Elsevier Ltd. All rights reserved.

Particle in a box in PT-symmetric quantum mechanics and an electromagnetic analog

Science.gov (United States)

Dasarathy, Anirudh; Isaacson, Joshua P.; Jones-Smith, Katherine; Tabachnik, Jason; Mathur, Harsh

2013-06-01

In PT-symmetric quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be Hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PT-symmetric quantum mechanics by constructing a simple model that is the PT-symmetric analog of a particle in a box. The model has the usual particle-in-a-box Hamiltonian but boundary conditions that respect PT symmetry rather than Hermiticity. We find that for a broad class of PT-symmetric boundary conditions the model respects the condition of unbroken PT symmetry, namely, that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the PT-symmetric inner product. Thus we obtain a simple soluble model that fulfills all the requirements of PT-symmetric quantum mechanics. In the second part of this paper we formulate a variational principle for PT-symmetric quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner line shape in transmission and a Fano line shape in reflection; by contrast, in the corresponding Hermitian case the line shapes always have a Breit-Wigner form in both transmission and reflection.

Effectiveness of operation tools developed by KEKB operators

International Nuclear Information System (INIS)

Sugino, K.; Satoh, Y.; Kitabayashi, T.

2004-01-01

The main tasks of KEKB (High Energy Accelerator Research Organization B-physics) operators are beam tuning and injection, operation logging, monitoring of accelerator conditions and safety management. New beam tuning methods are frequently applied to KEKB in order to accomplish high luminosity. In such a situation, various operation tools have been developed by the operators to realize efficient operation. In this paper, we describe effectiveness of tools developed by the operators. (author)

Time-dependent version of crypto-Hermitian quantum theory

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2008-01-01

Roč. 78, č. 8 (2008), 085003/1-085003/5 ISSN 1550-7998 R&D Projects: GA ČR GA202/07/1307; GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : KLEIN-GORDON FIELDS * PSEUDO-HERMITICITY * HILBERT-SPACE Subject RIV: BE - Theoretical Physics Impact factor: 5.050, year: 2008

Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

OpenAIRE

Ndayiragije, François; Van Assche, Walter

2013-01-01

Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to $r>1$ different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Followi...

Review of operational aids for nuclear plant operators

International Nuclear Information System (INIS)

Kisner, R.A.

1983-01-01

Many approaches are being explored to improve the safety of nuclear plant operations. One approach is to supply high-quality, relevant information by means of computer-based diagnostic systems to assist plant operators in performing their operational and safety-related roles. The evaluation of operational aids to ensure safe plant operations is a necessary function of NRC. This work has two purposes: to collect limited data on a diversity of operational aids, and to provide a method for evaluating the safety implications of the functions of proposed operational aids. After a discussion of the method evaluation now under study, this paper outlines this data collection to date

Control of the rings of exceptional points in photonic crystal slabs

DEFF Research Database (Denmark)

Kaminski, Piotr Marek; Breinbjerg, Olav; Mørk, Jesper

2017-01-01

shown that when the system becomes non-Hermitian, e.g. it is an open system exhibiting radiation losses, Dirac cones can be deformed spawning rings of exceptional points [2]. Within the ring, the dispersion follows the two-dimensional flat band which provides a high density of states and therefore high...

Fulltext PDF

Indian Academy of Sciences (India)

[3] A Knutson and TTao, The Honeycomb model of the Berenstein-Zelevinsky cone I: Proof of the saturation conjecture, preprint dated January 3,1999. [4] W Fulton, Eigenvalues of sums of Hermitian matrices (after A.Klyachko), Seminaire Bourbaki, 1998. R Bhatia, Statistics and Mathematics Unit,Indian Statistical Institute, 7, ...

Statistical-mechanical formulation of Lyapunov exponents

International Nuclear Information System (INIS)

Tanase-Nicola, Sorin; Kurchan, Jorge

2003-01-01

We show how the Lyapunov exponents of a dynamic system can, in general, be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive concepts and techniques of approximation can hence be borrowed

Nonlocal Operational Calculi for Dunkl Operators

Directory of Open Access Journals (Sweden)

Ivan H. Dimovski

2009-03-01

Full Text Available The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusinski type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value problems for Dunkl functional-differential equations $P(D_ku = f$ with a given polynomial $P$ is proposed. The solution of these equations in mean-periodic functions reduces to such problems. Necessary and sufficient condition for existence of unique solution in mean-periodic functions is found.

Synergy, a co-operative innovation for joint operations

International Nuclear Information System (INIS)

Todd, C.; Feuchtwanger, T.; Moberg, R.; Lesser, L.

1993-01-01

Industry cooperation in the operation of the large Swan Hills oil field in western Alberta is described. Declining production and increasing costs required innovative approaches to field operation. Traditional operation involved one operator making the majority of decisions with funding controlled by numerous non-operating joint owners, and can suffer from interaction problems due to the inherenty competitive nature of the petroleum industry. The new mode of operation stresses trust, cooperation, teamwork, resource sharing, and continuous improvement. The synergy involves sharing best practices, information, knowledge and expertise, combining resources, and standardizing procedures and specifications. The new mode of operation has resulted in an improved performance of up to 15%. The cooperation lessons learnt at Swan Hills may have broad application across the petroleum industry. 6 refs., 6 figs

The problem of electric sources in Einstein's Hermite-symmetric field theory

International Nuclear Information System (INIS)

Kreisel, E.

1986-01-01

The possibility is investigated to introduce a geometric source without A-invariance and Hermite-symmetry breaking of Einstein's Hermitian relativity. It would be very meaningful to interpret a source of this kind as electric current. With this extension Einstein's unitary field theory contains Einstein's gravitation, electromagnetism and the gluonic vacuum of chromodynamics. (author)

On the Ext algebras of parabolic Verma modules and A infinity-structures

DEFF Research Database (Denmark)

Klamt, Angela; Stroppel, Catharina

2012-01-01

We study the Ext-algebra of the direct sum of all parabolic Verma modules in the principal block of the Bernstein–Gelfand–Gelfand category O for the Hermitian symmetric pair (gln+m,gln¿glm) and present the corresponding quiver with relations for the cases n=1,2. The Kazhdan–Lusztig combinatorics ...

Control of exceptional points in photonic crystal slabs

DEFF Research Database (Denmark)

Kaminski, Piotr Marek; Taghizadeh, Alireza; Breinbjerg, Olav

2017-01-01

Various ways of controlling the extent of the ring of exceptional points in photonic crystal slabs are investigated. The extent of the ring in photonic crystal slabs is found to vary with the thickness of the slab. This enables recovery of Dirac cones in open, non-Hermitian systems, such as a pho...

Quantum star-graph analogues of PT-symmetric square wells

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2012-01-01

Roč. 90, č. 12 (2012), s. 1287-1293 ISSN 0008-4204 R&D Projects: GA ČR GAP203/11/1433 Institutional support: RVO:61389005 Keywords : non-Hermitian interactions * exactly solvable models * quantum graphs * equilateral q-pointed star * Robin boundary condition Subject RIV: BE - Theoretical Physics Impact factor: 0.902, year: 2012

Helium in chirped laser fields as a time-asymmetric atomic switch

Czech Academy of Sciences Publication Activity Database

Kaprálová-Žďánská, Petra Ruth; Moiseyev, N.

2014-01-01

Roč. 141, č. 1 (2014), "014307-1"-"014307-14" ISSN 0021-9606 R&D Projects: GA ČR GAP205/11/0571 Institutional support: RVO:68378271 Keywords : laser excitation * chirped pulses * non-hermitian quantum mechanics * time-asymmetry Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 2.952, year: 2014

Does Operational Risk Disclosure Quality Increase Operating Cash Flows?

Directory of Open Access Journals (Sweden)

Haitham Nobanee

2017-12-01

Full Text Available This study aims to measure the degree of operational risk disclosure and examine its impact on operating cash flow of banks listed on the UAE Abu Dhabi Stock Exchange (ADX and Dubai Financial Market (DFM during the period 2003-2016. The authors conducted content analysis of the annual reports to measure the degree of operational risk disclosure. In addition, they used dynamic panel data regressions to analyze the impact of operational risk disclosure on the operating cash flow generated by the banks. The results show a low degree of operational risk disclosure for all UAE banks, both Islamic and conventional. In addition, the results show no association between the levels of disclosure of operational risk and cash flow for all banks, conventional and Islamic. Operational risk disclosure of Islamic banks has not been examined by any prior researchers. In addition, this paper examines the potential impact of operational risk disclosure on the operating cash flow generated by the banks.

The Golden-Thompson inequality: Historical aspects and random matrix applications

International Nuclear Information System (INIS)

Forrester, Peter J.; Thompson, Colin J.

2014-01-01

The Golden-Thompson inequality, Tr (e A+B ) ⩽ Tr (e A e B ) for A, B Hermitian matrices, appeared in independent works by Golden and Thompson published in 1965. Both of these were motivated by considerations in statistical mechanics. In recent years the Golden-Thompson inequality has found applications to random matrix theory. In this article, we detail some historical aspects relating to Thompson's work, giving in particular a hitherto unpublished proof due to Dyson, and correspondence with Pólya. We show too how the 2 × 2 case relates to hyperbolic geometry, and how the original inequality holds true with the trace operation replaced by any unitarily invariant norm. In relation to the random matrix applications, we review its use in the derivation of concentration type lemmas for sums of random matrices due to Ahlswede-Winter, and Oliveira, generalizing various classical results

Multithreaded implicitly dealiased convolutions

Science.gov (United States)

Roberts, Malcolm; Bowman, John C.

2018-03-01

Implicit dealiasing is a method for computing in-place linear convolutions via fast Fourier transforms that decouples work memory from input data. It offers easier memory management and, for long one-dimensional input sequences, greater efficiency than conventional zero-padding. Furthermore, for convolutions of multidimensional data, the segregation of data and work buffers can be exploited to reduce memory usage and execution time significantly. This is accomplished by processing and discarding data as it is generated, allowing work memory to be reused, for greater data locality and performance. A multithreaded implementation of implicit dealiasing that accepts an arbitrary number of input and output vectors and a general multiplication operator is presented, along with an improved one-dimensional Hermitian convolution that avoids the loop dependency inherent in previous work. An alternate data format that can accommodate a Nyquist mode and enhance cache efficiency is also proposed.

Globally conformal invariant gauge field theory with rational correlation functions

CERN Document Server

Nikolov, N M; Todorov, I T; CERN. Geneva; Todorov, Ivan T.

2003-01-01

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields $V_{\\kappa} (x_1, x_2)$ of dimension $(\\kappa, \\kappa)$. For a {\\it globally conformal invariant} (GCI) theory we write down the OPE of $V_{\\kappa}$ into a series of {\\it twist} (dimension minus rank) $2\\kappa$ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field. We argue that the theory of a GCI hermitian scalar field ${\\cal L} (x)$ of dimension 4 in $D = 4$ Minkowski space such that the 3-point functions of a pair of ${\\cal L}$'s and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density ${\\cal L} (x)$.

Equation-of-motion O(N) electronic structure studies of very large systems (N ∼ 107)

International Nuclear Information System (INIS)

Michalewicz, M.T.

1999-01-01

Extremely fast parallel implementation of the equation-of-motion method for electronic structure computations is presented. The method can be applied to non-periodic, disordered nanocrystalline samples, transition metal oxides and other systems. The equation-of-motion method exhibits linear scaling, O(N), runs with a speed of up to 43 GFLOPS on a NEC SX-4 vector-parallel supercomputer with 32 processors and computes electronic densities of states (DOS) for multi-million atom samples in mere minutes. The largest test computation performed was for the electronic DOS for a TiO 2 sample consisting of 7,623,000 atoms. Mathematically, this is equivalent to obtaining the spectrum of an n x n Hermitian operator (Hamiltonian) where n = 38, 115, 000. We briefly discuss the practical implications of being able to perform electronic structure computations of this great speed and scale. Copyright (1999) CSIRO Australia

Operator programs and operator processes

NARCIS (Netherlands)

Bergstra, J.A.; Walters, P.

2003-01-01

We define a notion of program which is not a computer program but an operator program: a detailed description of actions performed and decisions taken by a human operator (computer user) performing a task to achieve a goal in a simple setting consisting of that user, one or more computers and a

From EGEE Operations Portal towards EGI Operations Portal

Science.gov (United States)

Cordier, Hélène; L'Orphelin, Cyril; Reynaud, Sylvain; Lequeux, Olivier; Loikkanen, Sinikka; Veyre, Pierre

Grid operators in EGEE have been using a dedicated dashboard as their central operational tool, stable and scalable for the last 5 years despite continuous upgrade from specifications by users, monitoring tools or data providers. In EGEE-III, recent regionalisation of operations led the Operations Portal developers to conceive a standalone instance of this tool. We will see how the dashboard reorganization paved the way for the re-engineering of the portal itself. The outcome is an easily deployable package customized with relevant information sources and specific decentralized operational requirements. This package is composed of a generic and scalable data access mechanism, Lavoisier; a renowned php framework for configuration flexibility, Symfony and a MySQL database. VO life cycle and operational information, EGEE broadcast and Downtime notifications are next for the major reorganization until all other key features of the Operations Portal are migrated to the framework. Features specifications will be sketched at the same time to adapt to EGI requirements and to upgrade. Future work on feature regionalisation, on new advanced features or strategy planning will be tracked in EGI- Inspire through the Operations Tools Advisory Group, OTAG, where all users, customers and third parties of the Operations Portal are represented from January 2010.

q-bosons and the q-analogue quantized field

International Nuclear Information System (INIS)

Nelson, C.A.

1994-01-01

The q-analogue coherent states |z > q are used to identify physical signatures for the presence of a q-analogue quantized radiation field in the | > q classical limit where |z| is large. In this quantum-optics-like limit, the fractional uncertainties of most physical quantities (momentum, position, amplitude, phase) which characterize the quantum field are O(1). They only vanish as O(1/|z|) when q = 1. However, for the number operator, N, and the N-Hamiltonian for a free q-boson gas, H N = ℎω(N + 1/2), the fractional uncertainties do still approach zero. A signature for q-boson counting statistics is that (ΔN) 2 / → 0 as |z| → ∞. Except for its O(1) fractional uncertainty, the q-generalization of the Hermitian phase operator of Pegg and Barnett, φ q , still exhibits normal classical behavior. The standard number-phase uncertainty-relation, ΔN Δφ q = 1/2, and the approximate commutation relation, [N,φ q ] = i, still hold for the single-mode q-analogue quantized field. So, N and φ q are almost canonically conjugate operators in the |z > q classical limit. The |z > q CS's minimize this uncertainty relation for moderate |z| 2

Your Lung Operation: After Your Operation

Medline Plus

Full Text Available ... Careers at ACS Careers at ACS About ACS Career Types Working at ACS ... ( 0 ) Cart Donate American College of Surgeons Education Patients and Family Skills Programs Your Lung Operation Your Lung Operation DVD ...

Your Lung Operation: After Your Operation

Medline Plus

Full Text Available ... to Participate Resources Webinars for Young Surgeons YFA E-News YFA Advocacy Essay Contest Resident and Associate ... ACS Leader International Exchange Scholar Program Resources RAS E-News Medical Students Operation Giving Back Operation Giving ...

The spinorial geometry of supersymmetric backgrounds

International Nuclear Information System (INIS)

Gillard, J; Gran, U; Papadopoulos, G

2005-01-01

We propose a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N = 1 and some N = 2, N = 3 and N = 4 backgrounds. In the N = 2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N = 2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N = 2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure. The spacelike Killing vector field leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds preserving more than two supersymmetries, N > 2. We investigate a class of N = 3 and N = 4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi-Yau compactifications with fluxes to one dimension

The spinorial geometry of supersymmetric backgrounds

Energy Technology Data Exchange (ETDEWEB)

Gillard, J; Gran, U; Papadopoulos, G [Department of Mathematics, King' s College London, Strand, London WC2R 2LS (United Kingdom)

2005-03-21

We propose a new method to solve the Killing spinor equations of 11-dimensional supergravity based on a description of spinors in terms of forms and on the Spin(1, 10) gauge symmetry of the supercovariant derivative. We give the canonical form of Killing spinors for backgrounds preserving two supersymmetries, N = 2, provided that one of the spinors represents the orbit of Spin(1, 10) with stability subgroup SU(5). We directly solve the Killing spinor equations of N = 1 and some N = 2, N = 3 and N = 4 backgrounds. In the N = 2 case, we investigate backgrounds with SU(5) and SU(4) invariant Killing spinors and compute the associated spacetime forms. We find that N = 2 backgrounds with SU(5) invariant Killing spinors admit a timelike Killing vector and that the space transverse to the orbits of this vector field is a Hermitian manifold with an SU(5)-structure. Furthermore, N = 2 backgrounds with SU(4) invariant Killing spinors admit two Killing vectors, one timelike and one spacelike. The space transverse to the orbits of the former is an almost Hermitian manifold with an SU(4)-structure. The spacelike Killing vector field leaves the almost complex structure invariant. We explore the canonical form of Killing spinors for backgrounds preserving more than two supersymmetries, N > 2. We investigate a class of N = 3 and N = 4 backgrounds with SU(4) invariant spinors. We find that in both cases the space transverse to a timelike vector field is a Hermitian manifold equipped with an SU(4)-structure and admits two holomorphic Killing vector fields. We also present an application to M-theory Calabi-Yau compactifications with fluxes to one dimension.

Maximal couplings in PT-symmetric chain models with the real spectrum of energies

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2007-01-01

Roč. 40, č. 18 (2007), s. 4863-4875 ISSN 1751-8113 R&D Projects: GA MŠk LC06002; GA ČR GA202/07/1307 Institutional research plan: CEZ:AV0Z10480505 Keywords : non-hermitian hamiltonians * quantum -mechanics * expectional points Subject RIV: BE - Theoretical Physics Impact factor: 1.680, year: 2007

Scattering in the PT-symmetric Coulomb potential

Czech Academy of Sciences Publication Activity Database

Levai, G.; Siegl, P.; Znojil, Miloslav

2009-01-01

Roč. 42, č. 29 (2009), 295201/1-295201/9 ISSN 1751-8113 R&D Projects: GA ČR GA202/07/1307; GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : NON-HERMITIAN HAMILTONIANS * QUANTUM-MECHANICS * EQUATIONS Subject RIV: BE - Theoretical Physics Impact factor: 1.577, year: 2009

Fundamental length in quantum theories with PT-symmetric Hamiltonians

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2009-01-01

Roč. 80, č. 4 (2009), 045022/1-045022/20 ISSN 1550-7998 R&D Projects: GA MŠk LC06002; GA ČR GA202/07/1307 Institutional research plan: CEZ:AV0Z10480505 Keywords : non-Hermitian Hamiltonians * anharmonic-oscillators * noncommutative space Subject RIV: BE - Theoretical Physics Impact factor: 4.922, year: 2009

Complete set of inner products for a discrete PT-symmetric square-well Hamiltonian

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2009-01-01

Roč. 50, č. 12 (2009), 122105/1-122105/19 ISSN 0022-2488 R&D Projects: GA MŠk LC06002; GA ČR GA202/07/1307 Institutional research plan: CEZ:AV0Z10480505 Keywords : bound states * Hermitian matrices * Hilbert spaces Subject RIV: BE - Theoretical Physics Impact factor: 1.318, year: 2009

Equivalence of quotient Hilbert modules

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

w), that is, γ is an anti-holomorphic frame for E. In the case of n > 1, a similar construction of an anti-holomorphic hermitian vector bundle of rank n can be given. In our case, it is easy to verify that K(·, w), the reproducing kernel at w, is a common ...

Elementary operators on self-adjoint operators

Science.gov (United States)

Molnar, Lajos; Semrl, Peter

2007-03-01

Let H be a Hilbert space and let and be standard *-operator algebras on H. Denote by and the set of all self-adjoint operators in and , respectively. Assume that and are surjective maps such that M(AM*(B)A)=M(A)BM(A) and M*(BM(A)B)=M*(B)AM*(B) for every pair , . Then there exist an invertible bounded linear or conjugate-linear operator and a constant c[set membership, variant]{-1,1} such that M(A)=cTAT*, , and M*(B)=cT*BT, .

WKB analysis of PT-symmetric Sturm–Liouville problems

International Nuclear Information System (INIS)

Bender, Carl M; Jones, Hugh F

2012-01-01

Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schrödinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the case with regular Hermitian Sturm–Liouville problems, the eigenvalues of the PT-symmetric Sturm–Liouville problem grow like n 2 for large n. However, the novelty is that a PT eigenvalue problem on a finite domain typically exhibits a sequence of critical points at which pairs of eigenvalues cease to be real and become complex conjugates of one another. For the potentials considered here this sequence of critical points is associated with a turning point on the imaginary axis in the complex plane. WKB analysis is used to calculate the asymptotic behaviours of the real eigenvalues and the locations of the critical points. The method turns out to be surprisingly accurate even at low energies. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry

International Nuclear Information System (INIS)

Birchall, Christopher; Schomerus, Henning

2012-01-01

We formulate Gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a PT or a PTT ' time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues in the spectrum vanishes if all classical scales are kept fixed. Numerically, we find that the transition from real to complex eigenvalues in the various ensembles display a different dependence on the coupling strength between the two resonators. These differences can be linked to the level spacing statistics in the Hermitian limit of the considered models. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

Numerical solutions of magnetohydrodynamic stability of axisymmetric toroidal plasmas using cubic B-spline finite element method

International Nuclear Information System (INIS)

Cheng, C.Z.

1988-12-01

A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, θ, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle θ and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical β/sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab

On particle creation by black holes. [Quantum mechanical state vector, gravitational collapse, Hermition scalar field, density matrix

Energy Technology Data Exchange (ETDEWEB)

Wald, R M [Chicago Univ., Ill. (USA). Lab. for Astrophysics and Space Research

1975-11-01

Hawking's analysis of particle creation by black holes is extended by explicity obtaining the expression for the quantum mechanical state vector PSI which results from particle creation starting from the vacuum during gravitational collapse. We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail with black body emission (orig./BJ).

Solving modified systems with multiple right-hand sides

Energy Technology Data Exchange (ETDEWEB)

Simoncini, V.; Gallopoulos, E. [Univ. of Patras (Greece)

1996-12-31

In this talk we discuss the iterative solution of large linear systems of the form (A + USV{sup H})X = B, where A is an n x n non-Hermitian matrix, USV{sup H} is a rank-r modification of A and B is of rank s with s, r {much_lt} n. We analyze several approaches that exploit the structure of the coefficient matrix so as to solve the systems more efficiently than if one were to apply a non-hermitian solver to the original systems. In the development of procedures, we take into account the presence of both the low-rank modification and the several right-hand sides. Interesting issues connected to this problem originate from the quest for techniques that accelerate the underlying iterative solvers: preconditioning (e.g. inner-outer iteration strategies), domain decomposition, and continuation methods. Experiments are provided to analyze the behavior of the methods depending on the structure of the rectangular matrices. Preconditioning strategies are explored for an efficient implementation on the transformed systems.

Operator bosonization on Riemann surfaces: new vertex operators

International Nuclear Information System (INIS)

Semikhatov, A.M.

1989-01-01

A new formalism is proposed for the construction of an operator theory of generalized ghost systems (bc theories of spin J) on Riemann surfaces (loop diagrams of the theory of closed strings). The operators of the bc system are expressed in terms of operators of the bosonic conformal theory on a Riemann surface. In contrast to the standard bosonization formulas, which have meaning only locally, operator Baker-Akhiezer functions, which are well defined globally on a Riemann surface of arbitrary genus, are introduced. The operator algebra of the Baker-Akhiezer functions generates explicitly the algebraic-geometric τ function and correlation functions of bc systems on Riemann surfaces

Quantization and Quantum-Like Phenomena: A Number Amplitude Approach

Science.gov (United States)

Robinson, T. R.; Haven, E.

2015-12-01

Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrödinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrödinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.

Operating systems

CERN Document Server

Tsichritzis, Dionysios C; Rheinboldt, Werner

1974-01-01

Operating Systems deals with the fundamental concepts and principles that govern the behavior of operating systems. Many issues regarding the structure of operating systems, including the problems of managing processes, processors, and memory, are examined. Various aspects of operating systems are also discussed, from input-output and files to security, protection, reliability, design methods, performance evaluation, and implementation methods.Comprised of 10 chapters, this volume begins with an overview of what constitutes an operating system, followed by a discussion on the definition and pr

Operational calculus

CERN Document Server

Boehme, Thomas K

1987-01-01

Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-ho

Spatial Operations

Directory of Open Access Journals (Sweden)

Anda VELICANU

2010-09-01

Full Text Available This paper contains a brief description of the most important operations that can be performed on spatial data such as spatial queries, create, update, insert, delete operations, conversions, operations on the map or analysis on grid cells. Each operation has a graphical example and some of them have code examples in Oracle and PostgreSQL.

Horizons of stability

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2008-01-01

Roč. 41, č. 24 (2008), 244027/1-244027/16 ISSN 1751-8113 R&D Projects: GA ČR GA202/07/1307; GA MŠk LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : SYMMETRIC QUANTUM -MECHANICS * NON-HERMITIAN HAMILTONIANS * REAL ENERGY-SPECTRA Subject RIV: BE - Theoretical Physics Impact factor: 1.540, year: 2008

PT-symmetric Quantum Chain Models

Directory of Open Access Journals (Sweden)

M. Znojil

2007-01-01

Full Text Available A review is given of certain tridiagonal N-dimensional non-Hermitian J-parametric real-matrix quantum Hamiltonians H(N. The domains Ɗ(N of reality of their spectra of energies are studied, with particular attention paid to their exceptional-point boundaries ∂Ɗ(N. The strongest admissible couplings are specified in closed form for all N.

Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2013-01-01

Roč. 336, SEP (2013), s. 98-111 ISSN 0003-4916 R&D Projects: GA ČR GAP203/11/1433 Institutional support: RVO:61389005 Keywords : Non-Hermitian quantum Hamiltonian * exceptional point * phase transition * exactly solvable model Subject RIV: BE - Theoretical Physics Impact factor: 3.065, year: 2013 http://www.sciencedirect.com/science/article/pii/S0003491613001267

Low Complexity Tail-Biting Trellises for Some Extremal Self-Dual Codes

OpenAIRE

Olocco , Grégory; Otmani , Ayoub

2002-01-01

International audience; We obtain low complexity tail-biting trellises for some extremal self-dual codes for various lengths and fields such as the [12,6,6] ternary Golay code and a [24,12,8] Hermitian self-dual code over GF(4). These codes are obtained from a particular family of cyclic Tanner graphs called necklace factor graphs.

Deformation quantization with separation of variables of an endomorphism bundle

OpenAIRE

Karabegov, Alexander

2013-01-01

Given a holomorphic Hermitian vector bundle and a star-product with separation of variables on a pseudo-Kaehler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle which also has the appropriately generalized property of separation of variables. For this star product we prove a generalization of Gammelgaard's graph-theoretic formula.

Diagonalization of the mass matrices

International Nuclear Information System (INIS)

Rhee, S.S.

1984-01-01

It is possible to make 20 types of 3x3 mass matrices which are hermitian. We have obtained unitary matrices which could diagonalize each mass matrix. Since the three elements of mass matrix can be expressed in terms of the three eigenvalues, msub(i), we can also express the unitary matrix in terms of msub(i). (Author)

Random walks and a simple chirally invariant lattice Hamiltonian without fermion doubling

International Nuclear Information System (INIS)

Belyea, C.I.

1992-01-01

It is shown that there is a simple chirally-invariant lattice Hamiltonian for fermions which is doubling-free but non-Hermitian and which may be valuable in lattice Hamiltonian studies of quantum chromodynamics. A connection is established between the existence of random walk representations of spinor propagators and this doubling-free formulation, in analogy with Wilson fermions. 15 refs

Fuzzy torus via q-Parafermion

International Nuclear Information System (INIS)

Aizawa, N; Chakrabarti, R

2007-01-01

We note that the recently introduced fuzzy torus can be regarded as a q-deformed parafermion. Based on this picture, classification of the Hermitian representations of the fuzzy torus is carried out. The result involves Fock-type representations and new finite-dimensional representations for q being a root of unity as well as already known finite-dimensional ones

THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS

Directory of Open Access Journals (Sweden)

Natalia Bakhova

2011-03-01

Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.

Operation planning device

International Nuclear Information System (INIS)

Watanabe, Takashi; Odakawa, Naoto; Erikuchi, Makoto; Okada, Masayuki; Koizumi, Atsuhiko.

1996-01-01

The device of the present invention provides a device suitable for monitoring a reactor core state and operation replanning in terms of reactor operation. Namely, (1) an operation result difference judging means judges that replanning is necessary when the operation results deviates from the operation planning, (2) an operation replanning rule data base storing means stores a deviation key which shows various kinds of states where the results deviate from the planning and a rule for replanning for returning to the operation planning on every deviating key, (3) an operation replanning means forms a new operation planning in accordance with the rule which is retrieved based on the deviation key, (4) an operation planning optimizing rule data base storing means evaluates the reformed planning and stores it on every evaluation item, (5) an operation planning optimization means correct the operation planning data so as to be optimized when the evaluation of the means (4) is less than a reference value, and (6) an operation planning display means edits adaptable operation planning data and the result of the evaluation and displays them. (I.S.)

Uncertainty principle in loop quantum cosmology by Moyal formalism

Science.gov (United States)

Perlov, Leonid

2018-03-01

In this paper, we derive the uncertainty principle for the loop quantum cosmology homogeneous and isotropic Friedmann-Lemaiter-Robertson-Walker model with the holonomy-flux algebra. The uncertainty principle is between the variables c, with the meaning of connection and μ having the meaning of the physical cell volume to the power 2/3, i.e., v2 /3 or a plaquette area. Since both μ and c are not operators, but rather the random variables, the Robertson uncertainty principle derivation that works for hermitian operators cannot be used. Instead we use the Wigner-Moyal-Groenewold phase space formalism. The Wigner-Moyal-Groenewold formalism was originally applied to the Heisenberg algebra of the quantum mechanics. One can derive it from both the canonical and path integral quantum mechanics as well as the uncertainty principle. In this paper, we apply it to the holonomy-flux algebra in the case of the homogeneous and isotropic space. Another result is the expression for the Wigner function on the space of the cylindrical wave functions defined on Rb in c variables rather than in dual space μ variables.

Quantum field theory in curved space-time

International Nuclear Information System (INIS)

Najmi, A.-H.

1982-09-01

The problem of constructing states for quantum field theories in nonstationary background space-times is set out. A formalism in which the problem of constructing states can be attacked more easily than at present is presented. The ansatz of energy-minimization as a means of constructing states is formulated in this formalism and its general solution for the free scalar field is found. It has been known, in specific cases, that such states suffer from the problem of unitary inequivalence (the pathology). An example in Minowski space-time is presented in which global operators, such as the particle-number operator, do not exist but all physical observables, such as the renormalized energy density are finite. This model has two Fock-sectors as its space of physical states. A simple extension of this model, i.e. enlarging the Fock-space of states is found not to remedy the pathology: in a Robertson-Walker space-time the quantum field acquires an infinite amount of renormalized energy density to the future of the hypersurface on which the energy density is minimized. Finally, the solution of the ansatz of energy minimization for the free, massive Hermitian fermion field is presented. (author)

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

International Nuclear Information System (INIS)

Hibberd, K.E.; Dunning, C.; Links, J.

2006-01-01

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PT-symmetric wavefunctions defined on a contour in the complex plane

Charged particle motion in a time-dependent flux-driven ring: an exactly solvable model

International Nuclear Information System (INIS)

Luan, P-G; Tang, C-S

2007-01-01

We consider a charged particle driven by a time-dependent flux threading a quantum ring. The dynamics of the charged particle is investigated using a classical treatment, a Fourier expansion technique, a time-evolution method, and the Lewis-Riesenfeld approach. We have shown that, by properly managing the boundary conditions, a time-dependent wavefunction can be obtained using a general non-Hermitian time-dependent invariant, which is a specific linear combination of initial angular-momentum and azimuthal-angle operators. It is shown that the linear invariant eigenfunction can be realized as a Gaussian-type wavepacket with a peak moving along the classical angular trajectory, while the distribution of the wavepacket is determined by the ratio of the coefficient of the initial angle to that of the initial canonical angular momentum. From the topologically nontrivial nature as well as the classical trajectory and angular momentum, one can determine the dynamical motion of the wavepacket. It should be noted that the peak position is no longer an expectation value of the angle operator, and hence the Ehrenfest theorem is not directly applicable in such a topologically nontrivial system

From Copenhagen to Neo-Copenhagen Interpretation

Science.gov (United States)

de Muynck, Willem M.

2007-12-01

Positive and negative features of the Copenhagen interpretation are discussed. As positive features can be mentioned its pragmatism and its awareness of the crucial role of measurement. However, the main part of the contribution is devoted to the negative features, to wit, its pragmatism (once again), its confounding of preparation and measurement, its classical account of measurement, its completeness claims, the ambiguity of its notion of correspondence, its confused notion of complementarity. It is demonstrated how confusions and paradoxes stemming from the negative features of the Copenhagen interpretation can be dealt with in an amended interpretation, to be referred to as `neo-Copenhagen interpretation', in which the role of the measuring instrument is taken seriously by recognizing the quantum mechanical character of its interaction with the microscopic object. The ensuing necessity of extending the notion of a quantum mechanical observable from the Hermitian operator of the standard formalism to the positive operator-valued measure of a generalized formalism yields a sound mathematical basis for a transition from the Copenhagen contextualistic-realist interpretation to the neo-Copenhagen empiricist one. Applications to the uncertainty relations and to the Bell inequalities are briefly discussed.

Operational amplifiers

CERN Document Server

Dostal, Jiri

1993-01-01

This book provides the reader with the practical knowledge necessary to select and use operational amplifier devices. It presents an extensive treatment of applications and a practically oriented, unified theory of operational circuits.Provides the reader with practical knowledge necessary to select and use operational amplifier devices. Presents an extensive treatment of applications and a practically oriented, unified theory of operational circuits

Operational circular No. 1 (Rev. 1) – Operational circulars

CERN Multimedia

HR Department

2011-01-01

Operational Circular No. 1 (Rev. 1) is applicable to members of the personnel and other persons concerned. Operational Circular No. 1 (Rev. 1) entitled "Operational circulars", approved following discussion at the Standing Concertation Committee meeting on 4 May 2011, is available on the intranet site of the Human Resources Department: https://hr-docs.web.cern.ch/hr-docs/opcirc/opcirc.asp It cancels and replaces Operational Circular No. 1 entitled "Operational Circulars” of December 1996. This new version clarifies, in particular, that operational circulars do not necessarily arise from the Staff Rules and Regulations, and the functional titles have been updated to bring them into line with the current CERN organigram. Department Head Office  

Systemic Operational Design: Enhancing the Joint Operation Planning Process

National Research Council Canada - National Science Library

Delacruz, Victor J

2007-01-01

Operational level commanders and their staffs require relevant and current joint doctrine that articulates the critical function of operational design and its role in the Joint Operation Planning Process (JOPP...

3D GIS spatial operation based on extended Euler operators

Science.gov (United States)

Xu, Hongbo; Lu, Guonian; Sheng, Yehua; Zhou, Liangchen; Guo, Fei; Shang, Zuoyan; Wang, Jing

2008-10-01

The implementation of 3 dimensions spatial operations, based on certain data structure, has a lack of universality and is not able to treat with non-manifold cases, at present. ISO/DIS 19107 standard just presents the definition of Boolean operators and set operators for topological relationship query, and OGC GeoXACML gives formal definitions for several set functions without implementation detail. Aiming at these problems, based mathematical foundation on cell complex theory, supported by non-manifold data structure and using relevant research in the field of non-manifold geometry modeling for reference, firstly, this paper according to non-manifold Euler-Poincaré formula constructs 6 extended Euler operators and inverse operators to carry out creating, updating and deleting 3D spatial elements, as well as several pairs of supplementary Euler operators to convenient for implementing advanced functions. Secondly, we change topological element operation sequence of Boolean operation and set operation as well as set functions defined in GeoXACML into combination of extended Euler operators, which separates the upper functions and lower data structure. Lastly, we develop underground 3D GIS prototype system, in which practicability and credibility of extended Euler operators faced to 3D GIS presented by this paper are validated.

Examination of Operation Quality for High-frequent Railway Operation

DEFF Research Database (Denmark)

Landex, Alex; Kaas, Anders H.

2009-01-01

take the first train in their direction. The article examines four different approaches to examine operation quality for high-frequent operation that are based on the experiences of the passengers. These approaches are the service frequency of the operation, travel time extension, a combination......The examination of operation quality for high-frequent operation requires other approaches than the typical evaluation of punctuality (trains on time) and reliability (operated trains). This is because passengers in high-frequent railway systems do not necessarily notice train delays as they just...... of the service frequency and travel time approaches, and passenger delays. The service frequency and travel time approaches are simple measurements with low complexity and complement each other. Therefore, the article recommends combining the service frequency and travel time approaches to get a more accurate...

Quantum phase transition and quench dynamics in the anisotropic Rabi model

Science.gov (United States)

Shen, Li-Tuo; Yang, Zhen-Biao; Wu, Huai-Zhi; Zheng, Shi-Biao

2017-01-01

We investigate the quantum phase transition (QPT) and quench dynamics in the anisotropic Rabi model when the ratio of the qubit transition frequency to the oscillator frequency approaches infinity. Based on the Schrieffer-Wolff transformation, we find an anti-Hermitian operator that maps the original Hamiltonian into a one-dimensional oscillator Hamiltonian within the spin-down subspace. We analytically derive the eigenenergy and eigenstate of the normal and superradiant phases and demonstrate that the system undergoes a second-order quantum phase transition at a critical border. The critical border is a straight line in a two-dimensional parameter space which essentially extends the dimensionality of QPT in the Rabi model. By combining the Kibble-Zurek mechanism and the adiabatic dynamics method, we find that the residual energy vanishes as the quench time tends to zero, which is a sharp contrast to the universal scaling where the residual energy diverges in the same limit.

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

Science.gov (United States)

Marston, J. B.; Hastings, M. B.

2005-03-01

The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

Science.gov (United States)

Chou, Chia-Chun; Kouri, Donald J

2013-04-25

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions

Energy Technology Data Exchange (ETDEWEB)

Mostafazadeh, Ali [Department of Mathematics, Koc University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul (Turkey); Mehri-Dehnavi, Hossein [Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of)], E-mail: amostafazadeh@ku.edu.tr, E-mail: mehrideh@iasbs.ac.ir

2009-03-27

A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete biorthonormal system consisting of the eigenfunctions of the Hamiltonian operator and its adjoint. We establish the equivalence of this description with the mathematicians' definition of spectral singularities for the potential v(x) = z{sub -}{delta}(x + a) + z{sub +}{delta}(x - a), where z{sub {+-}} and a are respectively complex and real parameters and {delta}(x) is the Dirac delta function. We offer a through analysis of the spectral properties of this potential and determine the regions in the space of the coupling constants z{sub {+-}} where it admits bound states and spectral singularities. In particular, we find an explicit bound on the size of certain regions in which the Hamiltonian is quasi-Hermitian and examine the consequences of imposing PT-symmetry.

Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions

International Nuclear Information System (INIS)

Mostafazadeh, Ali; Mehri-Dehnavi, Hossein

2009-01-01

A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete biorthonormal system consisting of the eigenfunctions of the Hamiltonian operator and its adjoint. We establish the equivalence of this description with the mathematicians' definition of spectral singularities for the potential v(x) = z - δ(x + a) + z + δ(x - a), where z ± and a are respectively complex and real parameters and δ(x) is the Dirac delta function. We offer a through analysis of the spectral properties of this potential and determine the regions in the space of the coupling constants z ± where it admits bound states and spectral singularities. In particular, we find an explicit bound on the size of certain regions in which the Hamiltonian is quasi-Hermitian and examine the consequences of imposing PT-symmetry

An algorithm for the calculation of three-dimensional ICRF fields in tokamak geometry

International Nuclear Information System (INIS)

Smithe, D.N.; Kammash, T.

1987-01-01

A computational scheme is developed which permits tractable calculation of three-dimensional full-wave solutions to the Vlasov-Maxwell equations under typical ion cyclotron range of frequencies (ICRF) experimental conditions. The method is unique in that power deposition to the plasma is determined via the anti-Hermitian part of a truncated warm plasma dielectric operator, rather than as the result of an assumed phenomenological collision frequency. The resulting computer code allows arbitrary variation of density, temperature, magnetic field and minority concentration in the poloidal plane by performing a convolution of poloidal modes to produce a coupled system of differential equations in the radial variable. By assuming no inhomogeneity along the toroidal axis, an inverse transform over k parallel is performed, yielding the global three-dimensional fast wave field solutions. The application of the code to TFTR-like plasmas shows a mild resonance structure in antenna loading related to the changing number of wavelengths between the antenna and the resonance layer. (author)

Microscale vortex laser with controlled topological charge

Science.gov (United States)

Wang, Xing-Yuan; Chen, Hua-Zhou; Li, Ying; Li, Bo; Ma, Ren-Min

2016-12-01

A microscale vortex laser is a new type of coherent light source with small footprint that can directly generate vector vortex beams. However, a microscale laser with controlled topological charge, which is crucial for virtually any of its application, is still unrevealed. Here we present a microscale vortex laser with controlled topological charge. The vortex laser eigenmode was synthesized in a metamaterial engineered non-Hermitian micro-ring cavity system at exceptional point. We also show that the vortex laser cavity can operate at exceptional point stably to lase under optical pumping. The microscale vortex laser with controlled topological charge can serve as a unique and general building block for next-generation photonic integrated circuits and coherent vortex beam sources. The method we used here can be employed to generate lasing eigenmode with other complex functionalities. Project supported by the “Youth 1000 Talent Plan” Fund, Ministry of Education of China (Grant No. 201421) and the National Natural Science Foundation of China (Grant Nos. 11574012 and 61521004).

An algorithm for the calculation of 3-D ICRF [Ion Cyclotron Range of Frequencies] fields in tokamak geometry

International Nuclear Information System (INIS)

Smithe, D.N.; Colestock, P.L.; Kashuba, R.J.; Kammash, T.

1987-04-01

A computational scheme is developed which permits tractable calculation of three-dimensional full-wave solutions to the Maxwell-Vlasov equations under typical Ion Cyclotron Range of Frequencies (ICRF) experimental conditions. The method is unique in that power deposition to the plasma is determined via the anti-Hermitian part of a truncated warm-plasma dielectric operator, rather than as the result of an assumed phenomenological collision frequency. The resulting computer code allows arbitrary variation of density, temperature, magnetic field, and minority concentration in the poloidal plane by performing a convolution of poloidal modes to produce a coupled system of differential equations in the radial variable. By assuming no inhomogeneity along the toroidal axis, an inverse transform over k/sub parallel/ is performed to yield the full three-dimensional field solutions. The application of the code to TFTR-like plasmas shows a mild resonance structure in antenna loading related to the changing number of wavelengths between antenna and the resonance layer. 48 figs

Delta-function potential with a complex coupling

International Nuclear Information System (INIS)

Mostafazadeh, Ali

2006-01-01

We explore the Hamiltonian operator H = -d 2 /dx 2 + zδ(x), where x element of R, δ(x) is the Dirac delta function and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a spectral singularity at E = -z 2 /4 element of R + . For Re(z) 2 /4. For the case that Re(z) > 0, H has a real, positive, continuous spectrum that is free from spectral singularities. For this latter case, we construct an associated biorthonormal system and use it to perform a perturbative calculation of a positive-definite inner product that renders H self-adjoint. This allows us to address the intriguing question of the nonlocal aspects of the equivalent Hermitian Hamiltonian for the system. In particular, we compute the energy expectation values for various Gaussian wave packets to show that the non-Hermiticity effect diminishes rapidly outside an effective interaction region

An efficient quantum algorithm for spectral estimation

Science.gov (United States)

Steffens, Adrian; Rebentrost, Patrick; Marvian, Iman; Eisert, Jens; Lloyd, Seth

2017-03-01

We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well—consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate non-Hermitian matrices. Our algorithm features an efficient quantum-classical division of labor: the time-critical steps are implemented in quantum superposition, while an interjacent step, requiring much fewer parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms.

Sustainability of environment-assisted energy transfer in quantum photobiological complexes

Energy Technology Data Exchange (ETDEWEB)

Zloshchastiev, Konstantin G. [Institute of Systems Science, Durban University of Technology (South Africa)

2017-09-15

It is shown that quantum sustainability is a universal phenomenon which emerges during environment-assisted electronic excitation energy transfer (EET) in photobiological complexes (PBCs), such as photosynthetic reaction centers and centers of melanogenesis. We demonstrate that quantum photobiological systems must be sustainable for them to simultaneously endure continuous energy transfer and keep their internal structure from destruction or critical instability. These quantum effects occur due to the interaction of PBCs with their environment which can be described by means of the reduced density operator and effective non-Hermitian Hamiltonian (NH). Sustainable NH models of EET predict the coherence beats, followed by the decrease of coherence down to a small, yet non-zero value. This indicates that in sustainable PBCs, quantum effects survive on a much larger time scale than the energy relaxation of an exciton. We show that sustainable evolution significantly lowers the entropy of PBCs and improves the speed and capacity of EET. (copyright 2017 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

[Pre-operation evaluation and intra-operation management of cochlear implantation].

Science.gov (United States)

Zhang, Dao-xing; Hu, Bao-hua; Xiao, Yu-li; Shi, Bo-ning

2004-10-01

To summarize pre-operation evaluation experiences in cochlear implantation. Performing auditory evaluation and image analysis seriously in 158 severe hearing loss or total deaf cases before cochlear implantation, comparing their performance with the findings during and post operation. Among the total 158 cases, 116 cases with normal structure, 42 cases with the abnormal findings of the inner or middle ear. Stapedial gusher happened in 6 cases, 1 case was not predicted before operation. Except 1 case with serious malformation, the findings of other 157 cases in operation were consistent with the pre-operation evaluation. We helped all patients reconstruct auditory conduction with cochlear implantation, and the average hearing level up to 37.6 dB SPL. Performing image analysis seriously before operation and planning for operation according to HRCT can do great help to cochlear implantation. The operation under the HRCT instruction has less complications.

Operating experience feedback report - Solenoid-operated valve problems

International Nuclear Information System (INIS)

Ornstein, H.L.

1991-02-01

This report highlights significant operating events involving observed or potential common-mode failures of solenoid-operated valves (SOVs) in US plants. These events resulted in degradation or malfunction of multiple trains of safety systems as well as of multiple safety systems. On the basis of the evaluation of these events, the Office for Analysis and Evaluation of Operational Data (AEOD) of the US Nuclear Regulatory Commission (NRC) concludes that the problems with solenoid-operated valves are an important issue that needs additional NRC and industry attention. This report also provides AEOD's recommendations for actions to reduce the occurrence of SOV common-mode failures. 115 refs., 7 figs., 2 tabs

Hanaro operation

International Nuclear Information System (INIS)

Lee, Ji Bok; Jeon, Byung Jin; Kwack, Byung Ho

1997-01-01

HANARO was configurated its first operating core in 1995. Long term operation test was conducted up to 3-1 cycle during 1996, in order to investigate the reactor characteristics due to fuel depletion and additional fuel loading. Now HANARO has accumulated 168.4 days of total operation time and 2,687.5 MWD of total thermal output. Reactor analysis, producing operation datum and its validation with test, periodic inspection and maintenance of the facility are continuously conducted for safe operation of the HANARO. Conducted the verification tests for installed utilization facilities, and successfully performed the radiation emergency drill. The shutdown report of TRIGA Mark II and III was submitted to MOST, and decommissioning will be started from 1997. (author). 70 tabs., 50 figs., 27 refs

Survey of Operators Knowledge of Operation and Maintenance of ...

African Journals Online (AJOL)

Result showed that the machine failures encountered during operations were as a result of poor management, inadequate maintenance practices, and lack of spare parts, obsoleteness, overloading, careless operations and poor storage of machine after use. Recommendations were therefore given to improve the operation ...

Supermanifolds and Berezin's new integral

International Nuclear Information System (INIS)

Ne'eman, Y.

1984-01-01

Berezin's new integral over a supermanifold is introduced and some of its applications are discussed. Generalized superdifferential exterior forms are outlined. The application of the concept of complementary forms to the integration over a sub-supermanifold is discussed. Commutative differentials are treated as plain commuting variables. The necessary definitions for a scalar product, possibly hermitian, are given. Characteristic classes are discussed

Deformation quantization with separation of variables of an endomorphism bundle

Science.gov (United States)

Karabegov, Alexander

2014-01-01

Given a holomorphic Hermitian vector bundle E and a star-product with separation of variables on a pseudo-Kähler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle E∗ which also has the appropriately generalized property of separation of variables. For this star product we prove a generalization of Gammelgaard's graph-theoretic formula.

Non-Kaehler attracting manifolds

International Nuclear Information System (INIS)

Dall'Agata, Gianguido

2006-01-01

We observe that the new attractor mechanism describing IIB flux vacua for Calabi-Yau compactifications has a possible extension to the landscape of non-Kaehler vacua that emerge in heterotic compactifications with fluxes. We focus on the effective theories coming from compactifications on generalized half-flat manifolds, showing that the Minkowski 'attractor points' for 3-form fluxes are special-hermitian manifolds

Examples of pseudo-bosons in quantum mechanics

International Nuclear Information System (INIS)

Bagarello, F.

2010-01-01

We discuss two physical examples of the so-called pseudo-bosons, recently introduced in connection with pseudo-hermitian quantum mechanics. In particular, we show that the so-called extended harmonic oscillator and the Swanson model satisfy all the assumptions of the pseudo-bosonic framework introduced by the author. We also prove that the biorthogonal bases they produce are not Riesz bases.

Some Families of Asymmetric Quantum MDS Codes Constructed from Constacyclic Codes

Science.gov (United States)

Huang, Yuanyuan; Chen, Jianzhang; Feng, Chunhui; Chen, Riqing

2018-02-01

Quantum maximal-distance-separable (MDS) codes that satisfy quantum Singleton bound with different lengths have been constructed by some researchers. In this paper, seven families of asymmetric quantum MDS codes are constructed by using constacyclic codes. We weaken the case of Hermitian-dual containing codes that can be applied to construct asymmetric quantum MDS codes with parameters [[n,k,dz/dx

HFETR operation management

International Nuclear Information System (INIS)

Liu Rong; Yang Shuchun; Peng Jun; Zhou Shoukang

2003-01-01

Experiences and work methods with High Flux Engineering Test Reactor (HFETR) operation are introduced, which have been accumulated in a long period of operation, in the aspects as reactor operation, test, maintenance, operator training and incident management. It's clear that the safety operation of HFETR has been ensured, and the methods are valid. (authors)

Spacecraft operations

CERN Document Server

Sellmaier, Florian; Schmidhuber, Michael

2015-01-01

The book describes the basic concepts of spaceflight operations, for both, human and unmanned missions. The basic subsystems of a space vehicle are explained in dedicated chapters, the relationship of spacecraft design and the very unique space environment are laid out. Flight dynamics are taught as well as ground segment requirements. Mission operations are divided into preparation including management aspects, execution and planning. Deep space missions and space robotic operations are included as special cases. The book is based on a course held at the German Space Operation Center (GSOC).

Symmetry breaking in the double-well hermitian matrix models

International Nuclear Information System (INIS)

Brower, R.C.; Deo, N.; Jain, S.; Tan, C.I.

1993-01-01

We study symmetry breaking in Z 2 symmetric large N matrix models. In the planar approximation for both the symmetric double-well φ 4 model and the symmetric Penner model, we find there is an infinite family of broken symmetry solutions characterized by different sets of recursion coefficients R n and S n that all lead to identical free energies and eigenvalue densities. These solutions can be parameterized by an arbitrary angle θ(x), for each value of x=n/N 4 theory the double scaling string equations are parameterized by a conserved angular momentum parameter in the range 0≤l<∞ and a single arbitrary U(1) phase angle. (orig.)

Symmetry breaking in the double-well hermitian matrix models

CERN Document Server

Brower, R C; Jain, S; Tan, C I; Brower, Richard C.; Deo, Nevidita; Jain, Sanjay; Tan, Chung-I

1993-01-01

We study symmetry breaking in $Z_2$ symmetric large $N$ matrix models. In the planar approximation for both the symmetric double-well $\\phi^4$ model and the symmetric Penner model, we find there is an infinite family of broken symmetry solutions characterized by different sets of recursion coefficients $R_n$ and $S_n$ that all lead to identical free energies and eigenvalue densities. These solutions can be parameterized by an arbitrary angle $\\theta(x)$, for each value of $x = n/N < 1$. In the double scaling limit, this class reduces to a smaller family of solutions with distinct free energies already at the torus level. For the double-well $\\phi^4$ theory the double scaling string equations are parameterized by a conserved angular momentum parameter in the range $0 \\le l < \\infty$ and a single arbitrary $U(1)$ phase angle.

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

Science.gov (United States)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

Analytical results for non-Hermitian parity–time-symmetric and ...

Indian Academy of Sciences (India)

College of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, China ... The domain part of the email address of all email addresses used by the office of Indian Academy of Sciences, including those of the staff, the journals, various programmes, and Current ... Please take note of this change.

Advanced operation strategy for feed-and-bleed operation in an OPR1000

International Nuclear Information System (INIS)

Kim, Bo Gyung; Yoon, Ho Joon; Kim, Jaewhan; Kang, Hyun Gook

2016-01-01

Highlights: • Advanced operating strategy covers all necessary conditions for F&B operation. • Advanced operating strategy identifies the urgency of F&B operation. • An advanced operating strategy for F&B operation is developed using a decision tree. • Human error probability is re-estimated based on a thermohydraulic analysis and K-HRA method. • An advanced operation strategy provides indications under various plant situations. - Abstract: When the secondary side is unavailable in a pressurized water reactor (PWR), heat from the core will accumulate in the primary side causing core damage. In this situation a heat removal mechanism called feed-and-bleed operation (F&B operation) must be used, which is a process of directly cooling the primary reactor cooling system (RCS). However, conventional operation strategy in emergency operating procedures (EOPs) does not cover all possible conditions to initiate F&B operation. If the EOP informs on the urgency of F&B operation, operators will be able to more clearly make decisions regarding F&B operation initiation. In order to cover all possible scenarios for F&B operation and systematically inform its urgency, an advanced operating strategy using a decision tree is developed in this study. The plant condition can be classified according to failure of secondary side, RCS pressure condition, injectable inventory to RCS, and remaining core inventory. RCS pressure, core level, and RCS temperature are representative indicators which provide information regarding the initiation of F&B operation. Indicators can be selected based on their detectability and quantification, and a decision tree is developed according to combinations of indicators. To estimate the effects of the advanced operation strategy, human error probability (HEP) of F&B operation is re-estimated based on a thermohydraulic analysis. The available time for operators to initiate F&B operation is also re-estimated to obtain more realistic data. This

Operator-based metric for nuclear operations automation assessment

Energy Technology Data Exchange (ETDEWEB)

Zacharias, G.L.; Miao, A.X.; Kalkan, A. [Charles River Analytics Inc., Cambridge, MA (United States)] [and others

1995-04-01

Continuing advances in real-time computational capabilities will support enhanced levels of smart automation and AI-based decision-aiding systems in the nuclear power plant (NPP) control room of the future. To support development of these aids, we describe in this paper a research tool, and more specifically, a quantitative metric, to assess the impact of proposed automation/aiding concepts in a manner that can account for a number of interlinked factors in the control room environment. In particular, we describe a cognitive operator/plant model that serves as a framework for integrating the operator`s information-processing capabilities with his procedural knowledge, to provide insight as to how situations are assessed by the operator, decisions made, procedures executed, and communications conducted. Our focus is on the situation assessment (SA) behavior of the operator, the development of a quantitative metric reflecting overall operator awareness, and the use of this metric in evaluating automation/aiding options. We describe the results of a model-based simulation of a selected emergency scenario, and metric-based evaluation of a range of contemplated NPP control room automation/aiding options. The results demonstrate the feasibility of model-based analysis of contemplated control room enhancements, and highlight the need for empirical validation.

Operative Start Time Does Not Affect Post-Operative Infection Risk.

Science.gov (United States)

Guidry, Christopher A; Davies, Stephen W; Willis, Rhett N; Dietch, Zachary C; Shah, Puja M; Sawyer, Robert G

2016-10-01

Surgical care is delivered 24 h a day at most institutions. Alarmingly, some authors have found that certain operative start times are associated with greater morbidity and mortality rates. This effect has been noted in both the public and private sector. Although some of these differences may be related to process, they may also be caused by the human circadian rhythm and corresponding changes in host defenses. We hypothesized that the time of day of an operation would impact the frequency of certain post-operative outcomes significantly. Cases at a single tertiary-care center reported to the American College of Surgeons National Surgical Quality Improvement Program over a 10-year period were identified. Operative start times were divided into six-hour blocks, with 6 am to noon serving as the reference. Standard univariable techniques were applied. Multivariable logistic regression with mixed effects modeling then was used to determine the relation between operative start times and infectious outcomes, controlling for surgeon clustering. Statistical significance was set at p operative infectious complication. Seventy percent of these infections (n = 1,506) were surgical site infections. On univariable analysis considering all cases, nighttime and evening operations had higher rates of post-operative infections than those in performed during the day (9.1% from 6 am to noon; 9.7% from noon to 6 pm; 14.8% from 6 pm to midnight; and 14.4% from midnight to 6 am; p operative start time was not associated with the risk of post-operative infection, even when emergency cases were considered independently. Our data suggest that operative start times have no correlation with post-operative infectious complications. Further work is required to identify the source of the time-dependent outcome variability observed in previous studies.

Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators

International Nuclear Information System (INIS)

Jefferies, Brian; Johnson, Gerald W.; Nielsen, Lance

2007-01-01

The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A 1 ,..., A n and associated continuous Borel probability measures μ 1 , ?, μ n on [0,1]. Fix A 1 ,..., A n . Then each choice of an n-tuple (μ 1 ,...,μ n ) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A 1 , ..., A n are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi

Co-Operative Advances in Behavioral Health and Performance Research and Operations

Science.gov (United States)

VanderArk, Stephen T.; Leveton, Lauren B.

2011-01-01

In organizations that engage in both operations and applied research, with operational needs guiding research questions and research informing improved operations, the ideal goal is a synergy of ideas and information. In reality, this ideal synergy is often lacking. Real-time operational needs driving day-to-day decisions, lack of communication, lag time in getting research advances plugged into operations can cause both areas to suffer from this gap between operations and research. At Johnson Space Center, the Behavior Health and Performance group (BHP) strives to bridge this gap by following a Human Research Program framework: Expectations of future operational needs identify the knowledge gaps; the gaps in turn guide research leading to a product that is transitioned into operations. Thus, the direction those of us in research take is in direct response to current and future needs of operations. Likewise, those of us in operations actively seek knowledge that is supported by evidence-based research. We make an ongoing effort to communicate across the research and operations gap by working closely with each other and making a conscious effort to keep each other informed. The objective of the proposed panel discussion is to demonstrate through the following presentations the results of a successful collaboration between research and operations and to provide ASMA members with more practical knowledge and strategies for building these bridges to serve our field of practice well. The panel will consist of six presenters from BHP operations, internal BHP research, and external research instigated by BHP who together represent the entire BHP Research Transition to Operations Framework

Nuclear units operating improvement by using operating experience

International Nuclear Information System (INIS)

Rotaru, I.; Bilegan, I.C.

1997-01-01

The paper presents how the information experience can be used to improve the operation of nuclear units. This areas include the following items: conservative decision making; supervisory oversight; teamwork; control room distraction; communications; expectations and standards; operator training and fundamental knowledge, procedure quality and adherence; plant status awareness. For each of these topics, the information illustrate which are the principles, the lessons learned from operating experience and the most appropriate exemplifying documents. (authors)

Operating System Security

CERN Document Server

Jaeger, Trent

2008-01-01

Operating systems provide the fundamental mechanisms for securing computer processing. Since the 1960s, operating systems designers have explored how to build "secure" operating systems - operating systems whose mechanisms protect the system against a motivated adversary. Recently, the importance of ensuring such security has become a mainstream issue for all operating systems. In this book, we examine past research that outlines the requirements for a secure operating system and research that implements example systems that aim for such requirements. For system designs that aimed to

Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach

Energy Technology Data Exchange (ETDEWEB)

Xia, Hui-Zhi; Li, Chao; Yang, Qing; Yang, Ming, E-mail: mingyang@ahu.edu.cn [Key Laboratory of Opto-electronic Information Acquisition and Manipulation, Ministry of Education, School of Physics and Material Science, Anhui University Hefei (China); Cao, Zhuo-Liang [School of Electronic Information Engineering, Hefei Normal University (China)

2012-08-15

The operator entanglement of two-qubit joint unitary operations is revisited. The Schmidt number, an important attribute of a two-qubit unitary operation, may have connection with the entanglement measure of the unitary operator. We find that the entanglement measure of a two-qubit unitary operators is classified by the Schmidt number of the unitary operators. We also discuss the exact relation between the operator entanglement and the parameters of the unitary operator. (author)

Construction of vertex operators using operator formalism techniques

International Nuclear Information System (INIS)

Gato, B.; Massachusetts Inst. of Tech., Cambridge

1989-01-01

We derive vertex operators in oscillator form as an application of the conserved charges method developed by Vafa for the operator formalism in higher genus Riemann surfaces. This construction proves to be clear, direct and valid for the bosonic and fermionic strings as wells as for twisted strings on orbifolds. We discuss the method and construct vertex operators for the bosonic string moving on Z N orbifolds and for the fermionic string in the NSR formulation. (orig.)

Seminar 1. Joint Military Operations. Application of the Operational Reserve

National Research Council Canada - National Science Library

Copp, A

1997-01-01

.... As a means of achieving decisive effect at the operational level of war, the operational reserve should be considered an operational function and should be addressed as both a planning element...

A Study on the Operator Decision Support for Feed-and-Bleed Operation

International Nuclear Information System (INIS)

Kim, Bo Gyung; Kim, Sang Ho; Kang, Hyun Gook; Yoon, Ho Joon

2014-01-01

In the case of a combined accident that includes a failure of the secondary cooling system, it is difficult for operators to recognize the necessity of an feed and bleed (F and B) operation because a lot of parameters and alarms should be checked before a decision, and operators may spend a considerable amount of time arriving at the entry for a proper emergency operating procedure that contains the procedure for an F and B operation. Therefore, a clear identification of the success boundary of an F and B operation would help operators in their decision-making when a combined accident that includes a secondary cooling system failure occurs. This study will provide a useful guideline for the initiation of an F and B operation for operators. Cooling the RCS after a scram is one of the most important safety functions for preventing core damage. To support the operator in decision making whether to initiate the F and B operation, plant conditions requiring the initiation of an F and B operation were identified. Plant conditions are affected by the steam generator inventory, RCS inventory, core inventory, and safety injection availability. The combination of accident types, component availabilities, and the initiation time of an F and B operation affect the success of the F and B operation. Operators need clear information about the RCS condition when the steam generators, the RCS's main residual heat removal mechanism, become unavailable. When this happens, the initiation of an F and B operation becomes necessary. As the number of the state increases, the necessity of an F and B operation increases. Especially, the operator should initiate an F and B operation when the RCS condition enters State 3 for Type 1 incidents or State 3-2 for Type 2 incidents. The results of this study may be useful in providing information regarding the necessity and effects of an F and B operation in a quantitative manner. In particular, in the case of a combined accident including a

Tables of Products of Tensor Operators and Stevens Operators

DEFF Research Database (Denmark)

Lindgård, Per-Anker

1975-01-01

Numerical tables of products of tensor (Racah) operators, Rl,m(J), and Stevens operators Olm(J), working within a J-multiplet are given as a function of X=J(J+1). Examples of the use of the tables, such as the calculation of commutation relations and thermal averages are given.......Numerical tables of products of tensor (Racah) operators, Rl,m(J), and Stevens operators Olm(J), working within a J-multiplet are given as a function of X=J(J+1). Examples of the use of the tables, such as the calculation of commutation relations and thermal averages are given....

Exceptional points and quantum correlations in precise measurements

International Nuclear Information System (INIS)

Thilagam, A

2012-01-01

We examine the physical manifestations of exceptional points and passage times in a two-level system which is subjected to quantum measurements and which admits a non-Hermitian description. Using an effective Hamiltonian acting in the two-dimensional space spanned by the evolving initial and final states, the effects of highly precise quantum measurements in which the monitoring device interferes significantly with the evolution dynamics of the monitored two-level system is analyzed. The dynamics of a multipartite system consisting of the two-level system, a source of external potential and the measurement device is examined using correlation measures such as entanglement and non-classical quantum correlations. Results show that the quantum correlations between the monitored (monitoring) systems is considerably decreased (increased) as the measurement precision nears the exceptional point, at which the passage time is half of the measurement duration. The results indicate that the underlying mechanism by which the non-classical correlations of quantum systems are transferred from one subsystem to another may be better revealed via use of geometric approaches. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

Squeezed states from a quantum deformed oscillator Hamiltonian

Energy Technology Data Exchange (ETDEWEB)

Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)

2016-03-11

The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.

Numerical solutions of magnetohydrodynamic stability of axisymmetric toroidal plasmas using cubic B-spline finite element method

Energy Technology Data Exchange (ETDEWEB)

Cheng, C.Z.

1988-12-01

A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, theta, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical ..beta../sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab.

An Extreme Learning Machine Based on the Mixed Kernel Function of Triangular Kernel and Generalized Hermite Dirichlet Kernel

Directory of Open Access Journals (Sweden)

Senyue Zhang

2016-01-01

Full Text Available According to the characteristics that the kernel function of extreme learning machine (ELM and its performance have a strong correlation, a novel extreme learning machine based on a generalized triangle Hermitian kernel function was proposed in this paper. First, the generalized triangle Hermitian kernel function was constructed by using the product of triangular kernel and generalized Hermite Dirichlet kernel, and the proposed kernel function was proved as a valid kernel function of extreme learning machine. Then, the learning methodology of the extreme learning machine based on the proposed kernel function was presented. The biggest advantage of the proposed kernel is its kernel parameter values only chosen in the natural numbers, which thus can greatly shorten the computational time of parameter optimization and retain more of its sample data structure information. Experiments were performed on a number of binary classification, multiclassification, and regression datasets from the UCI benchmark repository. The experiment results demonstrated that the robustness and generalization performance of the proposed method are outperformed compared to other extreme learning machines with different kernels. Furthermore, the learning speed of proposed method is faster than support vector machine (SVM methods.

Operational Design for Peace Enforcement: Lessons for the Operational Staff

National Research Council Canada - National Science Library

Neumann, Michael

2004-01-01

U.S. involvement in Somalia serves as a useful case study of the unique challenges an operational staff may face when applying operational design to the planning and execution of a peace enforcement operation. U.S...

Operational symmetries basic operations in physics

CERN Document Server

Saller, Heinrich

2017-01-01

This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato’s and Kepler’s symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups an...

Modeling operators' emergency response time for chemical processing operations.

Science.gov (United States)

Murray, Susan L; Harputlu, Emrah; Mentzer, Ray A; Mannan, M Sam

2014-01-01

Operators have a crucial role during emergencies at a variety of facilities such as chemical processing plants. When an abnormality occurs in the production process, the operator often has limited time to either take corrective actions or evacuate before the situation becomes deadly. It is crucial that system designers and safety professionals can estimate the time required for a response before procedures and facilities are designed and operations are initiated. There are existing industrial engineering techniques to establish time standards for tasks performed at a normal working pace. However, it is reasonable to expect the time required to take action in emergency situations will be different than working at a normal production pace. It is possible that in an emergency, operators will act faster compared to a normal pace. It would be useful for system designers to be able to establish a time range for operators' response times for emergency situations. This article develops a modeling approach to estimate the time standard range for operators taking corrective actions or following evacuation procedures in emergency situations. This will aid engineers and managers in establishing time requirements for operators in emergency situations. The methodology used for this study combines a well-established industrial engineering technique for determining time requirements (predetermined time standard system) and adjustment coefficients for emergency situations developed by the authors. Numerous videos of workers performing well-established tasks at a maximum pace were studied. As an example, one of the tasks analyzed was pit crew workers changing tires as quickly as they could during a race. The operations in these videos were decomposed into basic, fundamental motions (such as walking, reaching for a tool, and bending over) by studying the videos frame by frame. A comparison analysis was then performed between the emergency pace and the normal working pace operations

Operational limits and conditions and operating procedures for research reactors. Safety guide

International Nuclear Information System (INIS)

2008-01-01

This publication provides practical guidance on all important aspects of developing, formulating and presenting the operational limits and conditions as well as the operating procedures for research reactors. It covers the concept of operational limits and conditions, their content, and the responsibilities of the operating organization with respect to their establishment, modification, documentation and compliance. The guidance also covers the training of operating personnel on performing periodic testing, established by the operational limits and conditions, and operating procedures

Operational behaviour of a reactor normal operation and disturbances

International Nuclear Information System (INIS)

Geyer, K.H.

1982-01-01

During normal operation, the following topics are dealt with: primary and secondary coolant circuits - full load operation - start-up and shutdown - steady state part load diagramm. During disturbances and incidents, the following procedures are discussed: identification and detection of the events - automatic actions - manual actions of the operator - provided indications - explanation of actuated systems - basic information of reactor protection system. (RW)

Condition Monitoring Of Operating Pipelines With Operational Modal Analysis Application

Directory of Open Access Journals (Sweden)

Mironov Aleksey

2015-12-01

Full Text Available In the petroleum, natural gas and petrochemical industries, great attention is being paid to safety, reliability and maintainability of equipment. There are a number of technologies to monitor, control, and maintain gas, oil, water, and sewer pipelines. The paper focuses on operational modal analysis (OMA application for condition monitoring of operating pipelines. Special focus is on the topicality of OMA for definition of the dynamic features of the pipeline (frequencies and mode shapes in operation. The research was conducted using two operating laboratory models imitated a part of the operating pipeline. The results of finite-element modeling, identification of pipe natural modes and its modification under the influence of virtual failure are discussed. The work considers the results of experimental research of dynamic behavior of the operating pipe models using one of OMA techniques and comparing dynamic properties with the modeled data. The study results demonstrate sensitivity of modal shape parameters to modification of operating pipeline technical state. Two strategies of pipeline repair – with continuously condition-based monitoring with proposed technology and without such monitoring, was discussed. Markov chain reliability models for each strategy were analyzed and reliability improvement factor for proposed technology of monitoring in compare with traditional one was evaluated. It is resumed about ability of operating pipeline condition monitoring by measuring dynamic deformations of the operating pipe and OMA techniques application for dynamic properties extraction.

Separable quadratic stochastic operators

International Nuclear Information System (INIS)

Rozikov, U.A.; Nazir, S.

2009-04-01

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)