The topological AC effect on non-commutative phase space
Energy Technology Data Exchange (ETDEWEB)
Li, Kang [Hangzhou Teachers College, Department of Physics, Hangzhou (China); The Abdus Salam International Center for Theoretical Physics, Trieste (Italy); Wang, Jianhua [Shaanxi University of Technology, Department of Physics, Hanzhong (China); The Abdus Salam International Center for Theoretical Physics, Trieste (Italy)
2007-05-15
The Aharonov-Casher (AC) effect in non-commutative (NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp's shift method. After solving the Dirac equations both on non-commutative space and non-commutative phase space by the new method, we obtain corrections to the AC phase on NC space and NC phase space, respectively. (orig.)
Classical mechanics in non-commutative phase space
Institute of Scientific and Technical Information of China (English)
WEI Gao-Feng; LONG Chao-Yun; LONG Zheng-Wen; QIN Shui-Jie; Fu Qiang
2008-01-01
In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space.The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity.First,new Poisson brackets have been defined in non-commutative phase space.They contain corrections due to the non-commutativity of coordinates and momenta.On the basis of this new Poisson brackets,a new modified second law of Newton has been obtained.For two cases,the free particle and the harmonic oscillator,the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys.Rev.D,2005,72:025010).The consistency between both methods is demonstrated.It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space.but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.
Phase space quantization, non-commutativity and the gravitational field
Chatzistavrakidis, Athanasios
2014-01-01
In this paper we study the structure of the phase space in non-commutative geometry in the presence of a non-trivial frame. Our basic assumptions are that the underlying space is a symplectic and parallelizable manifold. Furthermore, we assume the validity of the Leibniz rule and the Jacobi identities. We consider non-commutative spaces due to the quantization of the symplectic structure and determine the momentum operators that guarantee a set of canonical commutation relations, appropriately extended to include the non-trivial frame. We stress the important role of left vs. right acting operators and of symplectic duality. This enables us to write down the form of the full phase space algebra on these non-commutative spaces, both in the non-compact and in the compact case. We test our results against the class of 4D and 6D symplectic nilmanifolds, thus presenting a large set of non-trivial examples that realize the general formalism.
Institute of Scientific and Technical Information of China (English)
WEI Gao-Feng; LONG Chao-Yun; LONG Zheng-Wen; QIN Shui-Jie
2008-01-01
In this paper,the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space;the corresponding exact energy is obtained,and the analytic eigenfunction is presented in terms of the confluent hypergeometric function.It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.
Landau-like Atomic Problem on a Non-commutative Phase Space
Mamat, Jumakari; Dulat, Sayipjamal; Mamatabdulla, Hekim
2016-06-01
We study the motion of a neutral particle in symmetric gauge and in the framework of non-commutative Quantum Mechanics. Starting from the corresponding Hamiltonian we derive the eigenfunction and eigenvalues.
A Generalized Rule For Non-Commuting Operators in Extended Phase Space
Nasiri, S; Khademi, S.; Bahrami, S; Taati, F.
2005-01-01
A generalized quantum distribution function is introduced. The corresponding ordering rule for non-commuting operators is given in terms of a single parameter. The origin of this parameter is in the extended canonical transformations that guarantees the equivalence of different distribution functions obtained by assuming appropriate values for this parameter.
Parabosonic string and space-time non-commutativity
Energy Technology Data Exchange (ETDEWEB)
Seridi, M. A.; Belaloui, N. [Laboratoire de Physique Mathematique et Subatomique, Universite Mentouri Constantine (Algeria)
2012-06-27
We investigate the para-quantum extension of the bosonic strings in a non-commutative space-time. We calculate the trilinear relations between the mass-center variables and the modes and we derive the Virasoro algebra where a new anomaly term due to the non-commutativity is obtained.
Scalar fields in a non-commutative space
Bietenholz, Wolfgang; Mejía-Díaz, Héctor; Panero, Marco
2014-01-01
We discuss the lambda phi**4 model in 2- and 3-dimensional non-commutative spaces. The mapping onto a Hermitian matrix model enables its non-perturbative investigation by Monte Carlo simulations. The numerical results reveal a phase where stripe patterns dominate. In d=3 we show that in this phase the dispersion relation is deformed in the IR regime, in agreement with the property of UV/IR mixing. This "striped phase" also occurs in d=2. For both dimensions we provide evidence that it persists in the simultaneous limit to the continuum and to infinite volume ("Double Scaling Limit"). This implies the spontaneous breaking of translation symmetry.
The He-McKellar-Wilkens effect for spin-1 particles on non-commutative space
Institute of Scientific and Technical Information of China (English)
Li Kang; Sayipjamal Dulat; Wang Jian-Hua
2008-01-01
By using star product method,the He-McKellar-Wilkeus (HMW) effect for spin-one neutral particle on noncommutative (NC) space is studied.After solving the Kemmer-like equations on NC space,we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.
Non-commutative Complex Projective Spaces and the Standard Model
Dolan, Brian P
2003-01-01
The standard model fermion spectrum, including a right handed neutrino, can be obtained as a zero-mode of the Dirac operator on a space which is the product of complex projective spaces of complex dimension two and three. The construction requires the introduction of topologically non-trivial background gauge fields. By borrowing from ideas in Connes' non-commutative geometry and making the complex spaces `fuzzy' a matrix approximation to the fuzzy space allows for three generations to emerge...
Aharonov-Casher effect for spin-1 particles in a non-commutative space
Energy Technology Data Exchange (ETDEWEB)
Mirza, B.; Narimani, R.; Zarei, M. [Isfahan University of Technology, Department of Physics, Isfahan (Iran)
2006-11-15
In this work, the Aharonov-Casher (AC) phase is calculated for spin-1 particles in a non-commutative space. The AC phase has previously been calculated from the Dirac equation in a non-commutative space using a gauge-like technique. In the spin-1 case, we use the Kemmer equation to calculate the phase in a similar manner. It is shown that the holonomy receives non-trivial kinematical corrections. By comparing the new result with the already known spin-1/2 case, one may conjecture a generalized formula for the corrections to holonomy for higher spins. (orig.)
Simulation Results for U(1) Gauge Theory on Non-Commutative Spaces
Bietenholz, W; Nishimura, J; Susaki, Y; Torrielli, A; Volkholz, J
2007-01-01
We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing issue if Wilson loops are (partially) invariant under area-preserving diffeomorphisms. We show that non-perturbatively this invariance breaks, including the subgroup SL(2,R). In both cases, d=2 and d=4, we extrapolate our results to the continuum and infinite volume by means of a Double Scaling Limit. In d=4 this limit leads to a phase with broken translation symmetry, which is not affected by the perturbatively known IR instability. Therefore the photon may survive in a non-commutative world.
Bethe-Salpeter equation in non-commutative space
Directory of Open Access Journals (Sweden)
M. Haghighat
2005-06-01
Full Text Available We consider Bethe-Salpeter (BS equation for the bound state of two point particles in the non-commutative space-time. We subsequently explore the BS equation for spin0-spin0, spin1/2-spin1/2 and spin0-spin1/2 bound states. we show that the lowest order spin independent correction to energy spectrum in each case is of the order θ a 4 while the spin dependent one in NC space, is started at the order θ a 6.
LAMB SHIFT IN HYDROGEN-LIKE ATOM INDUCED FROM NON-COMMUTATIVE QUANTUM SPACE-TIME
Directory of Open Access Journals (Sweden)
S Zaim
2015-06-01
Full Text Available In this work we present an important contribution to the non-commutative approach to the hydrogen atom to deal with lamb shift corrections. This can be done by studying the Klein-Gordon equation in a non-commutative space-time as applied to the Hydrogen atom to extract the energy levels, by considering the second-order corrections in the non commutativity parameter and by comparing with the result of the current experimental results on the Lamb shift of the 2P level to extract a bound on the parameter of non-commutativity. Phenomenologically we show that the non-commutativity effects induce lamb shift corrections.
Non-commutative covering spaces and their symmetries
DEFF Research Database (Denmark)
Canlubo, Clarisson
dened and its corresponding Galois theory. Using this and basic concepts from algebraic geometryand spectral theory, we will give a full description of the general structure of non-centralcoverings. Examples of coverings of the rational and irrational non-commutative tori will alsobe studied. Using......-commutative covering space using Galois theory of Hopfalgebroids. We will look at basic properties of classical covering spaces that generalize to thenon-commutative framework. Afterwards, we will explore a series of examples. We will startwith coverings of a point and central coverings of commutative spaces and see...... how these areclosely tied up. Coupled Hopf algebras will be presented to give a general description of coveringsof a point. We will give a complete description of the geometry of the central coverings ofcommutative spaces using the coverings of a point. A topologized version of Hopf categories willbe...
Maireche Abdelmadjid
2015-01-01
In present search, we have studied the effect of the both non commutativity of three dimensional space and phase on the Schrödinger equation with companied Harmonic oscillator potential and it’s inverse, know by isotopic Harmonic oscillator plus inverse quadratic (h.p.i.) potential, we shown that the Hermitian NC Hamiltonian formed anisotropic operator and described many physics phenomena’s, we have also derived the exact degenerated spectrum for studied potential in the first order of two in...
Simulations results for U(1) gauge theory on non-commutative spaces
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, W. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Bigarini, A. [Univ. degli Studi di Perugia (Italy). Dipt. di Fisica; Nishimura, J. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Graduate Univ. for Advanced Studies Tsukuba (Japan). Dept. of Particle and Nuclear Physics; Susaki, Y. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Tsukuba Univ. (Japan). Graduate School of Pure and Applied Science; Torrielli, A. [Massachusetts Institute of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics, Lab. for Nuclear Sciences and Dept. of Physics; Volkholz, J. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2007-11-15
We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a noncommutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing issue if Wilson loops are (partially) invariant under area-preserving diffeomorphisms. We show that non-perturbatively this invariance breaks, including the subgroup SL(2,R). In both cases, d=2 and d=4, we extrapolate our results to the continuum and infinite volume by means of a Double Scaling Limit. In d=4 this limit leads to a phase with broken translation symmetry, which is not affected by the perturbatively known IR instability. Therefore the photon may survive in a non-commutative world. (orig.)
The numerical approach to quantum field theory in a non-commutative space
Panero, Marco
2016-01-01
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is presented, and their implications are reviewed. In addition, we also discuss how related numerical techniques have been recently applied in computer simulations of dimensionally reduced supersymmetric theories.
Aspects of perturbative quantum field theory on non-commutative spaces
Blaschke, Daniel N
2016-01-01
In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces when constructing various scalar, fermionic and gauge field theories on Moyal space, and especially how the UV/IR mixing problem was solved for certain models. Finally, I outline more recent progress in constructing a renormalizable gauge field model on non-commutative space, and how one might attempt to prove renormalizability of such a model using a generalized renormalization scheme adapted to the non-commutative (and hence non-local) setting.
Directory of Open Access Journals (Sweden)
Marco Panero
2006-11-01
Full Text Available We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.
Dirac equation, hydrogen atom spectrum and the Lamb shift in dynamical non-commutative spaces
Indian Academy of Sciences (India)
S A ALAVI; N REZAEI
2017-05-01
We derive the relativistic Hamiltonian of hydrogen atom in dynamical non-commutative spaces (DNCS or $\\tau$ -space). Using this Hamiltonian we calculate the energy shift of the ground state as well the $2P_{1/2}$, $2S_{1/2}$levels. In all the cases, the energy shift depends on the dynamical non-commutative parameter $\\tau$. Using the accuracy of the energy measurement, we obtain an upper bound for $\\tau$. We also study the Lamb shift in DNCS. Both $2P_{1/2}$ and $2S_{1/2}$ levels receive corrections due to dynamical non-commutativity of space which is in contrast with the non-dynamical non-commutative spaces (NDNCS or $\\theta$-space) in which the $2S_{1/2}$ level receives no correction.
Singlet particles as cold dark matter in θ-exact non-commutative space-time
Directory of Open Access Journals (Sweden)
S A A Alavi
2017-02-01
Full Text Available First, singlet dark matter annihilation into pair charged fermions and pair bosons was studied to the first order of non-commutativity parameter in perturbative model. Our results are different from the results reported in some previous studies. Then the problem is formulated in -exact non-commutative space-time and non-perturbative model, then the exact results are presented
Abdelmadjid Maireche
2016-01-01
A novel theoretical study for the exact solvability of nonrelativistic quantum spectrum systems for potential containing coulomb and quadratic terms is discussed used both Boopp’s shift method and standard perturbation theory in both noncommutativity two dimensional real space and phase (NC-2D: RSP), it has been observed that the exact corrections for the ground states spectrum of studied potential was depended on two infinitesimals parameters and which plays an opposite rolls, and we ha...
On Some Isomorphisms between Bounded Linear Maps and Non-Commutative Lp-Spaces
Directory of Open Access Journals (Sweden)
E. J. Atto
2014-04-01
Full Text Available We define a particular space of bounded linear maps using a Von Neumann algebra and some operator spaces. By this, we prove some isomorphisms, and using interpolation in some particular cases, we get analogue of non-commutative Lp spaces.
Relativistic Spectrum of Hydrogen Atom in Space-Time Non-Commutativity
Moumni, Mustafa; Zaim, Slimane; 10.1063/1.4715429
2012-01-01
We study space-time non-commutativity applied to the hydrogen atom via the Seiberg-Witten map and its phenomenological effects. We find that it modifies the Coulomb potential in the Hamiltonian and add an r-3 part. By calculating the energies from Dirac equation using perturbation theory, we study the modifications to the hydrogen spectrum. We find that it removes the degeneracy with respect to the total angular momentum quantum number and acts like a Lamb shift. Comparing the results with experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter. N.B: In precedent works (arXiv:0907.1904, arXiv:1003.5732 and arXiv:1006.4590), we have used the Bopp Shift formulation of non-commutativity but here use it \\`a la Seiberg-Witten in the Relativistic case.
Relativistic spectrum of hydrogen atom in the space-time non-commutativity
Energy Technology Data Exchange (ETDEWEB)
Moumni, Mustafa; BenSlama, Achour; Zaim, Slimane [Matter Sciences Department, Faculty of SE and SNV, University of Biskra (Algeria); Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria); Matter Sciences Department, Faculty of Sciences, University of Batna (Algeria)
2012-06-27
We study space-time non-commutativity applied to the hydrogen atom and its phenomenological effects. We find that it modifies the Coulomb potential in the Hamiltonian and add an r{sup -3} part. By calculating the energies from Dirac equation using perturbation theory, we study the modifications to the hydrogen spectrum. We find that it removes the degeneracy with respect to the total angular momentum quantum number and acts like a Lamb shift. Comparing the results with experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter.
Encoding Phases using Commutativity and Non-commutativity in a Logical Framework
Amblard, Maxime
2011-01-01
This article presents an extension of Minimalist Categorial Gram- mars (MCG) to encode Chomsky's phases. These grammars are based on Par- tially Commutative Logic (PCL) and encode properties of Minimalist Grammars (MG) of Stabler. The first implementation of MCG were using both non- commutative properties (to respect the linear word order in an utterance) and commutative ones (to model features of different constituents). Here, we pro- pose to adding Chomsky's phases with the non-commutative tensor product of the logic. Then we could give account of the PIC just by using logical prop- erties of the framework.
First Simulation Results for the Photon in a Non-Commutative Space
Bietenholz, W; Nishimura, J; Susaki, Y; Volkholz, J
2005-01-01
We present preliminary simulation results for QED in a non-commutative 4d space-time, which is discretized to a fuzzy lattice. Its numerical treatment becomes feasible after its mapping onto a dimensionally reduced twisted Eguchi-Kawai matrix model. In this formulation we investigate the Wilson loops and in particular the Creutz ratios. This is an ongoing project which aims at non-perturbative predictions for the photon, which can be confronted with phenomenology in order to verify the possible existence of non-commutativity in nature.
Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory
Landau, Olav Arnfinn
2011-01-01
This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o
Electrodynamics in Non-commutative Curved Space Time
Jafari, Abolfazl
2009-01-01
We study the issue of the electrodynamics theory in noncommutative curved space time (NCCST) with a new star-product. In this paper, the motion equation of electrodynamics and canonical energy-momentum tensor in noncommutative curved space time will be found. The most important point is the assumption of the noncommutative parameter ($\\theta$) be $x^{\\m}$-independent.
Non Hermitian quantum mechanics in non commutative space
Giri, Pulak Ranjan
2008-01-01
We study non Hermitian quantum systems in noncommutative space as well as a \\cal{PT} symmetric deformation of this space. Specifically, a \\mathcal{PT}-symmetric harmonic oscillator together with iC(x_1+x_2) interaction is discussed in this space and solutions are obtained. It is shown that in the \\cal{PT} deformed noncommutative space the Hamiltonian may or may not possess real eigenvalues depending on the choice of the noncommutative parameters. However, it is shown that in standard noncommutative space, the iC(x_1+x_2) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not \\mathcal{PT}-symmetric. A complex interacting anisotropic oscillator system has also been discussed.
Toeplitz Quantization for Non-commutating Symbol Spaces such as SUq(2
Directory of Open Access Journals (Sweden)
Sontz Stephen Bruce
2016-08-01
Full Text Available Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group SUq(2 is such an algebra. Unlike many quantization schemes, this Toeplitz quantization does not require a measure. The theory is based on the mathematical structures defined and studied in several recent papers of the author; those papers dealt with some specific examples of this new Toeplitz quantization. Annihilation and creation operators are defined as densely defined Toeplitz operators acting in a quantum Hilbert space, and their commutation relations are discussed. At this point Planck’s constant is introduced into the theory. Due to the possibility of non-commuting symbols, there are now two definitions for anti-Wick quantization; these two definitions are equivalent in the commutative case. The Toeplitz quantization introduced here satisfies one of these definitions, but not necessarily the other. This theory should be considered as a second quantization, since it quantizes non-commutative (that is, already quantum objects. The quantization theory presented here has two essential features of a physically useful quantization: Planck’s constant and a Hilbert space where natural, densely defined operators act.
Zaim, Slimane
2015-01-01
We study the effect of the non-commutativity on the creation of scalar particles from vacuum in the anisotropic universe space-time. We derive the deformed Klein-Gordon equation up to second order in the non-commutativity parameter using the general modified field equation. Then the canonical method based on Bogoliubov transformation is applied to calculate the probability of particle creation in vacuum and the corresponding number density in the $k$ mode. We deduce that the non-commutative space-time introduces a new source of particle creation.
Cosmic microwave background polarization in non-commutative space-time
Tizchang, S.; Batebi, S.; Haghighat, M.; Mohammadi, R.
2016-09-01
In the standard model of cosmology (SMC) the B-mode polarization of the CMB can be explained by the gravitational effects in the inflation epoch. However, this is not the only way to explain the B-mode polarization for the CMB. It can be shown that the Compton scattering in the presence of a background, besides generating a circularly polarized microwave, can lead to a B-mode polarization for the CMB. Here we consider the non-commutative (NC) space-time as a background to explore the CMB polarization at the last scattering surface. We obtain the B-mode spectrum of the CMB radiation by scalar perturbation of metric via a correction on the Compton scattering in NC-space-time in terms of the circular polarization power spectrum and the non-commutative energy scale. It can be shown that even for the NC scale as large as 20 TeV the NC-effects on the CMB polarization and the r parameter are significant. We show that the V-mode power spectrum can be obtained in terms of linearly polarized power spectrum in the range of micro- to nano-kelvin squared for the NC scale of about 1-20 TeV, respectively.
Cosmic microwave background polarization in non-commutative space-time
Energy Technology Data Exchange (ETDEWEB)
Tizchang, S.; Batebi, S. [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Haghighat, M. [Shiraz University, Department of Physics, Shiraz (Iran, Islamic Republic of); Mohammadi, R. [Iran Science and Technology Museum (IRSTM), Tehran (Iran, Islamic Republic of)
2016-09-15
In the standard model of cosmology (SMC) the B-mode polarization of the CMB can be explained by the gravitational effects in the inflation epoch. However, this is not the only way to explain the B-mode polarization for the CMB. It can be shown that the Compton scattering in the presence of a background, besides generating a circularly polarized microwave, can lead to a B-mode polarization for the CMB. Here we consider the non-commutative (NC) space-time as a background to explore the CMB polarization at the last scattering surface. We obtain the B-mode spectrum of the CMB radiation by scalar perturbation of metric via a correction on the Compton scattering in NC-space-time in terms of the circular polarization power spectrum and the non-commutative energy scale. It can be shown that even for the NC scale as large as 20 TeV the NC-effects on the CMB polarization and the r parameter are significant. We show that the V-mode power spectrum can be obtained in terms of linearly polarized power spectrum in the range of micro- to nano-kelvin squared for the NC scale of about 1-20 TeV, respectively. (orig.)
Self quartic interaction for a scalar field in a non-commutative space with Lorentz invariance
Energy Technology Data Exchange (ETDEWEB)
Neves, M.J.; Abreu, Everton M.C. [UFRRJ, Seropedica, RJ (Brazil)
2013-07-01
Full text: The framework Doplicher-Fredenhagen-Roberts (DFR) of a noncommutative (NC) space-time is considered as alternative approach to study the NC space-time of the early Universe. In this formalism, the parameter of noncommutative θ{sup μν} is promoted to a coordinate of the space-time. The consequence of this statement is that we are describing a NC field theory with Lorentz invariance in a space-time with extra-dimension. The addition of a canonical momentum associated to θ-coordinate is a extension of the NC DFR, in which the effects of a new physics can emerge in the propagation of the fields along the extra-dimension. This extension is called Doplicher-Fredenhagen-Roberts-Amorim (DFRA) NC space-time. The main concept that we would like to emphasize from the outset is that the formalism demonstrated here will not be constructed introducing a NC parameter in the system, as usual. It will be generated naturally from an already NC space. We study a scalar field with self-quartic interaction ϕ{sup 4} ∗ in the approach of non-commutative space with Lorentz invariance. We compare the two frameworks, DFR and DFRA NC space-time. We obtain the Feynman rules in the Fourier space for the scalar propagator and vertex. The divergences are analyzed at the one loop approximation, in which the non-commutativity scale can improve the ultraviolet behavior for the mass correction in the propagator. (author)
The Aharonov-Casher effect for spin-1 particles in non-commutative quantum mechanics
Dulat, Sayipjamal
2008-01-01
By using a generalized Bopp's shift formulation, instead of star product method, we investigate the Aharonov-Casher(AC) effect for a spin-1 neutral particle in non-commutative(NC) quantum mechanics. After solving the Kemmer equations both on a non-commutative space and a non-commutative phase space, we obtain the corrections to the topological phase of the AC effect for a spin-1 neutral particle both on a NC space and a NC phase space.
Non-commutative and commutative vacua effects in a scalar torsion scenario
Energy Technology Data Exchange (ETDEWEB)
Sheikhahmadi, Haidar, E-mail: h.sh.ahmadi@gmail.com [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of); Aghamohammadi, Ali, E-mail: a.aghamohamadi@iausdj.ac.ir [Sanandaj Branch, Islamic Azad University, Sanandaj (Iran, Islamic Republic of); Saaidi, Khaled, E-mail: ksaaidi@uok.ac.ir [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)
2015-10-07
In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
Non-commutative and commutative vacua effects in a scalar torsion scenario
Directory of Open Access Journals (Sweden)
Haidar Sheikhahmadi
2015-10-01
Full Text Available In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
Wigner Functions for harmonic oscillator in noncommutative phase space
Wang, Jianhua; Li, Kang; Dulat, Sayipjamal
2009-01-01
We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schr\\"{o}dinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the harmonic oscillator on NC space and NC phase space respectively.
Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics
Directory of Open Access Journals (Sweden)
Peter A. Horváthy
2006-12-01
Full Text Available Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1. Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
The Aharonov-Casher effect for spin-1 particles in non-commutative quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Dulat, S. [Xinjiang University, School of Physics Science and Technology, Urumqi (China); The Abdus Salam International Center for Theoretical Physics, Trieste (Italy); Li, Kang [Hangzhou Normal University, Department of Physics, Hangzhou (China); The Abdus Salam International Center for Theoretical Physics, Trieste (Italy)
2008-03-15
By using a generalized Bopp's shift formulation, instead of the star product method, we investigate the Aharonov-Casher (AC) effect for a spin-1 neutral particle in non-commutative (NC) quantum mechanics. After solving the Kemmer equations both on a non-commutative space and a non-commutative phase space, we obtain the corrections to the topological phase of the AC effect for a spin-1 neutral particle both on a NC space and a NC phase space. (orig.)
On Non-commutative Geodesic Motion
Ulhoa, S C; Santos, A F
2013-01-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
On non-commutative geodesic motion
Ulhoa, S. C.; Amorim, R. G. G.; Santos, A. F.
2014-07-01
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.
Non-commutative Nash inequalities
Energy Technology Data Exchange (ETDEWEB)
Kastoryano, Michael [NBIA, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen (Denmark); Temme, Kristan [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena California 91125 (United States)
2016-01-15
A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L{sub p} spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups.
Explicit Derivation of Yang-Mills Self-Dual Solutions on non-Commutative Harmonic Space
Belhaj, A; Sahraoui, E L; Saidi, E H
2001-01-01
We develop the noncommutative harmonic space (NHS) analysis to study the problem of solving the non-linear constraint eqs of noncommutative Yang-Mills self-duality in four-dimensions. We show that this space, denoted also as NHS($\\eta,\\theta$), has two SU(2) isovector deformations $\\eta^{(ij)}$ and $\\theta^{(ij)}$ parametrising respectively two noncommutative harmonic subspaces NHS($\\eta,0$) and NHS($0,\\theta$) used to study the self-dual and anti self-dual noncommutative Yang-Mills solutions. We formulate the Yang-Mills self-dual constraint eqs on NHS($\\eta,0$) by extending the idea of harmonic analyticity to linearize them. Then we give a perturbative self-dual solution recovering the ordinary one. Finally we present the explicit computation of an exact self-dual solution.
Bhar, Piyali
2014-01-01
In this paper we are interested to search whether wormhole solutions exists in different dimensional noncommutative inspired spacetime.It is well known that noncommutativity of the space is an outcome of the string theory and it replaced the usual point like object by a smeared object.Here we have chosen Lorentzian distribution as the density function in the noncommutative inspired spacetime.We have observed that the wormhole solution exists only in four and five dimension,however higher than five dimension no wormhole exists.
Energy Technology Data Exchange (ETDEWEB)
Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)
2014-12-01
In this paper we ask whether the wormhole solutions exist in different dimensional noncommutativity-inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point-like object by a smeared object. Here we have chosen the Lorentzian distribution as the density function in the noncommutativity-inspired spacetime. We have observed that the wormhole solutions exist only in four and five dimensions; however, in higher than five dimensions no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In the usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat. (orig.)
Chiral bosonization for non-commutative fields
Das, A; Méndez, F; López-Sarrion, J; Das, Ashok; Gamboa, Jorge; M\\'endez, Fernando; L\\'opez-Sarri\\'on, Justo
2004-01-01
A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to $(1+ \\theta^2)$ where $\\theta$ is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to $ c^{\\prime} = c \\sqrt{1+\\theta^2} $ where $c$ is the speed of light. Lorentz invariance remains intact if $c$ is rescaled by $c \\to c^{\\prime}$. The dispersion relation for bosons and fermions, in this case, is given by $\\omega = c^{\\prime} | k|$.
The space of Penrose tilings and the non-commutative curve with homogeneous coordinate ring k
Smith, S Paul
2011-01-01
We construct a non-commutative scheme that behaves as if it is the space of Penrose tilings of the plane. Let k be a field and B=k(y^2). We consider B as the homogeneous coordinate ring of a non-commutative projective scheme. The category of "quasi-coherent sheaves" on it is, by fiat, the quotient category QGr(B):=Gr(B)/Fdim(B) and the category of coherent sheaves on it is qgr(B):=gr(B)/fdim(B), where gr(B) is the category of finitely presented graded modules and fdim(B) is the full subcategory of finite dimensional graded modules. We show that QGr B is equivalent to Mod S, the category of left modules over the ring S that is the direct limit of the directed system of finite dimensional semisimple algebras S_n=M_{f_n}(k) + M_{f_{n-1}}(k) where f_{n-1} and f_n$ are adjacent Fibonacci numbers and the maps S_n \\to S_{n+1} are (a,b)--->(diag(a,b),a). When k is the complex numbers, the norm closure of S is the C^*-algebra Connes uses to view the space of Penrose tilings as a non-commutative space. Objects in QGr B...
A review of non-commutative gauge theories
Indian Academy of Sciences (India)
N G Deshpande
2003-02-01
Construction of quantum ﬁeld theory based on operators that are functions of non-commutative space-time operators is reviewed. Examples of 4 theory and QED are then discussed. Problems of extending the theories to () gauge theories and arbitrary charges in QED are considered. Construction of standard model on non-commutative space is then brieﬂy discussed. The phenomenological implications are then considered. Limits on non-commutativity from atomic physics as well as accelerator experiments are presented.
Non-commutativity in polar coordinates
Energy Technology Data Exchange (ETDEWEB)
Edwards, James P. [Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria, Instituto de Fisica y Matematicas, Morelia, Michoacan (Mexico)
2017-05-15
We reconsider the fundamental commutation relations for non-commutative R{sup 2} described in polar coordinates with non-commutativity parameter θ. Previous analysis found that the natural transition from Cartesian coordinates to the traditional polar system led to a representation of [r, φ] as an everywhere diverging series. In this article we compute the Borel resummation of this series, showing that it can subsequently be extended throughout parameter space and hence provide an interpretation of this commutator. Our analysis provides a complete solution for arbitrary r and θ that reproduces the earlier calculations at lowest order and benefits from being generally applicable to problems in a two-dimensional non-commutative space. We compare our results to previous literature in the (pseudo-)commuting limit, finding a surprising spatial dependence for the coordinate commutator when θ >> r{sup 2}. Finally, we raise some questions for future study in light of this progress. (orig.)
Exploring the thermodynamics of non-commutative scalar fields
Brito, Francisco A
2015-01-01
We study the thermodynamic properties of the Bose-Einstein condensate (BEC) in the context of the quantum field theory with non-commutative target space. Our main goal is to investigate in which temperature and/or energy regimes the non-commutativity can characterize some influence in the BEC properties described by a relativistic massive non-commutative boson gas. The non-commutative parameters play a key role in the modified dispersion relations of the non-commutative fields, leading to a new phenomenology. We have obtained the condensate fraction, internal energy, pressure and specific heat of the system and taken ultra-relativistic (UR) and non-relativistic limits (NR). The non-commutative effects in the thermodynamic properties of the system are discussed. We found that there appear interesting signatures around the critical temperature.
Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups
Energy Technology Data Exchange (ETDEWEB)
Guedes, Carlos; Oriti, Daniele [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany); Raasakka, Matti [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam (Germany); LIPN, Institut Galilée, Université Paris-Nord, 99, av. Clement, 93430 Villetaneuse (France)
2013-08-15
The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-product carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.
Parity-dependent non-commutative quantum mechanics
Chung, Won Sang
2017-01-01
In this paper, we consider the non-commutative quantum mechanics (NCQM) with parity (or space reflection) in two dimensions. Using the parity operators Ri, we construct the deformed Heisenberg algebra with parity in the non-commutative plane. We use this algebra to discuss the isotropic harmonic Hamiltonian with parity.
Gaussian processes in non-commutative probability theory
Guţǎ, M.I.
2002-01-01
The generalisation of the notion of Gaussian processes from probability theory is investigated in the context of non-commutative probability theory. A non-commutative Gaussian process is viewed as a linear map from an infinite dimensional (real) Hilbert space into an algebra with involution and a po
Chiral bosonization for non-commutative fields
Energy Technology Data Exchange (ETDEWEB)
Das, Ashok [Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627-0171 (United States)]. E-mail: das@pas.rochester.edu; Gamboa, Jorge [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile); Mendez, Fernando [INFN, Laboratorio Nazionali del Gran Sasso, SS, 17bis, 67010 Asergi, L' Aquila (Italy); Lopez-Sarrion, Justo [Departamento de Fisica Teorica, Universidad de Zaragoza, Zaragoza 50009 (Spain)
2004-05-01
A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to (1+{theta}{sup 2}) where {theta} is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to c' = c(1+{theta}{sup 2}){sup 1/2} where c is the speed of light. Lorentz invariance remains intact if c is rescaled by c{yields}c'. The dispersion relation for bosons and fermions, in this case, is given by {omega} = c' vertical bar k vertical bar. (author)
Bastos, Catarina; Dias, Nuno Costa; Prata, João Nuno
2012-01-01
We show that a possible violation of the Robertson-Schr\\"odinger uncertainty principle may signal the existence of a deformation of the Heisenberg-Weyl algebra. More precisely, we prove that any Gaussian in phase-space (even if it violates the Robertson-Schr\\"odinger uncertainty principle) is always a quantum state of an appropriate non-commutative extension of quantum mechanics. Conversely, all canonical non-commutative extensions of quantum mechanics display states that violate the Robertson-Schr\\"odinger uncertainty principle.
Dimensional regularization and renormalization of non-commutative QFT
Gurau, R
2007-01-01
Using the recently introduced parametric representation of non-commutative quantum field theory, we implement here the dimensional regularization and renormalization of the vulcanized $\\Phi^{\\star 4}_4$ model on the Moyal space.
Non-Commutative Geometry, Categories and Quantum Physics
Bertozzini, Paolo; Lewkeeratiyutkul, Wicharn
2008-01-01
After an introduction to some basic issues in non-commutative geometry (Gel'fand duality, spectral triples), we present a "panoramic view" of the status of our current research program on the use of categorical methods in the setting of A.Connes' non-commutative geometry: morphisms/categories of spectral triples, categorification of Gel'fand duality. We conclude with a summary of the expected applications of "categorical non-commutative geometry" to structural questions in relativistic quantum physics: (hyper)covariance, quantum space-time, (algebraic) quantum gravity.
Non-commutativity in polar coordinates
Edwards, James P
2016-01-01
We reconsider the fundamental commutation relations for non-commutative $\\mathbb{R}^{2}$ described in polar coordinates with non-commutativity parameter $\\theta$. Previous analysis found that the natural transition from Cartesian coordinates to polars led to a representation of $\\left[\\hat{r}, \\hat{\\varphi}\\right]$ as an everywhere diverging series. We compute the Borel resummation of this series, showing that it can subsequently be extended throughout parameter space and hence provide an interpretation of this commutator. Our analysis provides a complete solution for arbitrary $r$ and $\\theta$ that reproduces the earlier calculations at lowest order. We compare our results to previous literature in the (pseudo-)commuting limit, finding a surprising spatial dependence for the coordinate commutator when $\\theta \\gg r^{2}$. We raise some questions for future study in light of this progress.
Two Approaches to Non-Commutative Geometry
Kisil, V V
1997-01-01
Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)--to Klein. We will see that they are not rivalling but are tied (by Galois). We also examine their modern life as philosophies of non-commutative geometry. Connections between different objects (see keywords) are discussed. Keywords: Heisenberg group, Weyl commutation relation, Manin plain, quantum groups, SL(2, R), Hardy space, Bergman space, Segal-Bargmann space, Szeg"o projection, Bergman projection, Clifford analysis, Moebius transformations, functional calculus, Weyl calculus (quantization), Berezin quantization, Wick ordering, quantum mechanics.
Gravity in Non-Commutative Geometry
Chamseddine, A H; Fröhlich, J
1993-01-01
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gravity. This field is geometrically interpreted as describing the distance between the two points in the internal space.
On the renormalization of non-commutative field theories
Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael
2013-01-01
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
Alexander, S; Magueijo, J; Alexander, Stephon; Brandenberger, Robert; Magueijo, Joao
2001-01-01
We show how a radiation dominated universe subject to space-time quantization may give rise to inflation as the radiation temperature exceeds the Planck temperature. We consider dispersion relations with a maximal momentum (i.e. a mimimum Compton wavelength, or quantum of space), noting that some of these lead to a trans-Planckian branch where energy increases with decreasing momenta. This feature translates into negative radiation pressure and, in well-defined circumstances, into an inflationary equation of state. We thus realize the inflationary scenario without the aid of an inflaton field. As the radiation cools down below the Planck temperature, inflation gracefully exits into a standard Big Bang universe, dispensing with a period of reheating. Thermal fluctuations in the radiation bath will in this case generate curvature fluctuations on cosmological scales whose amplitude and spectrum can be tuned to agree with observations.
Klein-Gordon oscillators in noncommutative phase space
Institute of Scientific and Technical Information of China (English)
WANG Jian-Hua; LI Kang; Dulat Sayipjamal
2008-01-01
We study the Klein-Gordon oscillators in non-commutative (NC) phase space.We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field.By solving the Klein-Gordon equation in NC phase space,we obtain the energy levels of the Klein-Gordon oscillators,where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.
The topological AC effect on noncommutative phase space
Li, K; Li, Kang; Wang, Jianhua
2006-01-01
The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is studied. Instead of using the star product method, we use a generalization of Bopp's shift method. After solving the Dirac equations both on noncommutative space and noncommutative phase space by the new method, we obtain the corrections to AC phase on NC space and NC phase space respectively.
Late time acceleration in a non-commutative model of modified cosmology
Energy Technology Data Exchange (ETDEWEB)
Malekolkalami, B., E-mail: b.malakolkalami@uok.ac.ir [Department of Physics, University of Kurdistan, Pasdaran St., Sanandaj (Iran, Islamic Republic of); Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir [Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz (Iran, Islamic Republic of); Vakili, B., E-mail: b-vakili@iauc.ac.ir [Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)
2014-12-12
We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.
Late time acceleration in a non-commutative model of modified cosmology
Malekolkalami, B.; Atazadeh, K.; Vakili, B.
2014-12-01
We investigate the effects of non-commutativity between the position-position, position-momentum and momentum-momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.
Late time acceleration in a non-commutative model of modified cosmology
Directory of Open Access Journals (Sweden)
B. Malekolkalami
2014-12-01
Full Text Available We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.
Non-linear Vacuum Phenomena in Non-commutative QED
Alvarez-Gaumé, Luís
2001-01-01
We show that the classic results of Schwinger on the exact propagation of particles in the background of constant field-strengths and plane waves can be readily extended to the case of non-commutative QED. It is shown that non-perturbative effects on constant backgrounds are the same as their commutative counterparts, provided the on-shell gauge invariant dynamics is referred to a non-perturbatively related space-time frame. For the case of the plane wave background, we find evidence of the effective extended nature of non-commutative particles, producing retarded and advanced effects in scattering. Besides the known `dipolar' character of non-commutative neutral particles, we find that charged particles are also effectively extended, but they behave instead as `half-dipoles'.
Non-topological non-commutativity in string theory
Guttenberg, Sebastian; Kreuzer, Maximilian; Rashkov, Radoslav
2007-01-01
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topolocial sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born--Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR--fields are also discus...
Functional approach to squeezed states in non commutative theories
Lubo, M
2004-01-01
We review some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and the commutators in these theories generically leads to a harmonic oscillator whose position mean value is not strictly equal to the one predicted by classical mechanics. This raises the question of the nature of quasi classical states in these models. We propose an extension based on a variational principle. The action considered is the sum of the squares of the terms associated to the non trivial Heisenberg uncertainty relations. We first verify that our proposal works in the usual theory: we recover the known gaussian functions and, besides them, other states which can be expressed as products of gaussians with specific hypergeometrics. We illustrate our construction in three models defined on a four dimensional phase space: two models endowed with a minimal length uncertainty and the non commutative p...
Quantum dynamics of simultaneously measured non-commuting observables
Hacohen-Gourgy, Shay; Martin, Leigh S.; Flurin, Emmanuel; Ramasesh, Vinay V.; Whaley, K. Birgitta; Siddiqi, Irfan
2016-10-01
In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenberg’s uncertainty principle limits the intrinsic precision of a state. Although theoretical work has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a ‘single quadrature’ measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification, adaptive measurement, measurement-based state steering and continuous quantum error correction. As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way to study how notions of contemporary
Energy Technology Data Exchange (ETDEWEB)
Privault, N. [Universite d`Evry, 91 (France)
1996-05-20
Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs.
Covariant non-commutative space–time
Directory of Open Access Journals (Sweden)
Jonathan J. Heckman
2015-05-01
Full Text Available We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation introduces a short-distance scale ℓp, and thus breaks scale invariance, but preserves all space–time isometries. The non-commutative algebra is defined on space–times with non-zero constant curvature, i.e. dS4 or AdS4. The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor. The polarization tensor takes active part in the non-commutative algebra, which for dS4 takes the form of so(5,1, while for AdS4 it assembles into so(4,2. The structure of the non-commutative correlation functions hints that the deformed theory contains gravitational interactions and a Regge-like trajectory of higher spin excitations.
Grand Unification in Non-Commutative Geometry
Chamseddine, A H; Fröhlich, J
1993-01-01
The formalism of non-commutative geometry of A. Connes is used to construct models in particle physics. The physical space-time is taken to be a product of a continuous four-manifold by a discrete set of points. The treatment of Connes is modified in such a way that the basic algebra is defined over the space of matrices, and the breaking mechanism is planted in the Dirac operator. This mechanism is then applied to three examples. In the first example the discrete space consists of two points, and the two algebras are taken respectively to be those of $2\\times 2$ and $1\\times 1$ matrices. With the Dirac operator containing the vacuum breaking $SU(2)\\times U(1)$ to $U(1)$, the model is shown to correspond to the standard model. In the second example the discrete space has three points, two of the algebras are identical and consist of $5\\times 5$ complex matrices, and the third algebra consists of functions. With an appropriate Dirac operator this model is almost identical to the minimal $SU(5)$ model of Georgi...
Some operator ideals in non-commutative functional analysis
Fidaleo, F
1997-01-01
We characterize classes of linear maps between operator spaces $E$, $F$ which factorize through maps arising in a natural manner via the Pisier vector-valued non-commutative $L^p$ spaces $S_p[E^*]$ based on the Schatten classes on the separable Hilbert space $l^2$. These classes of maps can be viewed as quasi-normed operator ideals in the category of operator spaces, that is in non-commutative (quantized) functional analysis. The case $p=2$ provides a Banach operator ideal and allows us to characterize the split property for inclusions of $W^*$-algebras by the 2-factorable maps. The various characterizations of the split property have interesting applications in Quantum Field Theory.
Non-commutative standard model: model building
Chaichian, Masud; Presnajder, P
2003-01-01
A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U sub * (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just 0,+-1. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the U sub * (3) x U sub * (2) x U sub * (1) gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherentCP violation and new neutrino interactions. (orig.)
Quantum Mechanics: Harbinger of a Non-Commutative Probability Theory?
Hiley, Basil J.
2014-01-01
In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to see the structure of quantum processes in terms of non-commutative probability theory, a non-Boolean structure of the implicate order which contains Boolean sub-structures which accommodates the explicate classical world. We move away from mechanical `wave...
Limit Algebras of Differential Forms in Non-Commutative Geometry
Indian Academy of Sciences (India)
S J Bhatt; A Inoue
2008-08-01
Given a C∗-normed algebra A which is either a Banach ∗-algebra or a Frechet ∗-algebra, we study the algebras ∞A and A obtained by taking respectively the projective limit and the inductive limit of Banach ∗-algebras obtained by completing the universal graded differential algebra ∗A of abstract non-commutative differential forms over A. Various quantized integrals on ∞A induced by a K-cycle on A are considered. The GNS-representation of ∞A defined by a d-dimensional non-commutative volume integral on a d+-summable K-cycle on A is realized as the representation induced by the left action of A on ∗A. This supplements the representation A on the space of forms discussed by Connes (Ch. VI.1, Prop. 5, p. 550 of [C]).
Non-commutative Field Theory on S^4
Nakayama, R; Nakayama, Ryuichi; Shimono, Yusuke
2004-01-01
In the previous paper (hep-th/0402010) we proposed a matrix configuration for a non-commutative S^4 (NC4S) and constructed a non-commutative (star) product for field theories on NC4S. This star product and the functions on NC4S turned out to be singular (ambiguous) on a circle on S^4. In the present paper we will show that any matrix can be expanded in terms of the matrix configuration representing NC4S just like any matrix can be expanded into symmetrized products of the matrix configuration for non-commutative S^2. Then we will show that the singularities of the functions on S^4 and the star product can be removed by covering the (commutative) manifold by coordinate neighborhoods and performing appropriate coordinate transformations. Finally a scalar field theory on NC4S is constructed. Our matrix configuration describes two S^4's joined at the circle and the Matrix theory action contains a projection matrix inside the trace to restrict the space of matrices to that for one S^4.
Non-topological non-commutativity in string theory
Energy Technology Data Exchange (ETDEWEB)
Guttenberg, S. [NCSR Demokritos, INP, Patriarchou Gregoriou and Neapoleos Str., 15310 Agia Paraskevi Attikis (Greece); Herbst, M. [CERN, 1211 Geneva 23 (Switzerland); Kreuzer, M. [Institute for Theoretical Physics, TU Wien, Wiedner Hauptstr. 8-10, 1040 Vienna (Austria); Rashkov, R. [Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna (Austria)
2008-04-15
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topological sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born-Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR-fields are also discussed. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Functional approach to squeezed states in non commutative theories
Lubo, Musongela
2004-05-01
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and the commutators in these theories generically leads to a harmonic oscillator whose positions and momenta mean values are not strictly equal to the ones predicted by classical mechanics. This raises the question of the nature of quasi classical states in these models. We propose an extension based on a variational principle. The action considered is the sum of the absolute values of the expressions associated to the non trivial Heisenberg uncertainty relations. We first verify that our proposal works in the usual theory i.e. we recover the known gaussian functions. Besides them, we find other states which can be expressed as products of gaussians with specific hyper geometrics. We illustrate our construction in two models defined on a four dimensional phase space: a model endowed with a minimal length uncertainty and the non commutative plane. Our proposal leads to second order partial differential equations. We find analytical solutions in specific cases. We briefly discuss how our proposal may be applied to the fuzzy sphere and analyze its shortcomings.
Energy-momentum tensors for non-commutative Abelian Proca field
Darabi, F
2014-01-01
We study two different possibilities of constructing the energy-momentum tensors for non-commutative Abelian Proca field, by using (i) general Noether theorem and (ii) coupling to a weak external gravitational field. Both energy-momentum tensors are not traceless due to the violation of Lorentz invariance in non-commutative spaces. In particular, we show that the obtained energy density of the latter case coincides exactly with that of obtained by Dirac quantization method.
Non-commutative multi-dimensional cosmology
Khosravi, N; Sepangi, H R
2006-01-01
A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these problems find natural solutions in a universe described by an increasing time parameter.
Can non-commutativity resolve the big-bang singularity?
Energy Technology Data Exchange (ETDEWEB)
Maceda, M.; Madore, J. [Laboratoire de Physique Theorique, Universite de Paris-Sud, Batiment 211, 91405, Orsay (France); Manousselis, P. [Department of Engineering Sciences, University of Patras, 26110, Patras (Greece); Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Theory Division, CERN, 1211, Geneva 23 (Switzerland)
2004-08-01
A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized. (orig.)
Discrete Symmetries In Lorentz-Invariant Non-Commutative QED
Morita, K
2003-01-01
It is pointed out that the usual $\\theta$-algebra assumed for non-commuting coordinates is not $P$- and $T$-invariant, unless one {\\it formally} transforms the non-commutativity parameter $\\theta^{\\mu\
Non-commutative time-frequency tomography
Man'ko, V I
1999-01-01
The characterization of non-stationary signals requires joint time and frequency information. However, time (t) and frequency (omega) being non-commuting variables there cannot be a joint probability density in the (t,omega) plane and the time-frequency distributions, that have been proposed, have difficult interpretation problems arising from negative or complex values and spurious components. As an alternative we propose to obtain time-frequency information by looking at the marginal distributions along rotated directions in the (t,omega) plane. The rigorous probability interpretation of the marginal distributions avoids all interpretation ambiguities. Applications to signal analysis and signal detection are discussed as well as an extension of the method to other pairs of non-commuting variables.
A non-perturbative study of non-commutative U(1) gauge theory
Energy Technology Data Exchange (ETDEWEB)
Nishimura, J. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Graduate Univ. for Advanced Studies (SOKENDAI), Tsukuba (Japan). Dept. of Particle and Nuclear Physics; Bietenholz, W. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Susaki, Y. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Tsukuba Univ. (Japan). Graduate School of Pure and Applied Science; Volkholz, J. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2007-06-15
We study U(1) gauge theory on a 4d non-commutative torus, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non- commutativity parameter {theta}, which provides evidence for a possible continuum theory. In the weak coupling symmetric phase, the dispersion relation involves a negative IR-singular term, which is responsible for the observed phase transition. (orig.)
Shadow of a charged rotating non-commutative black hole
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Sharif, M. [University of the Punjab, Department of Mathematics, Lahore (Pakistan); Pakistan Academy of Sciences, Islamabad (Pakistan); Iftikhar, Sehrish [University of the Punjab, Department of Mathematics, Lahore (Pakistan)
2016-11-15
This paper investigates the shadow of a charged rotating non-commutative black hole. For this purpose, we first formulate the null geodesics and study the effects of a non-commutative charge on the photon orbit. We then explore the effect of spin, angle of inclination as well as non-commutative charge on the silhouette of the shadow. It is found that shape of the shadow deviates from the circle with the decrease in the non-commutative charge. We also discuss observable quantities to study the deformation and distortion in the shadow cast by the black hole which decreases for small values of a non-commutative charge. Finally, we study the shadows in the presence of plasma. We conclude that the non-commutativity has a great impact on the black hole shadow. (orig.)
Shadow of a Charged Rotating Non-Commutative Black Hole
Sharif, M
2016-01-01
This paper investigates the shadow of a charged rotating non-commutative black hole. For this purpose, we first formulate the null geodesics and study the effects of non-commutative charge on the photon orbit. We then explore the effect of spin, angle of inclination as well as non-commutative charge on the silhouette of the shadow. It is found that shape of the shadow deviates from the circle with the decrease in the non-commutative charge. We also discuss observable quantities to study the deformation and distortion in the shadow cast by the black hole which decreases for small values of non-commutative charge. Finally, we study the shadows in the presence of plasma. We conclude that the non-commutativity has a great impact on the black hole shadow.
Non-commutative field theory and the parameters of Lorentz violation in QED
Directory of Open Access Journals (Sweden)
S Aghababaei
2011-09-01
Full Text Available Non-commutative field theory as a theory including the Lorentz violation can be constructed in two different ways. In the first method, the non-commutative fields are the same as the ordinary ones while the gauge group is restricted to U(n. For example, the symmetry group of standard model in non-commutative space is U(3×(2×U(1 which can be reduced to SU(3×SU(2×U(1 by two appropriate spontaneous symmetry breaking. In contrast, in the second method, the non-commutative gauge theory can be constructed for SU(n gauge group via Seiberg- Witten map. In this work, we want to find the relation between the NC-parameter and the Lorentz violation parameters for the first method and compare our results with what is already found in the second one. At the end, we obtain new limits on non-commutative parameter by using the existing bounds on the Lorentz Violation parameters.
Canonical approach to the closed string non-commutativity
Energy Technology Data Exchange (ETDEWEB)
Davidovic, Lj.; Nikolic, B.; Sazdovic, B. [University of Belgrade, Institute of Physics, P.O.Box 57, Belgrade (Serbia)
2014-01-15
We consider the closed stringmoving in a weakly curved background and its totally T-dualized background. Using T-duality transformation laws, we find the structure of the Poisson brackets in the T-dual space corresponding to the fundamental Poisson brackets in the original theory. From this structure we see that the commutative original theory is equivalent to the non-commutative T-dual theory, whose Poisson brackets are proportional to the background fluxes times winding and momentum numbers. The noncommutative theory of the present article is more nongeometrical than T-folds and in the case of three space-time dimensions corresponds to the nongeometric space-time with R-flux. (orig.)
Rohwer, CM
2012-01-01
In this thesis we shall demonstrate that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the formalism used entails a description that is non-local in that it requires all orders of positional derivatives through the star product that is used ubiquitously to map operator multiplication onto function multiplication in non-commutative systems. It will be shown that there exist several equivalent local descriptions, which are arrived at via the introduction of additional degrees of freedom. Consequently non-commutative quantum mechanical position measurements necessarily confront us with some additional structure which is necessary to specify quantum states completely. The remainder of the thesis, will involve investigations into the physical interpretation of these additional degrees of freedom. For one particular local formulation, the corresponding classical theory will be used to demonstrate that the concept of extended...
A non-commuting twist in the partition function
Govindarajan, Suresh
2012-01-01
We compute a twisted index for an orbifold theory when the twist generating group does not commute with the orbifold group. The twisted index requires the theory to be defined on moduli spaces that are compatible with the twist. This is carried out for CHL models at special points in the moduli space where they admit dihedral symmetries. The commutator subgroup of the dihedral groups are cyclic groups that are used to construct the CHL orbifolds. The residual reflection symmetry is chosen to act as a `twist' on the partition function. The reflection symmetries do not commute with the orbifolding group and hence we refer to this as a non-commuting twist. We count the degeneracy of half-BPS states using the twisted partition function and find that the contribution comes mainly from the untwisted sector. We show that the generating function for these twisted BPS states are related to the Mathieu group M_{24}.
Radiative corrections to the non commutative photon propagator at one-loop order
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Boutalbi, E.; Kouadik, S. [Laboratory of Particle Physics and Statistical Physics, Ecole Normale Superieure BP 92 Vieux kouba (Algeria); Faculty of Technologies Sciences,University of Medea (Algeria)
2012-06-27
We study the non-commutative gauge theory on the Moyal space. We add the harmonic potential introduced by Grosse and Wulkenhaar to the Maxwell Lagrange as well as the Gauge fixation. We determine the non-commutative U{sub *}(1) Gauge action which is invariant under the BRST transformations in the matrix basis. We determine in this basis the quadratic parts and the vertex of the Gauge field A{sub {mu}} and of the Faddeev-Popov ghost fields c(bar sign)andc. Finally, we study the perturbative correction to one loop order of the one point function in the matrix basis.
High-Energy Scattering in Non-Commutative Field Theory
Kumar, J; Kumar, Jason; Rajaraman, Arvind
2005-01-01
We analyze high energy scattering for non-commutative field theories using the dual gravity description. We find that the Froissart-Martin bound still holds, but that cross-sections stretch in the non-commutative directions in a way dependent on the infrared cutoff. This puzzling behavior suggests new aspects of UV/IR mixing.
Coincidence and ﬁxed point results for non-commuting maps
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Abdul Latif
2008-06-01
Full Text Available In the setting of Banach spaces, some results on the existence of coincidence and common fixed points for single-valued and multivalued non-commuting maps with and without contractive type conditions are obtained.
Quantum Analysis - Non-Commutative Differential and Integral Calculi
Suzuki, Masuo
1997-01-01
A new scheme of quantum analysis, namely a non-commutative calculus of operator derivatives and integrals is introduced. This treats differentiation of an operator-valued function with respect to the relevant operator in a Banach space. In this new scheme, operator derivatives are expressed in terms of the relevant operator and its inner derivation explicitly. Derivatives of hyperoperators are also defined. Some possible applications of the present calculus to quantum statistical physics are briefly discussed. Acknowledgements The author would like to thank Professor H. Araki, Professor K. Aomoto, Professor H. Hiai, Professor N. Obata and Dr. R.I. McLachlan for useful comments. Added in proof. Recently it has been proven that the quantum derivatives {dn f(A)/ dAn} are invariant for any choice of definitions of the differential df(A) satisfying the Leibniz rule and the linearity (M. Suzuki, J. Math. Phys.).->
Brownian Motion in Non-Commutative Super-Yang-Mills
Fischler, Willy; Garcia, Walter Tangarife
2012-01-01
Using the gauge/gravity correspondence, we study the dynamics of a heavy quark in strongly-coupled non-commutative Super-Yang-Mills at finite temperature. We propose a Langevin equation that accounts for the effects of non-commutativity and resembles the structure of Brownian motion in the presence of a magnetic field. As expected, fluctuations along non-commutative directions are generically correlated. Our results show that the viscosity of the plasma is smaller than the commutative case and that the diffusion properties of the quark are unaffected by non-commutativity. Finally, we compute the random force autocorrelator and verify that the fluctuation-dissipation theorem holds in the presence of non-commutativity.
Inflation on a non-commutative space–time
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Xavier Calmet
2015-07-01
Full Text Available We study inflation on a non-commutative space–time within the framework of enveloping algebra approach which allows for a consistent formulation of general relativity and of the standard model of particle physics. We show that within this framework, the effects of the non-commutativity of spacetime are very subtle. The dominant effect comes from contributions to the process of structure formation. We describe the bound relevant to this class of non-commutative theories and derive the tightest bound to date of the value of the non-commutative scale within this framework. Assuming that inflation took place, we get a model independent bound on the scale of space–time non-commutativity of the order of 19 TeV.
Inflation on a non-commutative space–time
Energy Technology Data Exchange (ETDEWEB)
Calmet, Xavier, E-mail: x.calmet@sussex.ac.uk; Fritz, Christopher, E-mail: c.fritz@sussex.ac.uk
2015-07-30
We study inflation on a non-commutative space–time within the framework of enveloping algebra approach which allows for a consistent formulation of general relativity and of the standard model of particle physics. We show that within this framework, the effects of the non-commutativity of spacetime are very subtle. The dominant effect comes from contributions to the process of structure formation. We describe the bound relevant to this class of non-commutative theories and derive the tightest bound to date of the value of the non-commutative scale within this framework. Assuming that inflation took place, we get a model independent bound on the scale of space–time non-commutativity of the order of 19 TeV.
Computational commutative and non-commutative algebraic geometry
Cojocaru, S; Ufnarovski, V
2005-01-01
This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.
Gravitational radiation in dynamical noncommutative spaces
Alavi, S A
2015-01-01
The gravitational radiation in dynamical non-commutative spaces (DNCS) is explored. we derive the corrections due to dynamical noncommutativity on the gravitational potential. We obtain the DNC corrections on the angular velocity as well as the radiated power of the system. By calculating the period decay of the system and using the observational data we obtain an upper bound for the DNS parameter {\\tau} . We also study quantum interference induced by gravitational potential in usual non-commutative and dynamical non-commutative spaces. The phase difference induced by gravity is calculated on two different paths and then, it is compared with the phase difference induced by gravity in commutative space.
Strong Planck constraints on braneworld and non-commutative inflation
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain); Kuroyanagi, Sachiko; Ohashi, Junko; Tsujikawa, Shinji, E-mail: calcagni@iem.cfmac.csic.es, E-mail: skuro@rs.tus.ac.jp, E-mail: j1211703@ed.tus.ac.jp, E-mail: shinji@rs.kagu.tus.ac.jp [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2014-03-01
We place observational likelihood constraints on braneworld and non-commutative inflation for a number of inflaton potentials, using Planck, WMAP polarization and BAO data. Both braneworld and non-commutative scenarios of the kind considered here are limited by the most recent data even more severely than standard general-relativity models. At more than 95 % confidence level, the monomial potential V(φ)∝φ{sup p} is ruled out for p ≥ 2 in the Randall-Sundrum (RS) braneworld cosmology and, for p > 0, also in the high-curvature limit of the Gauss-Bonnet (GB) braneworld and in the infrared limit of non-commutative inflation, due to a large scalar spectral index. Some parameter values for natural inflation, small-varying inflaton models and Starobinsky inflation are allowed in all scenarios, although some tuning is required for natural inflation in a non-commutative spacetime.
Non-commutative computer algebra and molecular computing
Directory of Open Access Journals (Sweden)
Svetlana Cojocaru
2001-12-01
Full Text Available Non-commutative calculations are considered from the molecular computing point of view. The main idea is that one can get more advantage in using molecular computing for non-commutative computer algebra compared with a commutative one. The restrictions, connected with the coefficient handling in Grobner basis calculations are investigated. Semigroup and group cases are considered as more appropriate. SAGBI basis constructions and possible implementations are discussed.
Non-commutative computer algebra and molecular computing
2001-01-01
Non-commutative calculations are considered from the molecular computing point of view. The main idea is that one can get more advantage in using molecular computing for non-commutative computer algebra compared with a commutative one. The restrictions, connected with the coefficient handling in Grobner basis calculations are investigated. Semigroup and group cases are considered as more appropriate. SAGBI basis constructions and possible implementations are discussed.
Relations between Non-Commutative and Commutative Spacetime
Tezuka, K I
2001-01-01
Spacetime non-commutativity appears in string theory. In this paper, the non-commutativity in string theory is reviewed. At first we review that a Dp-brane is equivalent to a configuration of infinitely many D($p-2$)-branes. If we consider the worldvolume as that of the Dp-brane, coordinates of the Dp-brane is commutative. On the other hand if we deal with the worldvolume as that of the D($p-2$)-branes, since coordinates of many D-branes are promoted to matrices the worldvolume theory is non-commutative one. Next we see that using a point splitting reguralization gives a non-commutative D-brane, and a non-commutative gauge field can be rewritten in terms of an ordinary gauge field. The transformation is called the Seiberg-Witten map. And we introduce second class constraints as boundary conditions of an open string. Since Neumann and Dirichlet boundary conditions are mixed in the constraints when the open string is coupled to a NS B field, the end points of the open string is non-commutative.
A Dream of Yukawa — Non-Local Fields out of Non-Commutative Spacetime —
Naka, Shigefumi; Toyoda, Haruki; Takanashi, Takahiro; Umezawa, Eizo
The coordinates of κ-Minkowski spacetime form Lie algebraic elements, in which time and space coordinates do not commute in spite of that space coordinates commute each other. The non-commutativity is realized by a Planck-length-scale constant κ - 1( ne 0), which is a universal constant other than the light velocity under the κ-Poincare transformation. Such a non-commutative structure can be realized by SO(1,4) generators in dS4 spacetime. In this work, we try to construct a κ-Minkowski like spacetime with commutative 4-dimensional spacetime based on Adsn+1 spacetime. Another aim of this work is to study invariant wave equations in this spacetime from the viewpoint of non-local field theory by H. Yukawa, who expected to realize elementary particle theories without divergence according to this viewpoint.
Marginal and non-commutative deformations via non-abelian T-duality
Hoare, Ben
2016-01-01
In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-$\\beta$-deformations and non-commutative deformations of ${\\cal N}=4$ super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.
Non-commutative dynamics of spinning D0 branes
Loh, D; Sahakian, V V; Loh, Duane; Rudolfa, Kit; Sahakian, Vatche
2004-01-01
Rotational dynamics is known to polarize D0 branes into higher dimensional fuzzy Dp-branes: the tension forces between D0 branes provide the centripetal acceleration, and a puffed up spinning configuration stabilizes. In this work, we consider a rotating cylindrical formation of finite height, wrapping a compact cycle of the background space along the axis of rotation. We find a myriad of interesting results: an intriguing relation between the angular speed, the geometry of the cylinder, and the scale of non-commutativity; instabilities for small radii in relation to the height of the cylinder - reminiscent of the Gregory-LaFlamme phenomenon; a critical radius corresponding to the case where the area of the cylinder is proportional to the number of D0 branes - reminiscent of Matrix black holes; and no power radiated away through D0 brane charge. The instabilities appear to lead to the lateral collapse of the cylinder into possibly a slinky configuration, akin to the Matrix string.
Non-commutative solitons and strong-weak duality
Energy Technology Data Exchange (ETDEWEB)
Blas, Harold [Departamento de Matematica - ICET, Universidade Federal de Mato Grosso, Av. Fernando Correa, s/n, Coxipo, 78060-900, Cuiaba - MT (Brazil)]. E-mail: blas@cpd.ufmt.br; Carrion, Hector L. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro (Brazil); Rojas, Moises [Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150 CEP 22290-180, Rio de Janeiro-RJ (Brazil)
2005-03-01
Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either U(1)xU(1) or U(1){sub C} corresponding to the Lechtenfeld et al. (NCSG{sub 1}) or Grisaru-Penati (NCSG{sub 2}) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT{sub 1,2} models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM{sub 1,2} models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter {theta} for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG{sub 1} {r_reversible} NCMT{sub 1} is promising since it is expected to hold on the quantum level. (author)
Non-commutative solitons and strong-weak duality
Energy Technology Data Exchange (ETDEWEB)
Blas, H. [Univerdidade Federal de Mato Grosso, Cuiaba, MT (Brazil). Dept. de Matematica]. E-mail: blas@cpd.ufmt.br; Carrion, H.L. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]. E-mail: mlm@if.ufrj.br; Rojas, M. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: mrojas@cbpf.br
2004-07-01
Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either U(1)xU(1) or U(1){sub C} corresponding to the Lechtenfeld et al. (NCSG{sub 1}) or Grisaru- Penati (NCSG{sub 2}) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT{sub 1,2} models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM{sub 1,2} models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC parameter {theta} for the corresponding Toda and matter fields describing the strong-weak phases, respectively. The correspondence NCSG{sub 1} {r_reversible} NCMT{sub 1} is promising since it is expected to hold on the quantum level (author)
Optimization of polynomials in non-commuting variables
Burgdorf, Sabine; Povh, Janez
2016-01-01
This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.
Non-commutativity from coarse grained classical probabilities
Wetterich, C
2010-01-01
Non-commutative quantum physics at the atom scale can arise from coarse graining of a classical statistical ensemble at the Planck scale. Position and momentum of an isolated particle are classical observables which remain computable in terms of the coarse grained information. However, the commuting classical product of position and momentum observables is no longer defined in the coarse grained system, which is therefore described by incomplete statistics. The microphysical classical statistical ensemble at the Planck scale admits an alternative non-commuting product structure for position and momentum observables which is compatible with the coarse graining. Measurement correlations for isolated atoms are based on this non-commutative product structure. We present an explicit example for these ideas. It also realizes the discreteness of the spin observable within a microphysical classical statistical ensemble.
A non-commutative framework for topological insulators
Bourne, C.; Carey, A. L.; Rennie, A.
2016-04-01
We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of non-commutative index theory of operator algebras. In particular, we formulate the index problems using Kasparov theory, both complex and real. We show that the periodic table of topological insulators and superconductors can be realized as a real or complex index pairing of a Kasparov module capturing internal symmetries of the Hamiltonian with a spectral triple encoding the geometry of the sample’s (possibly non-commutative) Brillouin zone.
Non-commutative black holes in D dimensions
Klimcík, C; Pompos, A
1994-01-01
Recently introduced classical theory of gravity in non-commutative geometry is studied. The most general (four parametric) family of D dibensional static spherically symmetric spacetimes is identified and its properties are studied in detail. For wide class of the choices of parameters, the corresponding spacetimes have the structure of asymptotically flat black holes with a smooth event horizon hiding the curvature singularity. A specific attention is devoted to the behavior of components of the metric in non-commutative direction, which are interpreted as the black hole hair.
Exotic Galilean Symmetry and Non-Commutative Mechanics
Directory of Open Access Journals (Sweden)
Peter A. Horváthy
2010-07-01
Full Text Available Some aspects of the ''exotic'' particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized non-commutative models are also discussed. Minimal as well as anomalous coupling to an external electromagnetic field is presented. Supersymmetric extension is also considered. Exotic Galilean symmetry is also found in Moyal field theory. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.
Modular Theory, Non-Commutative Geometry and Quantum Gravity
Directory of Open Access Journals (Sweden)
Wicharn Lewkeeratiyutkul
2010-08-01
Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.
Bassetto, A; Torrielli, A
2002-01-01
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with $n$ windings a non trivial scaling intertwines $n$ and $N$. In the non-commutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger group $U(\\infty)$. We perform an explicit perturbative calculation of such a loop up to ${\\cal O}(g^6)$; rather surprisingly, we find that in the contribution from the crossed graphs (the genuine non-commutative terms) the scaling we mentioned occurs for large $n$ and $N$ in the limit of maximal non-commutativity $\\theta=\\infty$. We present arguments in favour of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Winger Function for Spin Half Non-commutativeLandau Problem%自旋1/2非对易朗道问题的Wigner函数（英文）
Institute of Scientific and Technical Information of China (English)
王亚辉; 剡江峰; 袁毅
2011-01-01
With great significance in describing the state of quantum system,the Wigner function of the spin half non-commutative Landau problem is studied in this paper.On the basis of the review of the Wigner function in the commutative space,which is subject to the ＊-eigenvalue equation,Hamiltonian of the spin half Landau problem in the non-commutative phase space is given.Then,energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the non-commutative phase space are obtained by means of the ＊-eigenvalue equation（or Moyal equation）.%Wigner函数在对量子体系状态的描述方面具有重要的意义。讨论了自旋1/2非对易朗道问题的Wigner函数。首先回顾了对易空间中Wigner函数所服从的星本征方程,然后给出了非对易相空间中自旋1/2朗道问题的Hamiltonian,最后利用星本征方程（Moyal方程）计算了非对易相空间中自旋1/2朗道问题具有矩阵表示形式的Wigner函数及其能级。
Abdelmadjid Maireche
2016-01-01
The main objective of this search work is to study a three dimensional space-phase modified Schrödinger equation with energy dependent potential plus three terms: , and is carried out. Together with the Boopp’s shift method and standard perturbation theory the new energy spectra shown to be dependent with new atomic quantum in the non-commutative three dimensional real spaces and phases symmetries (NC-3D: RSP) and we have also constructed the corresponding deformed noncommutative Hamiltonia...
Directory of Open Access Journals (Sweden)
FENG Chaojun
2014-08-01
Full Text Available Inflation could be also driven by kinetic terms of the inflaton field,which is called the K-inflation model.During the inflation epoch,one could not neglect gravitational effect since the energy was so much high.According to general relativity,gravity is described by space-time geometry.By considering the space-time uncertainty,it is found that all the modes were created inside the Hubble horizon,and it contributes a linear term in the spectral index of the scalar and tensor power spectral.
The non-commutative Weil algebra
1999-01-01
Let G be a connected Lie group with Lie algebra g. The Duflo map is a vector space isomorphism between the symmetric algebra S(g) and the universal enveloping algebra U(g) which, as proved by Duflo, restricts to a ring isomorphism from invariant polynomials onto the center of the universal enveloping algebra. The Duflo map extends to a linear map from compactly supported distributions on the Lie algebra g to compactly supported distributions on the Lie group G, which is a ring homomorphism fo...
The Z-> gamma gamma,gg decays in the non-commutative standard model
Behr, W; Duplancic, G; Schupp, P; Trampetic, J; Wess, J
2003-01-01
On non-commutative spacetime, the standard model (SM) allows new, usually SM forbidden, triple gauge boson interactions to occur. In this letter we propose the SM strictly forbidden Z-> gamma gamma and Z->gg decay modes coming from the gauge sector of the non-commutative standard model (NCSM) as a place where non-commutativity could be experimentally discovered. (orig.)
Non-singular Brans–Dicke collapse in deformed phase space
Energy Technology Data Exchange (ETDEWEB)
Rasouli, S.M.M., E-mail: mrasouli@ubi.pt [Departamento de Física, Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200 Covilhã (Portugal); Centro de Matemática e Aplicações (CMA - UBI), Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200 Covilhã (Portugal); Physics Group, Qazvin Branch, Islamic Azad University, Qazvin (Iran, Islamic Republic of); Ziaie, A.H., E-mail: ah_ziaie@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G. C., Evin, 19839 Tehran (Iran, Islamic Republic of); Department of Physics, Shahid Bahonar University, PO Box 76175, Kerman (Iran, Islamic Republic of); Jalalzadeh, S., E-mail: shahram.jalalzadeh@unila.edu.br [Federal University of Latin-American Integration, Technological Park of Itaipu PO box 2123, Foz do Iguaçu-PR, 85867-670 (Brazil); Moniz, P.V., E-mail: pmoniz@ubi.pt [Departamento de Física, Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200 Covilhã (Portugal); Centro de Matemática e Aplicações (CMA - UBI), Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200 Covilhã (Portugal)
2016-12-15
We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.
Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach
Bertram, Wolfgang
2013-01-01
By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...
The entropy of dense non-commutative fermion gases
Kriel, Johannes N
2011-01-01
We investigate the properties of two- and three-dimensional non-commutative fermion gases with fixed total z-component of angular momentum, J_z, and at high density for the simplest form of non-commutativity involving constant spatial commutators. Analytic expressions for the entropy and pressure are found. The entropy exhibits non-extensive behaviour while the pressure reveals the presence of incompressibility in two, but not in three dimensions. Remarkably, for two-dimensional systems close to the incompressible density, the entropy is proportional to the square root of the system size, i.e., for such systems the number of microscopic degrees of freedom is determined by the circumference, rather than the area (size) of the system. The absence of incompressibility in three dimensions, and subsequently also the absence of a scaling law for the entropy analogous to the one found in two dimensions, is attributed to the form of the non-commutativity used here, the breaking of the rotational symmetry it implies a...
Quantum phase transitions in the noncommutative Dirac Oscillator
Panella, O
2014-01-01
We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the non-commutative plane. It is shown that the effect of non-commutativity is twofold: $i$) momentum non commuting coordinates simply shift the critical value ($B_{\\text{cr}}$) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); $ii$) non-commutativity in the space coordinates induces a new critical value of the magnetic field, $B_{\\text{cr}}^*$, where there is a second quantum phase transition (right-left), --this critical point disappears in the commutative limit--. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetisation of the system. Possible applications to the physics of silicene and graphene are briefly discussed.
A Partial Unification Model in Non-commutative Geometry
Hanlon, B E
1994-01-01
We consider the construction of $SU(2)_{L}\\otimes SU(2)_{R}\\otimes SU(4)$ partial unification models as an example of phenomenologically acceptable unification models in the absence of supersymmetry in non-commutative geometry. We exploit the Chamseddine, Felder and Fr\\"ohlich generalization of the Connes and Lott model building prescription. By introducing a bi-module structure and appropriate permutation symmetries we construct a model with triplet Higgs fields in the $SU(2)$ sectors and spontaneous breaking of $SU(4)$.
Supergravity and Light-Like Non-commutativity
Alishahiha, M; Russo, Jorge G; Alishahiha, Mohsen; Oz, Yaron; Russo, Jorge G.
2000-01-01
We construct dual supergravity descriptions of field theories and little string theories with light-like non-commutativity. The field theories are realized on the world-volume of Dp branes with light-like NS $B$ field and M5 branes with light-like $C$ field. The little string theories are realized on the world-volume of NS5 branes with light-like RR $A$ fields. The supergravity backgrounds are closely related to the $A=0,B=0,C=0$ backgrounds. We discuss the implications of these results. We also construct dual supergravity descriptions of ODp theories realized on the worldvolume of NS5 branes with RR backgrounds.
Non-commutative multiple-valued logic algebras
Ciungu, Lavinia Corina
2014-01-01
This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.
A black hole cast on a non-commutative background
Mbonye, Manasse R
2010-01-01
In this work we describe a black hole, set on a non-commutative background. The model, which is relatively simple, is an exact solution of the Einstein Field Equations. Based on a proposition we put forward, we argue that introducing a matter density field on a non-commutative background sets up a mechanism that deforms the field into two distinct fields, one residing dominantly on the lattice tops (hereafter, on-cell) and the other residing dominantly in the inter-lattice regions (hereafter, off-cell). The two fields have different physical and themodynamic characterics which we describe, and some of which play a role in halting collpse to a singularity. For example, not surprisingly the on-cell (off-cell) fields manifest standard on-shell (off-shell) characteristics, respectively. Both the density and the net mass-energy are unchanged by the deformation mechanism. In our treatment the mass of a black hole defines its own size scale L of the interior region it occupies. Moreover, such a length is quantized, ...
Non-commutative geometry as a realization of varying speed of light cosmology
Alexander, S H S; Alexander, Stephon H.S.; Magueijo, Jo\\~ao
2001-01-01
We examine the cosmological implications of space-time non-commutativity, discovering yet another realization of the varying speed of light model. Our starting point is the well-known fact that non-commutativity leads to deformed dispersion relations, relating energy and momentum, implying a frequency dependent speed of light. A Hot Big Bang Universe therefore experiences a higher speed of light as it gets hotter. We study the statistical physics of this "deformed radiation", recovering standard results at low temperatures, but a number of novelties at high temperatures: a deformed Planck's spectrum, a temperature dependent equation of state $w=p/\\rho$ (ranging from 1/3 to infinity), a new Stephan-Boltzmann law, and a new entropy relation. These new photon properties closely mimic those of phonons in crystals, hardly a surprising analogy. They combine to solve the horizon and flatness problems, explaining also the large entropy of the Universe. We also show how one would find a direct imprint of non-commutati...
Non-commutative U(1) Gauge Theory on R**4 with Oscillator Term
Blaschke, Daniel N; Schweda, Manfred
2007-01-01
Inspired by the renormalizability of the non-commutative $\\Phi^4$ model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory.
Non-commutative Iwasawa theory for modular forms
Coates, John; Liang, Zhibin; Stein, William; Sujatha, Ramdorai
2012-01-01
The aim of the present paper is to give evidence, largely numerical, in support of the non-commutative main conjecture of Iwasawa theory for the motive of a primitive modular form of weight k>2 over the Galois extension of Q obtained by adjoining to Q all p-power roots of unity, and all p-power roots of a fixed integer m>1. The predictions of the main conjecture are rather intricate in this case because there is more than one critical point, and also there is no canonical choice of periods. Nevertheless, our numerical data agrees perfectly with all aspects of the main conjecture, including Kato's mysterious congruence between the cyclotomic Manin p-adic L-function, and the cyclotomic p-adic L-function of a twist of the motive by a certain non-abelian Artin character of the Galois group of this extension.
Non-commuting variations in mathematics and physics a survey
Preston, Serge
2016-01-01
This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equa...
Non-commutative tachyon action and D-brane geometry
Herbst, Manfred; Kreuzer, M; Herbst, Manfred; Kling, Alexander; Kreuzer, Maximilian
2002-01-01
We analyse open string correlators in non-constant background fields, including the metric $g$, the antisymmetric $B$-field, and the gauge field $A$. Working with a derivative expansion for the background fields, but exact in their constant parts, we obtain a tachyonic on-shell condition for the inserted functions and extract the kinetic term for the tachyon action. The 3-point correlator yields a non-commutative tachyon potential. We also find a remarkable feature of the differential structure on the D-brane: Although the boundary metric $G$ plays an essential role in the action, the natural connection on the D-brane is the same as in closed string theory, i.e. it is compatible with the bulk metric and has torsion $H=dB$. This means, in particular, that the parallel transport on the brane is independent of the gauge field $A$.
Non-commutative Poisson Algebra Structures on the Lie Algebra son(CQ)
Institute of Scientific and Technical Information of China (English)
Jie Tong; Quanqin Jin
2007-01-01
Non-commutative Poisson algebras are the algebras having both an associativealgebra structure and a Lie algebra structure together with the Leibniz law.In this paper,the non-commutative poisson algebra structures on son(CQ) are determined.
Infinite divisibility and a non-commutative Boolean-to-free Bercovici-Pata bijection
Belinschi, Serban T; Vinnikov, Victor
2010-01-01
We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata bijection. An important tool is Voiculescu's subordination property for operator-valued free convolution.
NON-COMMUTATIVE POISSON ALGEBRA STRUCTURES ON LIE ALGEBRA sln(fCq) WITH NULLITY M
Institute of Scientific and Technical Information of China (English)
Jie TONG; Quanqin JIN
2013-01-01
Non-commutative Poisson algebras are the algebras having both an associa-tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on the Lie algebras sln(fCq) are determined.
A computational non-commutative geometry program for disordered topological insulators
Prodan, Emil
2017-01-01
This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the co...
Non-commutative solitons and strong-weak duality
Blas, H; Rojas, M
2005-01-01
Some properties of the non-commutative versions of the sine-Gordon model (NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our method relies on the NC extension of integrable models and the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM) associated to the group GL(2), in which the Toda field belongs to certain representations of either $U(1){x} U(1)$ or $U(1)_{C}$ corresponding to the Lechtenfeld et al. (NCSG$_{1}$) or Grisaru-Penati (NCSG$_{2}$) proposals for the NC versions of the sine-Gordon model, respectively. Besides, the relevant NCMT$_{1, 2}$ models are written for two (four) types of Dirac fields corresponding to the Moyal product extension of one (two) copy(ies) of the ordinary massive Thirring model. The NCATM$_{1,2}$ models share the same one-soliton (real Toda field sector of model 2) exact solutions, which are found without expansion in the NC ...
Notes on "quantum gravity" and non-commutative geometry
Gracia-Bondia, Jose M
2010-01-01
I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide against just selling my mathematical wares, and for a survey, necessarily very selective, but taking a global phenomenological approach to its subject matter. After all, non-commutative geometry does not purport yet to solve the riddle of quantum gravity; it is more of an insurance policy against the probable failure of the other approaches. The plan is as follows: the introduction invites students to the fruitful doubts and conundrums besetting the application of even classical gravity. Next, the first experiments detecting quantum gravitational states inoculate us a healthy dose of skepticism on some of the current ideologies. In Section 3 we look at the action for general relativity as a consequence of gauge theory for quantum tensor fields. Section 4 briefly deals with the...
Non commutative quantum spacetime with topological vortex states, and dark matter in the universe
Patwardhan, A
2003-01-01
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There is a variety of physics possible till the nucleosynthesis epoch is reached. The use of topology and non commutative geometry in cosmology is a recent approach. This paper considers the possibility of topological solutions of a vortex kind given by non commutative structures. These are interpreted as dark matter, with the grand unified Yang-Mills field theory energy scale used to describe its properties. The relation of the model with other existing theories is discussed.
Energy Technology Data Exchange (ETDEWEB)
Amini, Nina H. [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States); CNRS, Laboratoire des Signaux et Systemes (L2S) CentraleSupelec, Gif-sur-Yvette (France); Miao, Zibo; Pan, Yu; James, Matthew R. [Australian National University, ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Canberra, ACT (Australia); Mabuchi, Hideo [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States)
2015-12-15
The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice. (orig.)
Determinants of self-employment among commuters and non-commuters
DEFF Research Database (Denmark)
Backman, M.; Karlsson, C.
2016-01-01
We analyse the determinants of self-employment and focus on the contextual environment. By distinguishing between commuters and non-commuters we are able to analyse the influence from the work and home environment, respectively. Our results indicate a significant difference between non-commuters ......We analyse the determinants of self-employment and focus on the contextual environment. By distinguishing between commuters and non-commuters we are able to analyse the influence from the work and home environment, respectively. Our results indicate a significant difference between non......-commuters and commuters in terms of the role of networks for becoming self-employed. Our results indicate that it is the business networks where people work, rather than where they live that exerts a positive influence on the probability of becoming self-employed. These effects are further robust over educational...
2015-01-01
In this paper we present a deterministic polynomial time algorithm for testing if a symbolic matrix in non-commuting variables over $\\mathbb{Q}$ is invertible or not. The analogous question for commuting variables is the celebrated polynomial identity testing (PIT) for symbolic determinants. In contrast to the commutative case, which has an efficient probabilistic algorithm, the best previous algorithm for the non-commutative setting required exponential time (whether or not randomization is ...
On Non-Commutative Correction of the G\\"odel-type Metric
Ulhoa, S C; Amorim, R G G
2015-01-01
In this paper, we will study non-commutative corrections in the metric tensor for the G\\"{o}del-type universe, a model that has as its main characteristic the possibility of violation of causality, allowing therefore time travel. We also find that the critical radius in such a model, which eventually will determine the time travel possibility, is modified due to the non commutativity of spatial coordinates.
Energy Technology Data Exchange (ETDEWEB)
Chao, Alexander Wu; /SLAC
2012-03-01
As accelerator technology advances, the requirements on accelerator beam quality become increasingly demanding. Facing these new demands, the topic of phase space gymnastics is becoming a new focus of accelerator physics R&D. In a phase space gymnastics, the beam's phase space distribution is manipulated and precision tailored to meet the required beam qualities. On the other hand, all realization of such gymnastics will have to obey accelerator physics principles as well as technological limitations. Recent examples of phase space gymnastics include Emittance exchanges, Phase space exchanges, Emittance partitioning, Seeded FELs and Microbunched beams. The emittance related topics of this list are reviewed in this report. The accelerator physics basis, the optics design principles that provide these phase space manipulations, and the possible applications of these gymnastics, are discussed. This fascinating new field promises to be a powerful tool of the future.
Bożejko, Marek; Lytvynov, Eugene
2011-03-01
Let T be an underlying space with a non-atomic measure σ on it. In [ Comm. Math. Phys. 292, 99-129 (2009)] the Meixner class of non-commutative generalized stochastic processes with freely independent values, {ω=(ω(t))_{tin T}} , was characterized through the continuity of the corresponding orthogonal polynomials. In this paper, we derive a generating function for these orthogonal polynomials. The first question we have to answer is: What should serve as a generating function for a system of polynomials of infinitely many non-commuting variables? We construct a class of operator-valued functions {Z=(Z(t))_{tin T}} such that Z( t) commutes with ω( s) for any {s,tin T}. Then a generating function can be understood as {G(Z,ω)=sum_{n=0}^infty int_{T^n}P^{(n)}(ω(t_1),dots,ω(t_n))Z(t_1)dots Z(t_n)} {σ(dt_1) dots σ(dt_n)} , where {P^{(n)}(ω(t_1),dots,ω(t_n))} is (the kernel of the) n th orthogonal polynomial. We derive an explicit form of G( Z, ω), which has a resolvent form and resembles the generating function in the classical case, albeit it involves integrals of non-commuting operators. We finally discuss a related problem of the action of the annihilation operators {partial_t,t in T} . In contrast to the classical case, we prove that the operators ∂ t related to the free Gaussian and Poisson processes have a property of globality. This result is genuinely infinite-dimensional, since in one dimension one loses the notion of globality.
Non-singular Brans-Dicke collapse in deformed phase space
Rasouli, S M M; Jalalzadeh, S; Moniz, P V
2016-01-01
We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans-Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature [M.A. Scheel, S.L. Shapiro and S.A. Teukolsky, Phys. Rev. D. 51, 4236 (1995)], that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding pha...
Functional approach to coherent states in non commutative theories
Lubo, M
2003-01-01
In many high dimensional noncommutative theories, no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. This differs from the usual theory where the squeezed states possess this property. The important role played by these states when recovering classical mechanics as a limit of quantum theory makes necessary the investigation of the possible generalizations in the noncommutative context. We propose an extension based on a variational principle. The action considered is the sum of the squares of the terms associated to the non trivial Heisenberg uncertainty relations. We first verify that our proposal works in the usual theory: we find the known gaussian functions and, besides them, other states which can be expressed as products of gaussians with specific hypergeometrics. We illustrate our construction in three models defined on a four dimensional phase space: two models endowed with a minimal length uncertainty and the popular case in which the commutators of the positions ...
A non-commutative n-particle 3D Wigner quantum oscillator
King, R C; Stoilova, N I; Van der Jeugt, J
2003-01-01
An n-particle 3-dimensional Wigner quantum oscillator model is constructed explicitly. It is non-canonical in that the usual coordinate and linear momentum commutation relations are abandoned in favour of Wigner's suggestion that Hamilton's equations and the Heisenberg equations are identical as operator equations. The construction is based on the use of Fock states corresponding to a family of irreducible representations of the Lie superalgebra sl(1|3n) indexed by an A-superstatistics parameter p. These representations are typical for p\\geq 3n but atypical for p<3n. The branching rules for the restriction from sl(1|3n) to gl(1) \\oplus so(3) \\oplus sl(n) are used to enumerate energy and angular momentum eigenstates. These are constructed explicitly and tabulated for n\\leq 2. It is shown that measurements of the coordinates of the individual particles gives rise to a set of discrete values defining nests in the 3-dimensional configuration space. The fact that the underlying geometry is non-commutative is sh...
Matrix Configurations for Spherical 4-branes and Non-commutative Structures on S^4
Nakayama, R; Nakayama, Ryuichi; Shimono, Yusuke
2004-01-01
We present a Matrix theory action and Matrix configurations for spherical 4-branes. The dimension of the representations is given by N=2(2j+1) (j=1/2,1,3/2,...). The algebra which defines these configurations is not invariant under SO(5) rotations but under SO(3) \\otimes SO(2). We also construct a non-commutative product for field theories on S^4 in terms of that on S^2. An explicit formula of the non-commutative product which corresponds to the N=4 dim representation of the non-commutative S^4 algebra is worked out. Because we use S^2 \\otimes S^2 parametrization of S^4, our S^4 is doubled and the non-commutative product and functions on S^4 are indeterminate on a great circle (S^1) on S^4. We will however, show that despite this mild singularity it is possible to write down a finite action integral of the non-commutative field thoery on S^4. NS-NS B field background on S^4 which is associated with our Matrix S^4 configurations is also constructed.
The Kepler problem in the Snyder space
Leiva, Carlos; Villanueva, J R
2012-01-01
In this paper we study the Kepler problem in the non commutative Snyder scenario. We characterize the deformations in the Poisson bracket algebra under a mimic procedure from quantum standard formulations and taking into account a general recipe to build the noncommutative phase space coordinates (in the sense of Poisson brackets). We obtain an expression to the deformed potential, and then the consequences in the precession of the orbit of Mercury are calculated. This result allows us to find an estimated value for the non commutative deformation parameter introduced.
The Kepler problem in the Snyder space
Indian Academy of Sciences (India)
Carlos Leiva; Joel Saavedra; J R Villanueva
2013-06-01
In this paper the Kepler problem in the non-commutative Snyder scenario was studied. The deformations were characterized in the Poisson bracket algebra under a mimic procedure from quantum standard formulations by taking into account a general recipe to build the noncommutative phase space coordinates (in the sense of Poisson brackets). An expression for the deformed potential was obtained, and then the consequences in the precession of the orbit of Mercury were calculated. The result could be used for finding an estimated value for the non-commutative deformation parameter.
Blaschke, D. N.; Grosse, H.; Schweda, M.
2007-09-01
Inspired by the renormalizability of the non-commutative Φ4 model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term in a BRST invariant manner. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory.
Energy Technology Data Exchange (ETDEWEB)
Varshovi, Amir Abbass [School of Mathematics, Institute for Research in Fundamental Sciences (IPM) and School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of)
2013-07-15
The theory of α*-cohomology is studied thoroughly and it is shown that in each cohomology class there exists a unique 2-cocycle, the harmonic form, which generates a particular Groenewold-Moyal star product. This leads to an algebraic classification of translation-invariant non-commutative structures and shows that any general translation-invariant non-commutative quantum field theory is physically equivalent to a Groenewold-Moyal non-commutative quantum field theory.
Twisted rings and moduli stacks of "fat" point modules in non-commutative projective geometry
Chan, Daniel
2010-01-01
The Hilbert scheme of point modules was introduced by Artin-Tate-Van den Bergh to study non-commutative graded algebras. The key tool is the construction of a map from the algebra to a twisted ring on this Hilbert scheme. In this paper, we study moduli stacks of more general "fat" point modules, and show that there is a similar map to a twisted ring associated to the stack. This is used to provide a sufficient criterion for a non-commutative projective surface to be birationally PI. It is hoped that such a criterion will be useful in understanding Mike Artin's conjecture on the birational classification of non-commutative surfaces.
Non-Commutative Integration, Zeta Functions and the Haar State for SU{sub q}(2)
Energy Technology Data Exchange (ETDEWEB)
Matassa, Marco, E-mail: marco.matassa@gmail.com [SISSA (Italy)
2015-12-15
We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU{sub q}(2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU{sub q}(2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU{sub q}(2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension.
Non-Commutative Integration, Zeta Functions and the Haar State for SU q (2)
Matassa, Marco
2015-12-01
We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU q (2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU q (2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU q (2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension.
Double Compactified d = 11 Supermembrane Dual as a Non-Commutative Super-Maxwell Theory
Martin, I; Restuccia, A
2000-01-01
The physical hamiltonian of the double compactified D=11 supermembrane dual with non trivial wrapping is explicitly obtained. It contains cubic and quartic interacting terms. It exactly agrees with the hamiltonian formulation of non-commutative super-Maxwell theory on the world volume, minimally coupled to seven scalars fields corresponding to the transverse coordinates to the brane. The non commutative star product is intrinsically obtained from the simplectic 2-form defined by the minimal configuration of the hamiltonian, that is by the pull-back to the world volume of the canonical conection 1-form on the Hopf fibring over $CP_n$. The constraint generating the area preserving diffeomorphism is reformulated as the Gauss constraint of the non-commutative super-Maxwell theory.
Duality and gauge invariance of non-commutative spacetime Podolsky electromagnetic theory
Abreu, Everton M. C.; Fernandes, Rafael L.; Mendes, Albert C. R.; Neto, Jorge Ananias; Neves, Mario, Jr.
2017-01-01
The interest in higher derivative field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this paper, we have introduced the non-commutative (NC) version of the Podolsky theory and we investigated the effect of the non-commutativity over its original gauge invariance property. We have demonstrated precisely that the non-commutativity spoiled the primary gauge invariance of the original action under this primary gauge transformation. After that we have used the Noether dualization technique to obtain a dual and gauge invariant action. We have demonstrated that through the introduction of a Stueckelberg field in this NC model, we can also recover the primary gauge invariance. In this way, we have accomplished a comparison between both methods.
An alternative way to explain how non-commutativity arises in the bosonic string theory
De Andrade, M A
2015-01-01
In this work we will investigate how the non-commutativity arises into the string theory, \\textit{i.e.}, how the bosonic string theory attaches to a D3-brane in the presence of magnetic fields. In order to accomplish the proposal, we departure from the commutative two-dimensional harmonic oscillator, which after the application of the general Bopp's shifts Matrix Method, the non-commutative version of the two-dimensional harmonic oscillator is obtained. After that, this non-commutative harmonic oscillator will be mapped into the bosonic string theory in the light cone frame, which it now appears as a bosonic string theory attached to a D3-brane.
On Non-commuting Sets in a Finite p-group with Derived Subgroup of Prime Order
Institute of Scientific and Technical Information of China (English)
Wang Yu-lei; Liu He-guo
2016-01-01
Let G be a finite group. A nonempty subset X of G is said to be non-commuting if xy = yx for any x, y ∈ X with x = y. If |X| ≥ |Y| for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order.
Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, W. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Bigarini, A. [Univ. degli Studi di Perugia (Italy). Dipt. di Fisica]|[INFN, Sezione di Perugia (Italy)]|[Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Torrielli, A. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics, Lab. for Nuclear Sciences
2007-06-15
We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)
On the non-commutative Local Main Conjecture for elliptic curves with complex multiplication
Venjakob, Otmar
2012-01-01
This paper is a natural continuation of the joint work [6] on non-commutative Main Conjectures for CM elliptic curves: now we concentrate on the local Main Conjecture or more precisely on the epsilon-isomorphism conjecture by Fukaya and Kato in [20]. Our results rely heavily on Kato's unpublished proof of (commutative) epsilon-isomorphisms for one dimensional representations of G_{Q_p} in [24]. For the convenience of the reader we give a slight modification or rather reformulation of it in the language of [20] and extend it to the (slightly non-commutative) semi-global setting.
Invertibility of random submatrices via the Non-Commutative Bernstein Inequality
Chrétien, Stéphane
2011-01-01
Let $X$ be a $n\\times p$ matrix. We provide a detailed study of the quasi isometry property for random submatrices of $X$ obtained by uniform column sampling. The analysis relies on a tail decoupling argument with explicit constants and a recent version of the Non-Commutative Bernstein inequality (NCBI) [14]. Our results complement those obtained in [13] for the moments of submatrices. They also generalize and improve on those in [2], which are based on a Non-Commutative Kahane- Kintchine inequality (NCKI).
Compactified D=11 Supermembranes and Symplectic Non-Commutative Gauge Theories
Martin, I; Restuccia, A
2001-01-01
It is shown that a double compactified D=11 supermembrane with non trivial wrapping may be formulated as a symplectic non-commutative gauge theory on the world volume. The symplectic non commutative structure is intrinsically obtained from the symplectic 2-form on the world volume defined by the minimal configuration of its hamiltonian. The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume. Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemman surface with a symplectic connection.
Causality in non-commutative quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Haque, Asrarul; Joglekar, Satish D [Department of Physics, I.I.T. Kanpur, Kanpur 208 016 (India)], E-mail: ahaque@iitk.ac.in, E-mail: sdj@iitk.ac.in
2008-05-30
We study causality in noncommutative quantum field theory with a space-space noncommutativity. We employ the S operator approach of Bogoliubov-Shirkov (BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between the T* product and the T product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and another in the Yukawa theory. In particular, in the context of a noncommutative Yukawa theory, with the interaction Lagrangian {psi}-bar(x)*{psi}(x)*{phi}(x), is observed to be causality violating even in the case of space-space noncommutativity for which {theta}{sup 0i} = 0.
Compactification on phase space
Lovelady, Benjamin; Wheeler, James
2016-03-01
A major challenge for string theory is to understand the dimensional reduction required for comparison with the standard model. We propose reducing the dimension of the compactification by interpreting some of the extra dimensions as the energy-momentum portion of a phase-space. Such models naturally arise as generalized quotients of the conformal group called biconformal spaces. By combining the standard Kaluza-Klein approach with such a conformal gauge theory, we may start from the conformal group of an n-dimensional Euclidean space to form a 2n-dimensional quotient manifold with symplectic structure. A pair of involutions leads naturally to two n-dimensional Lorentzian manifolds. For n = 5, this leaves only two extra dimensions, with a countable family of possible compactifications and an SO(5) Yang-Mills field on the fibers. Starting with n=6 leads to 4-dimensional compactification of the phase space. In the latter case, if the two dimensions each from spacetime and momentum space are compactified onto spheres, then there is an SU(2)xSU(2) (left-right symmetric electroweak) field between phase and configuration space and an SO(6) field on the fibers. Such a theory, with minor additional symmetry breaking, could contain all parts of the standard model.
Quantized equations of motion in non-commutative theories
Heslop, P; Heslop, Paul; Sibold, Klaus
2004-01-01
Quantum field theories based on interactions which contain the Moyal star product suffer, in the general case when time does not commute with space, from several diseases: quantum equation of motions contain unusual terms, conserved currents can not be defined and the residual spacetime symmetry is not maintained. All these problems have the same origin: time ordering does not commute with taking the star product. Here we show that these difficulties can be circumvented by a new definition of time ordering: namely with respect to a light-cone variable. In particular the original spacetime symmetries SO(1,1) x SO(2) and translation invariance turn out to be respected. Unitarity is guaranteed as well.
Einstein–Podolski–Rosen paradox, non-commuting operator, complete wavefunction and entanglement
Indian Academy of Sciences (India)
Andrew Das Arulsamy
2014-03-01
Einstein, Podolski and Rosen (EPR) have shown that any wavefunction (subject to the Schrödinger equation) can describe the physical reality completely, and any two observables associated with two non-commuting operators can have simultaneous reality. In contrast, quantum theory claims that the wavefunction can capture the physical reality completely, and the physical quantities associated with two non-commuting operators cannot have simultaneous reality. The above contradiction is known as the EPR paradox. Here, we unambiguously expose that there is a hidden assumption made by EPR, which gives rise to this famous paradox. Putting the assumption right this time leads us not to the paradox, but only reinforces the correctness of the quantum theory. However, it is shown here that the entanglement phenomenon between two physically separated particles (they were entangled prior to separation) can only be proven to exist with a `proper’ measurement.
Non-commutative geometry, the Bohm interpretation and the mind-matter relationship
Hiley, B. J.
2001-06-01
It is argued that in order to address the mind/matter relationship, we will have to radically change the conceptual structure normally assumed in physics. Rather than fields and/or particles-in-interaction described in the traditional Cartesian order based a local evolution in spacetime, we need to introduce a more general notion of process described by a non-commutative algebra. This will have radical implications for both for physical processes and for geometry. By showing how the Bohm interpretation of quantum mechanics can be understood within a non-commutative structure, we can give a much clearer meaning to the implicate order introduced by Bohm. It is through this implicate order that mind and matter can be seen as different aspects of the same general process.
Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory
Molina, Mercedes
2016-01-01
Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he...
Marginal and non-commutative deformations via non-abelian T-duality
Hoare, Ben; Thompson, Daniel C.
2017-02-01
In this short article we develop recent proposals to relate Yang-Baxter sigmamodels and non-abelian T-duality. We demonstrate explicitly that the holographic spacetimes associated to both (multi-parameter)- β-deformations and non-commutative deformations of N = 4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.
Non-commutative residue of projections in Boutet de Monvel's calculus
DEFF Research Database (Denmark)
Gaarde, Anders
2007-01-01
Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. This partially answers a question raised...... in a recent collaboration with Grubb, namely whether the residue is zero on sectorial projections for boundary value problems: This is confirmed to be true when the sectorial projections is in the calculus....
Non-commutative residue of projections in Boutet de Monvel's calculus
DEFF Research Database (Denmark)
Gaarde, Anders
2007-01-01
Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. This partially answers a question raised...... in a recent collaboration with Grubb, namely whether the residue is zero on sectorial projections for boundary value problems: This is confirmed to be true when the sectorial projections is in the calculus....
Sica, Louis
2012-01-01
The usual interpretation of the Greenberger, Horne, Zeilinger (GHZ) theorem is that only nonlocal hidden variables are consistent with quantum mechanics. This conclusion is reasoned from the fact that combinations of results of unperformed non-commutative measurement procedures (counterfactuals) do not agree with quantum mechanical predictions taking non-commutation into account. However, it is shown from simple counter-examples, that combinations of such counterfactuals are inconsistent with classical non-commutative measurement sequences as well. There is thus no regime in which the validity of combined non-commutative counterfactuals may be depended upon. As a consequence, negative conclusions regarding local hidden variables do not follow from the GHZ and Bell theorems as historically reasoned.
Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
2000-01-01
The axial anomaly in lattice gauge theories has topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological techniques. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which validates the Leibniz rule of exterior derivatives on the lattice. The topological nature of the ``Chern character'' on the lattice becomes manifest with NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions.
Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals
Vu, Le Anh; Nghia, Tran Thi Hieu
2011-01-01
The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e. five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbits) are orbits of zero or maximal dimension. The main result of the paper is the classification up to an isomorphism of all MD5-algebras with the non-commutative derived ideal. With this result, we have the complete classification of 5-dimensional solvable Lie algebras.
Muon $g-2$ measurements and non-commutative geometry of quantum beams
Indian Academy of Sciences (India)
Y Srivastava; A Widom
2004-03-01
We discuss a completely quantum mechanical treatment of the measurement of the anomalous magnetic moment of the muon. A beam of muons move in a strong uniform magnetic field and a weak focusing electrostatic field. Errors in the classical beam analysis are exposed. In the Dirac quantum beam analysis, an important role is played by non-commutative muon beam coordinates leading to a discrepancy between the classical and quantum theories. We obtain a quantum limit to the accuracy achievable in BNL type experiments. Some implications of the quantum corrected data analysis for supersymmetry are briefly mentioned.
Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
Energy Technology Data Exchange (ETDEWEB)
Chekhov, Leonid [Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia and School of Mathematics, Loughborough University, LE11 3TU Leicestershire (United Kingdom); Eynard, Bertrand [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Ribault, Sylvain [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Laboratoire Charles Coulomb UMR 5221 CNRS-UM2, Universite Montpellier 2, Place Eugene Bataillon, F-34095 Montpellier Cedex 5 (France)
2013-02-15
We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the energy-momentum tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov, and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.
On prime and semiprime rings with generalized derivations and non-commutative Banach algebras
Indian Academy of Sciences (India)
MOHD ARIF RAZA; NADEEM UR REHMAN
2016-08-01
Let $R$ be a prime ring of characteristic different from 2 and $m$ a fixed positive integer. If $R$ admits a generalized derivation associated with a nonzero deviation $d$ such that $[F(x), d(y)]_m = [x, y]$ for all $x$, $y$ in some appropriate subset of $R$, then $R$ is commutative. Moreover, we also examine the case $R$ is a semiprime ring. Finally, we apply the above result to Banach algebras, and we obtain a non-commutative version of the Singer--Werner theorem.
a Note on the Non-Commutative Laplace-Varadhan Integral Lemma
de Roeck, W.; Maes, Christian; Netočný, Karel; Rey-Bellet, Luc
We continue the study of the free energy of quantum lattice spin systems where to the local Hamiltonian H an arbitrary mean field term is added, a polynomial function of the arithmetic mean of some local observables X and Y that do not necessarily commute. By slightly extending a recent paper by Hiai, Mosonyi, Ohno and Petz [10], we prove in general that the free energy is given by a variational principle over the range of the operators X and Y. As in [10], the result is a non-commutative extension of the Laplace-Varadhan asymptotic formula.
Berry's Phase in Noncommutative Spaces
Institute of Scientific and Technical Information of China (English)
S. A. Alavi
2003-01-01
We discuss the perturbative aspects of noncommutative quantum mechanics. Then we study Berry's phase within the framework of noncommutative quantum mechanics. The results show deviations from the usual quantum mechanics, which depend on the parameter of space/space noncommutativity.
DiracQ: A Package for Algebraic Manipulation of Non-Commuting Quantum Variables
Directory of Open Access Journals (Sweden)
John G. Wright
2015-11-01
Full Text Available In several problems of quantum many body physics, one is required to handle complex expressions originating in the non-commutative nature of quantum operators. Their manipulation requires precise ordering and application of simplification rules. This can be cumbersome, tedious and error prone, and often a challenge to the most expert researcher. In this paper we present a software package DiracQ to facilitate such manipulations. The package DiracQ consists of functions based upon and extending considerably the symbolic capabilities of 'Mathematica'. With DiracQ, one can proceed with large scale algebraic manipulations of expressions containing combinations of ordinary numbers or symbols (the c-numbers and arbitrary sets of non-commuting variables (the q-numbers with user defined properties. The DiracQ package is user extendable and comes encoded with the algebraic properties of several standard operators in popular usage. These include Fermionic and Bosonic creation and annihilation operators, spin operators, and canonical position and momentum operators. An example book is provided with some suggestive calculations of large-scale algebraic manipulations.
M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
Costello, Kevin
2016-01-01
The $\\Omega$-background is defined for supergravity, and a very general class of such backgrounds is constructed for 11-dimensional supergravity. 11-dimensional supergravity in a certain $\\Omega$-background is shown to be equivalent to a 5-dimensional non-commutative gauge theory of Chern-Simons type. M2 and M5 branes are expressed as 1 and 2-dimensional extended objects in the 5-dimensional gauge theory. This 5-dimensional gauge theory is shown to admit a consistent quantization with two coupling constants, despite being formally non-renormalizable. A check of a twisted version of AdS/CFT is performed relating this 5-dimensional non-commutative gauge theory to the theory on N M5 branes, wrapping an $A_{k-1}$ singularity and placed in an $\\Omega$-background. The operators on the M5 branes, in the $\\Omega$-background, are described by a certain chiral algebra which in the large N limit becomes a $W_{k+\\infty}$ algebra. This chiral algebra is recovered from the 5-dimensional gauge theory. This argument also pro...
Charge and/or spin limits for black holes at a non-commutative scale
Paik, Biplab
2017-08-01
In the commutative geometrical background, one finds the total charge ( Q) and/or the total angular momentum ( J) of a generalized black hole of mass M to be bounded by the condition Q^2+( J{/}M) ^2≤ M^2, whereas the inclusion of the concept of non-commutativity in geometry leads to a much more richer result. It predicts that the upper limit to Q and/or J is not fixed but depends on the mass/length scale of black holes; it (the upper limit to Q and/or J) goes towards a `commutative limit' when {M≫ √{θ}} (√{θ} characterizes the minimal length scale) and rapidly diminishes towards zero with M decreasing in the strongly non-commutative regime, until approaching a perfect zero value for {M˜eq 1.904√{θ}}. We have performed separate calculations for a pure Kerr or a pure Reissner-Nordström black hole, and briefly done it for a generalized black hole.
Charge and/or spin limits for black holes at a non-commutative scale
Indian Academy of Sciences (India)
BIPLAB PAIK
2017-08-01
In the commutative geometrical background, one finds the total charge $\\mathcal{(Q)}$ and/or the total angular momentum $\\mathcal{(J)}$ of a generalized black hole of mass $M$ to be bounded by the condition $\\mathcal{Q^{2} + (J/M)^{2} \\leq M^{2}}$, whereas the inclusion of the concept of non-commutativity in geometry leads to a much more richer result. It predicts that the upper limit to $\\mathcal{Q}$ and/or $\\mathcal{J}$ is not fixed but depends on the mass/length scale of black holes; it (the upper limit to $\\mathcal{Q}$ and/or $\\mathcal{J}$ ) goes towards a ‘commutative limit’ when $M \\gg \\sqrt{\\vartheta} (\\sqrt{\\vartheta}$ characterizes the minimal length scale) and rapidly diminishes towards zero with $M$ decreasing in the strongly non-commutative regime, until approaching a perfect zero value for $M \\simeq 1.904\\sqrt{\\vartheta}$. We have performed separate calculations for a pure Kerr or a pure Reissner–Nordström black hole, and briefly done it for a generalized black hole.
Liao, Y
2003-01-01
A framework was recently proposed for doing perturbation theory on non-commutative (NC) spacetime. It preserves the unitarity of the S matrix and differs from the naive, popular approach already at the lowest order in perturbation when time does not commute with space. In this work, we investigate its phenomenological implications at linear colliders, especially the TESLA at DESY, through the processes of e sup + e sup --> mu sup +mu sup - ,H sup + H sup - ,H sup 0 H sup 0. We find that some NC effects computed previously are now modified and that there are new processes which now exhibit NC effects. Indeed, the first two processes get corrected at tree level as opposed to the null result in the naive approach, while the third one coincides with the naive result only in the low energy limit. The impact of the earth's rotation is incorporated. The NC signals are generally significant when the NC scale is comparable to the collider energy. If this is not the case, the non-trivial azimuthal angle distribution an...
Left-right symmetric gauge theory in non-commutative geometry on M{sub 4} x Z{sub N}
Energy Technology Data Exchange (ETDEWEB)
Okumura, Yoshitaka [Chubu Univ., Kasugai, Aichi (Japan)
1995-10-01
The left-right symmetric gauge model (LRSM) is reconstructed using the previously proposed formalism based on the non-commutative differential geometry extended on the discrete space M{sub 4} x Z{sub N}. This formalism is so flexible and applicable that not only the standard model but also the SU(5) grand unified model have already been reformulated in this formalism, which presents many attractive points such as the unified picture of the gauge field and Higgs field as the generalized connection in non-commutative geometry. LRSM is still alive as a model with the intermediate symmetry of the spontaneously broken SO(10) grand unified theory (GUT). Six sheets are prepared for LRSM (N=6), one is for SU(3){sub c} color symmetry and the rest of five are for SU(2){sub L} x SU(2){sub R} x U(1) symmetry. We can achieve the reformulation of LRSM with the quite different configurations of Higgs particles from the ordinary one. Namely, the left-right symmetric gauge groups are broken owing to two (2, 1) and two (1, 2) doublet Higgs fields with hypercharge 1, one (2, 2{sup *}) Higgs field, and one (1, 3) Higgs field with hypercharge -2. The fermion sectors are nicely incorporated so that the seesaw mechanism works well to make the right-handed neutrino super heavy and the left-handed neutrino super light. (author).
Murphy, Andrew; Haestad, Jace; Morgan, Thomas
2015-09-01
We report characteristics of closed classical orbits in an electric field in phase space produced in photoabsorption. Rydberg states of atomic and molecular hydrogen and helium are considered. The core potential used for the hydrogen molecule is an effective one electron one center core potential evaluated at the internuclear equilibrium distance. Poincare surfaces of section in phase space are generated by integrating the equations of motion in semiparabolic coordinates u = (r + z) 1 / 2 and v = (r - z) 1 / 2, and plotting the location in phase space (pv versus v) whenever u = 0, with the electric field in the z direction. Combination orbits produced by Rydberg electron core scattering are studied and the evolution in phase space of these combination orbits due to scattering from one closed orbit into another is investigated. Connections are made to measured laser photoabsorption experiments that excite Rydberg states (20 recurrence spectra. The phase space structures responsible for the spectra are identified.
De quelques questions relatives à la (co)homologie et à la descente en algèbre non commutative.
Nuss, P
2005-01-01
Le présent mémoire d'habilitation a pour objectif de donner une vue d'ensemble du contexte et de la teneur de nos travaux, ainsi qu'une présentation succincte de quelques directions de recherches ultérieures. Sa subdivision en trois chapitres reflète nos orientations thématiques : 1) (co)homologie de Hochschild et cyclique des algèbres ; 2) descente fidèlement plate non commutative ; 3) extensions (Hopf-)galoisiennes non commutatives
Lagrangian for Frenkel electron and position's non-commutativity due to spin
Deriglazov, Alexei A
2014-01-01
We construct relativistic-invariant spinning-particle Lagrangian without auxiliary variables. Spin is considered as a composed quantity constructed on the base of non-Grassmann vector-like variable. The variational problem guarantees both fixed value of spin and Frenkel condition on spin-tensor. Taking into account the Frenkel condition, we obtain, inevitably, relativistic corrections to the algebra of position variables: their classical brackets became noncommutative, with the "parameter of non-commutativity" proportional to the spin-tensor. This leads to a number of interesting consequences in quantum theory. We construct the relativistic quantum mechanics in canonical formalism (in physical-time parametrization) and in covariant formalism (in arbitrary parametrization). We show how state-vectors and operators of covariant formulation can be used to compute mean values of physical operators of position and spin. This proves relativistic covariance of canonical formalism. Various candidates for position and ...
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
Directory of Open Access Journals (Sweden)
Abdelmadjid MAIRECHE
2015-09-01
Full Text Available We obtain here the modified bound-states solutions for central fraction power singular potential (C.F.P.S. in noncommutative 3-dimensional non relativistic quantum mechanics (NC-3D NRQM. It has been observed that the commutative energy spectra was changed, and replaced degenerate new states, depending on four quantum numbers: j, l and sz=±1/2 corresponding to the two spins states of electron by (up and down and the deformed Hamiltonian formed by two new operators: the first describes the spin-orbit interaction , while the second obtained Hamiltonian describes the modified Zeeman effect (containing ordinary Zeeman effect in addition to the usual commutative Hamiltonian. We showed that the isotropic commutative Hamiltonian HCFPS will be in non commutative space anisotropic Hamiltonian HNC-CFPS.
State-Vector Space and Canonical Coherent States in Noncommutative Plane
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously include coordinate-coordinate non-commutativity and momentum-momentum non-commutativity, which leads to a kind of de-formed Heisenberg-Weyl algebra. Although there is no ordinary number representation in this state-vector space, several set of orthogonal and complete state-vectors can be derived which are common eigenvectors of corresponding pairs of commuting Hermitian operators. As a simple application of this state-vector space, an explicit form of two-dimensional canonical coherent state is constructed and its properties are discussed.
Longitudinal Phase Space Tomography with Space Charge
Hancock, S; Lindroos, M
2000-01-01
Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the non-linearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of...
Non-Commutative Worlds - Classical Constraints, Relativity and the Bianchi Identity
Kauffman, Louis H
2011-01-01
This paper shows how discrete measurement leads to commutators and how discrete derivatives are naturally represented by commutators in a non-commutative extension of the calculus in which they originally occurred. We show how the square root of minus one (i) arises naturally as a time-sensitive observable for an elementary oscillator. In this sense the square root of minus one is a clock and/or a clock/observer. This sheds new light on Wick rotation, which replaces t (temporal quantity) by it. In this view, the Wick rotation replaces numerical time with elementary temporal observation. The relationship of this remark with the Heisenberg commutator [P,Q]=ihbar is explained in the Introduction. After a review of previous work, the paper begins with a section of iterants - a generalization of the complex numbers as described above. This generalization includes all of matrix algebra in a temporal interpretation. We then give a generalization of the Feynman-Dyson derivation of electromagnetism in the context of n...
Row Sampling for Matrix Algorithms via a Non-Commutative Bernstein Bound
Magdon-Ismail, Malik
2010-01-01
We focus the use of \\emph{row sampling} for approximating matrix algorithms. We give applications to matrix multipication; sparse matrix reconstruction; and, \\math{\\ell_2} regression. For a matrix \\math{\\matA\\in\\R^{m\\times d}} which represents \\math{m} points in \\math{d\\ll m} dimensions, all of these tasks can be achieved in \\math{O(md^2)} via the singular value decomposition (SVD). For appropriate row-sampling probabilities (which typically depend on the norms of the rows of the \\math{m\\times d} left singular matrix of \\math{\\matA} (the \\emph{leverage scores}), we give row-sampling algorithms with linear (up to polylog factors) dependence on the stable rank of \\math{\\matA}. This result is achieved through the application of non-commutative Bernstein bounds. We then give, to our knowledge, the first algorithms for computing approximations to the appropriate row-sampling probabilities without going through the SVD of \\math{\\matA}. Thus, these are the first \\math{o(md^2)} algorithms for row-sampling based appro...
Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry
Boyle, Latham; Farnsworth, Shane
2015-04-01
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. Recently, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra U(1) B - L gauge symmetry, and a single extra complex scalar field σ, which is a singlet under SU(3)C × SU(2)L × U(1)Y , but has B - L = 2 . This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction. We acknowledge support from an NSERC Discovery Grant.
Rethinking Connes’ Approach to the Standard Model of Particle Physics Via Non-Commutative Geometry
Farnsworth, Shane; Boyle, Latham
2015-02-01
Connes’ non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra U{{(1)}B-L} gauge symmetry, and a single extra complex scalar field σ, which is a singlet under SU{{(3)}C}× SU{{(2)}L}× U{{(1)}Y}, but has B-L=2. This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction.
Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry
Farnsworth, Shane
2015-01-01
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra $U(1)_{B-L}$ gauge symmetry, and a single extra complex scalar field $\\sigma$, which is a singlet under $SU(3)_{C}\\times SU(2)_{L}\\times U(1)_{Y}$, but has $B-L=2$. This field has cosmological implications, and offers a new solu...
Lagrangian for Frenkel electron and position's non-commutativity due to spin
Energy Technology Data Exchange (ETDEWEB)
Deriglazov, Alexei A. [Universidade Federal de Juiz de Fora, Depto. de Matematica, ICE, Juiz de Fora, MG (Brazil); Tomsk Polytechnic University, Laboratory of Mathematical Physics, Tomsk (Russian Federation); Pupasov-Maksimov, Andrey M. [Universidade Federal de Juiz de Fora, Depto. de Matematica, ICE, Juiz de Fora, MG (Brazil)
2014-10-15
We construct a relativistic spinning-particle Lagrangian where spin is considered as a composite quantity constructed on the base of a non-Grassmann vector-like variable. The variational problem guarantees both a fixed value of the spin and the Frenkel condition on the spin-tensor. The Frenkel condition inevitably leads to relativistic corrections of the Poisson algebra of the position variables: their classical brackets became noncommutative. We construct the relativistic quantum mechanics in the canonical formalism (in the physical-time parametrization) and in the covariant formalism (in an arbitrary parametrization). We show how state vectors and operators of the covariant formulation can be used to compute the mean values of physical operators in the canonical formalism, thus proving its relativistic covariance. We establish relations between the Frenkel electron and positive-energy sector of the Dirac equation. Various candidates for the position and spin operators of an electron acquire clear meaning and interpretation in the Lagrangian model of the Frenkel electron. Our results argue in favor of Pryce's (d)-type operators as the spin and position operators of Dirac theory. This implies that the effects of non-commutativity could be expected already at the Compton wavelength. We also present the manifestly covariant form of the spin and position operators of the Dirac equation. (orig.)
Revisiting Connes' Finite Spectral Distance on Non-commutative Spaces : Moyal Plane and Fuzzy Sphere
Devi, Yendrembam Chaoba; Bose, Aritra N; Kumar, Kaushlendra; Chakraborty, Biswajit; Scholtz, Frederik G
2016-01-01
We revise and extend the algorithm provided in [1] to compute the finite Connes' distance between normal states. The original formula in [1] contains an error and actually only provides a lower bound. The correct expression, which we provide here, involves the computation of the infimum of an expression which involves the "transverse" component of the algebra element in addition to the "longitudinal" component of [1]. This renders the formula less user-friendly, as the determination of the exact transverse component for which the infimum is reached remains a non-trivial task, but under rather generic conditions it turns out that the Connes' distance is proportional to the trace norm of the difference in the density matrices, leading to considerable simplification. In addition, we can determine an upper bound of the distance by emulating and adapting the approach of [2] in our Hilbert-Schmidt operatorial formulation. We then look for an optimal element for which the upper bound is reached. We are able to find ...
Semiclassical Analysis of String/Gauge Duality on Non-commutative Space
Rashkov, R C; Yang, Y; Yang, Yi
2004-01-01
We use semiclassical method to study closed strings in the modified AdS_5*S^5 background with constant B-fields. The point-like closed strings and the streched closed strings rotating around the big circle of S^5 are considered. Quantization of these closed string leads to a time-dependent string spectrum, which we argue to correspond to the RG-flow of the dual noncommutative Yang Mills theory.
Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
Haghighat, M
2014-01-01
Comparing electronic Hydrogen with muonic Hydrogen shows that the discrepancy in measurement of the Lamb shift in the both systems are relatively of order of $(\\frac{m_\\mu}{m_e})^{4-5}$. We explore the spectrum of Hydrogen atom in noncommutative $QED$ to compare the noncommutative effects on the both bound states. We show that in the Lorentz violating noncommutative QED the ratio of NC-corrections is $(\\frac{m_\\mu}{m_e})^3$ while in the Lorentz conserving NCQED is $(\\frac{m_\\mu}{m_e})^5$. An uncertainty about $1 \\,Hz\\ll 3\\,kHz$ in the Lamb shift of Hydrogen atom leads to an NC correction about $10 \\,MHz$ in the Lorentz violating noncommutative QED and about $400 \\,GHz$ in the Lorentz conserving noncommutative QED.
Non-Commutative Fock-Darwin System and Magnetic Field Limits
Institute of Scientific and Technical Information of China (English)
YU Xiao-Min; LI Kang
2008-01-01
A Fock-Darwin system in noncommutative quantum mechanics is studied. By constructing Heisenberg algebra we obtain the levels on noncommutative space and noncommutative phase space, and give the corrections to the results in usual quantum mechanics. Moreover, to search the difference among the three spaces, the degeneracy is analysed by two ways, the value of (ω)/(ω)c and certain algebra realization (SU(2)and SU(1,1)), and some interesting properties in the magnetic field limit are exhibited, such as totally different degeneracy and magic number distribution for the given frequency or mass of a system in strong magnetic field.
Relativistic phase space dimensional recurrences
Delbourgo, Robert
2003-01-01
We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius $R$ and taking the limit as $R \\to \\infty$. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension.
Energy Technology Data Exchange (ETDEWEB)
Parker, E.N. [Univ. of Chicago, IL (United States)
1994-10-01
Space science began with the indirect phase where the activity in space was inferred from such terrestrial phenomena as geomagnetic storms, ionospheric variations, and fluctuations in the cosmic ray intensity. The direct phase was initiated with spaceflight placing instruments directly in space and permitting the direct observation of UV and X rays, as well as precision observations of solar luminosity variations. The evidence from these many direct studies, together with the historical record of terrestrial conditions, shows that the variations of the luminosity of the Sun affect the terrestrial atmosphere at all levels, with devastating changes in climate tracking the major changes in the activity level and luminosity of the Sun. The quantification and understanding of this vital connection should be the first priority of space science and geophysics, from oceans and atmosphere through the ionosphere, magnetosphere, and all the way to the convective zone of the Sun. It becomes the vital phase of space science, focused on the basic science of the changing habitability of Earth. 13 refs.
Quantum processes on phase space
Anastopoulos, C
2003-01-01
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for histories; this object is the decoherence functional of the consistent histories approach. If we take phases as well as probabilities as primitive elements of our theory, we abandon Kolmogorov probability and can describe quantum theory in terms of fundamental commutative observables, without being obstructed by Bell's and related theorems. Generalising the theory of stochastic processes, we develop the description of relative phases and probabilities for paths on the classical phase space. This description provides a theory of quantum processes. We identify a number of basic postulates and study its corresponding properties. We strongly emphasise the notion of conditioning and are able to write ``quantum differential equations'' as analogous to stochastic differential equations...
Sica, Louis
2011-01-01
As discussed below, Bell's inequalities and experimental results rule out commutative hidden variable models as a basis for Bell correlations, but not necessarily non-commutative probability models. A local probability model is constructed for Bell correlations based on non-commutative operations involving polarizers. As in the entanglement model, the Bell correlation is obtained from a probability calculus without explicit use of deterministic hidden variables. The probability calculus used is associated with chaotic light. Joint wave intensity correlations at spatially separated polarization analyzers are computed using common information originating at the source. When interpreted as photon count rates, these yield quantum mechanical joint probabilities after the contribution of indeterminate numbers of photon pairs greater than one is subtracted out. The formalism appears to give a local account of Bell correlations.
Non-commutative U(1) gauge theory on R{sub {theta}}{sup 4} with oscillator term and BRST symmetry
Energy Technology Data Exchange (ETDEWEB)
Blaschke, D.N.; Schweda, M. [Vienna Univ. of Technology, Institute for Theoretical Physics (Austria); Grosse, H. [Vienna Univ., Faculty of Physics(Austria)
2007-09-15
Inspired by the renormalizability of the non-commutative {phi}{sup 4} model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term in a BRST (Becchi-Rouet-Stora-Tyutin) invariant manner. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory. (authors)
Pati-Salam Unification from Non-commutative Geometry and the TeV-scale W_R boson
Aydemir, Ufuk; Sun, Chen; Takeuchi, Tatsu
2016-01-01
We analyze the compatibility of the unified left-right symmetric Pati-Salam models motivated by non-commutative geometry and the TeV scale right-handed W boson suggested by recent LHC data. We find that the unification/matching conditions place conflicting demands on the symmetry breaking scales and that generating the required W_R mass and coupling is non-trivial.
Longitudinal phase space tomography with space charge
Hancock, S.; Lindroos, M.; Koscielniak, S.
2000-12-01
Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the nonlinearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of the vacuum chamber parametrized by a single value of distributed reactive impedance and by a geometrical coupling coefficient. This is sufficient to model the dominant collective effects in machines of low to moderate energy. In contrast to simulation codes, binning is not an issue since the profiles to be differentiated are measured ones. The program is written in Fortran 90 with high-performance Fortran extensions for parallel processing. A major effort has been made to identify and remove execution bottlenecks, for example, by reducing floating-point calculations and recoding slow intrinsic functions. A pointerlike mechanism which avoids the problems associated with pointers and parallel processing has been implemented. This is required to handle the large, sparse matrices that the algorithm employs. Results obtained with and without the inclusion of space charge are presented and compared for proton beams in the CERN protron synchrotron booster. Comparisons
Phase space embedding of electrocardiograms
Richter, M; Richter, Marcus; Schreiber, Thomas
1998-01-01
We study properties of the human electrocardiogram under the working hypothesis that fluctuations beyond the regular structure of single cardiac cycles are unpredictable. On this background we discuss the possibility to use the phase space embedding method for this kind of signal. In particular, the specific nature of the stochastic or high dimensional component allows to use phase space embeddings for certain signal processing tasks. As practical applications, we discuss noise filtering, fetal ECG extraction, and the automatic detection of clinically relevant features. The main purpose of the paper is to connect results of embedding theory which had not been previously applied in practise, and practical applications which had not yet been justified theoretically.
Quantum Shuttle in Phase Space
DEFF Research Database (Denmark)
Novotny, Tomas; Donarini, Andrea; Jauho, Antti-Pekka
2003-01-01
Abstract: We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a crossover from the tunneling to the shuttling regime, thus...... extending the previously found classical results to the quantum domain. Further, a new dynamical regime is discovered, where the shuttling is driven exclusively by the quantum noise....
Late time acceleration in a non-commutative model of modified cosmology
Malekolkalami, B; Vakili, B
2014-01-01
We investigate the effects of noncommutativity between the position-position, position-momentum and momentum-momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such noncommutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of a $\\alpha$-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables takes the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.
Simplicity in simplicial phase space
Dittrich, Bianca
2010-01-01
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding to simplicial geometries. On the one hand, this could serve as a starting point for a derivation of spin foam models by canonical quantisation. On the other, it elucidates the interpretation of the boundary Hilbert space that arises in spin foam models. More precisely, we discuss different versions of the simplicity constraints, namely gauge-variant and gauge-invariant versions. In the gauge-variant version, the primary and secondary simplicity constraints take a similar form to the reality conditions known already in the context of (complex) Ashtekar variables. Subsequently, we describe the effect of these primary and secondary simplicity constraints on gauge-invariant variables. This allows us to illustrate their equivalence to the so-called diagonal, cross and edge simpli...
Passive longitudinal phase space linearizer
Directory of Open Access Journals (Sweden)
P. Craievich
2010-03-01
Full Text Available We report on the possibility to passively linearize the bunch compression process in electron linacs for the next generation x-ray free electron lasers. This can be done by using the monopole wakefields in a dielectric-lined waveguide. The optimum longitudinal voltage loss over the length of the bunch is calculated in order to compensate both the second-order rf time curvature and the second-order momentum compaction terms. Thus, the longitudinal phase space after the compression process is linearized up to a fourth-order term introduced by the convolution between the bunch and the monopole wake function.
Chaotic eigenfunctions in phase space
Nonnenmacher, S
1997-01-01
We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann-Husimi representations for quantum states, as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions, which reminds of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on ``chaotic eigenconstellations", we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions fo...
Institute of Scientific and Technical Information of China (English)
李怀兵; 丑武胜; 冯震
2011-01-01
Torque ripple is an important factor affecting the performance of Brushless DC motor (BLDCM).In this paper, the non-commutation torque ripple was analyzed, focusing on the torque ripple caused by PWM_ON modulation.The main part of the torque ripple was caused by the PWM_OFF, and the diode freewheeling of inactive phase can compensate the torque ripple to some extent.Meanwhile, hysteresis current control was proposed to suppress the non-commutation torque ripple.The simulation and experiment show the difference between the method and the traditional method, and prove the validity of the method suppressing the torque ripple during non-commutation.%无刷直流电机的转矩脉动是影响其性能的重要因素.该文针对非换相期间的转矩脉动进行了分析,重点研究了PWM_ON调制方式时的转矩脉动.PWM信号为"OFF"时续流引起的转矩脉动占主要部分,非导通相续流在一定程度上可以补偿PWM关断时造成的转矩脉动.同时,提出使用滞环电流控制方法,采用该方法可以抑制非换相期间转矩脉动.通过仿真分析和实验验证了该方法和传统方法的差异,证明了该方法在非换相期间抑制转矩脉动的有效性.
Non-commutative Fock-Darwin system and its magnetism properties
Institute of Scientific and Technical Information of China (English)
Yu Xiao-Min; Li Kang
2009-01-01
The Fock-Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space,but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further,we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures,the occurrence of the magnetization in a zero magnetic field and zero temperature limit,and so on.
A general formalism for phase space calculations
Norbury, John W.; Deutchman, Philip A.; Townsend, Lawrence W.; Cucinotta, Francis A.
1988-01-01
General formulas for calculating the interactions of galactic cosmic rays with target nuclei are presented. Methods for calculating the appropriate normalization volume elements and phase space factors are presented. Particular emphasis is placed on obtaining correct phase space factors for 2-, and 3-body final states. Calculations for both Lorentz-invariant and noninvariant phase space are presented.
Wilson Line Correlators in N=4 Non-commutative Gauge Theory on S^2 x S^2
Kitazawa, Y; Tomino, D
2004-01-01
We investigate the Wilson line correlators dual to supergravity multiplets in N=4 non-commutative gauge theory on S^2 x S^2. We find additional non-analytic contributions to the correlators due to UV/IR mixing in comparison to ordinary gauge theory. Although they are no longer BPS off shell, their renormalization effects are finite as long as they carry finite momenta. We propose a renormalization procedure to obtain local operators with no anomalous dimensions in perturbation theory. We reflect on our results from dual supergravity point of view. We show that supergravity can account for both IR and UV/IR contributions.
Indian Academy of Sciences (India)
Barbara Jasiulis-Gołdyn; Anna Kula
2012-08-01
The paper deals with the notions of weak stability and weak generalized convolution with respect to a generalized convolution, introduced by Kucharczak and Urbanik. We study properties of such objects and give examples of weakly stable measures with respect to the Kendall convolution. Moreover, we show that in the context of non-commutative probability, two operations: the -convolution and the (,1)-convolution satisfy the Urbanik’s conditions for a generalized convolution, interpreted on the set of moment sequences. The weak stability reveals the relation between two operations.
The eigenvalue problem in phase space.
Cohen, Leon
2017-07-27
We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
T-duality with H-flux. Non-commutativity, T-folds and G x G structure
Energy Technology Data Exchange (ETDEWEB)
Grange, P. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik; Schaefer-Nameki, S. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik]|[Hamburg Univ. (Germany). Zentrum fuer Mathematische Physik]|[California Inst. of Tech., Pasadena (United States)
2006-09-15
Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU(3) x SU(3) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU(3)-invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors. (orig.)
Chern-Simons in the Seiberg-Witten map for non-commutative Abelian gauge theories in 4D
Picariello, M; Sorella, S P; Picariello, Marco; Quadri, Andrea; Sorella, Silvio P.
2002-01-01
A cohomological BRST characterization of the Seiberg-Witten (SW) map is given. We prove that the coefficients of the SW map can be identified with elements of the cohomology of the BRST operator modulo a total derivative. As an example, it will be illustrated how the first coefficients of the SW map can be written in terms of the Chern-Simons three form. This suggests a deep topological and geometrical origin of the SW map. The existence of the map for both Abelian and non-Abelian case is discussed. By using a recursive argument and the associativity of the $\\star$-product, we shall be able to prove that the Wess-Zumino consistency condition for non-commutative BRST transformations is fulfilled. The recipe of obtaining an explicit solution by use of the homotopy operator is briefly reviewed in the Abelian case.
One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative p^{-2} U(1 Gauge Model
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2010-05-01
Full Text Available This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θ-deformed non-commutative p^{-2} model originally introduced by Gurau et al. [Comm. Math. Phys. 287 (2009, 275-290]. It is shown that breaking terms of the form used by Vilar et al. [J. Phys. A: Math. Theor. 43 (2010, 135401, 13 pages] and ourselves [Eur. Phys. J. C: Part. Fields 62 (2009, 433-443] to localize the BRST covariant operator (D^2θ^2D^2^{-1} lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.
Chaotic systems in complex phase space
Bender, Carl M; Hook, Daniel W; Weir, David J
2008-01-01
This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviors of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.
Transverse phase space and its multipole decomposition
Lorcé, Cédric
2016-01-01
Relativistic phase space distributions are very interesting objects as they allow one to gather the information extracted from various types of experiments into a single coherent picture. Focusing on the four-dimensional transverse phase space, we identified all the possible angular correlations providing at the same time a clear physical interpretation of all the leading-twist generalized and transverse-momentum dependent parton distributions. We also developed a convenient representation of this four-dimensional space.
Hydrogen Atom Spectrum in Noncommutative Phase Space
Institute of Scientific and Technical Information of China (English)
LI Kang; CHAMOUN Nidal
2006-01-01
@@ We study the energy levels of the hydrogen atom in the noncommutative phase space with simultaneous spacespace and momentum-momentum noncommutative relations. We find new terms compared to the case that only noncommutative space-space relations are assumed. We also present some comments on a previous paper [Alavi S A hep-th/0501215].
The Way to Phase Space Crystals
Guo, Lingzhen; Michael, Marthaler; Schön, Gerd
A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial periodicity, but it is driven by a time-dependent field. Under rotating wave approximation, the system can produce a periodic lattice structure in phase space. The band structure in quasienergy arises as a consequence of the n-fold discrete periodicity in phase space induced by this driving field. We propose explicit models to realize such a phase space crystal and analyze its band structure in the frame of a tightbinding approximation. The phase space lattice differs fundamentally from a lattice in real space, because its coordinate system, i.e., phase space, has a noncommutative geometry. The phase space crystal opens new ways to engineer energy band structures, with the added advantage that its properties can be changed in situ by tuning the driving field's parameters. Carl-Zeiss Stiftung.
Phase-space quantization of field theory.
Energy Technology Data Exchange (ETDEWEB)
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Chaotic systems in complex phase space
Indian Academy of Sciences (India)
Carl M Bender; Joshua Feinberg; Daniel W Hook; David J Weir
2009-09-01
This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two $\\mathcal{PT}$ -symmetric dynamical models in complex phase space exhibit strong qualitative similarities.
Phase Space Distribution of Riemann Zeros
Dutta, Parikshit
2016-01-01
We present the partition function of a most generic $U(N)$ single plaquette model in terms of representations of unitary group. Extremising the partition function in large N limit we obtain a relation between eigenvalues of unitary matrices and number of boxes in the most dominant Young tableaux distribution. Since, eigenvalues of unitary matrices behave like coordinates of free fermions whereas, number of boxes in a row is like conjugate momenta of the same, a relation between them allows us to provide a phase space distribution for different phases of the unitary model under consideration. This proves a universal feature that all the phases of a generic unitary matrix model can be described in terms of topology of free fermi phase space distribution. Finally, using this result and analytic properties of resolvent that satisfy Dyson-Schwinger equation, we present a phase space distribution of unfolded zeros of Riemann zeta function.
Compact phase space, cosmological constant, discrete time
Rovelli, Carlo
2015-01-01
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.
A fixed-point principle for a pair of non-commutative operators
Directory of Open Access Journals (Sweden)
Penumarthy Parvateesam Murthy
2014-09-01
Full Text Available In this paper, a fixed point principle for a pair of operators (fi,X,d, i = 1,2, where (X,d is a metric space and f1, f2: X → X, is established under the generalized uniform equivalence condition of different orbits generated by the maps f1 and f2 separately, which gives another generalization of the fixed point principle of Leader [1] and estimates approximations to the fixed points of both the operators simultaneously.
Heisenberg algebra for noncommutative Landau problem
Li, Kang; Cao, Xiao-Hua; Wang, Dong-Yan
2006-10-01
The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.
Heisenberg algebra for noncommutative Landau problem
Institute of Scientific and Technical Information of China (English)
Li Kang; Cao Xiao-Hua; Wang Dong-Yan
2006-01-01
The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.
Phase space methods for degenerate quantum gases
Dalton, Bryan J; Barnett, Stephen M
2015-01-01
Recent experimental progress has enabled cold atomic gases to be studied at nano-kelvin temperatures, creating new states of matter where quantum degeneracy occurs - Bose-Einstein condensates and degenerate Fermi gases. Such quantum states are of macroscopic dimensions. This book presents the phase space theory approach for treating the physics of degenerate quantum gases, an approach already widely used in quantum optics. However, degenerate quantum gases involve massive bosonic and fermionic atoms, not massless photons. The book begins with a review of Fock states for systems of identical atoms, where large numbers of atoms occupy the various single particle states or modes. First, separate modes are considered, and here the quantum density operator is represented by a phase space distribution function of phase space variables which replace mode annihilation, creation operators, the dynamical equation for the density operator determines a Fokker-Planck equation for the distribution function, and measurable...
Noether symmetries in the phase space
Díaz, Bogar; Galindo-Linares, Elizabeth; Ramírez-Romero, Cupatitzio; Silva-Ortigoza, Gilberto; Suárez-Xique, Román; Torres del Castillo, Gerardo F.; Velázquez, Mercedes
2014-09-01
The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Noether symmetries in the phase space
Directory of Open Access Journals (Sweden)
Bogar Díaz
2014-09-01
Full Text Available The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Positive phase space distributions and uncertainty relations
Kruger, Jan
1993-01-01
In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.
Identifying Phase Space Boundaries with Voronoi Tessellations
Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao
2016-11-24
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
Identifying Phase Space Boundaries with Voronoi Tessellations
Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T; Yang, Yuan-Pao
2016-01-01
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
Grassmann phase space theory for fermions
Energy Technology Data Exchange (ETDEWEB)
Dalton, Bryan J. [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria, 3122 (Australia); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow, G4 ONG (United Kingdom); Barnett, Stephen M. [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom)
2017-06-15
A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Formation of Ion Phase-Space Vortexes
DEFF Research Database (Denmark)
Pécseli, Hans; Trulsen, J.; Armstrong, R. J.
1984-01-01
The formation of ion phase space vortexes in the ion two stream region behind electrostatic ion acoustic shocks are observed in a laboratory experiment. A detailed analysis demonstrates that the evolution of such vortexes is associated with ion-ion beam instabilities and a nonlinear equation for ...
Semiclassical TEM image formation in phase space
Energy Technology Data Exchange (ETDEWEB)
Lubk, Axel; Röder, Falk
2015-04-15
Current developments in TEM such as high-resolution imaging at low acceleration voltages and large fields of view, the ever larger capabilities of hardware aberration correction and the systematic shaping of electron beams require accurate descriptions of TEM imaging in terms of wave optics. Since full quantum mechanic solutions have not yet been established for, e.g., the theory of aberrations, we are exploring semiclassical image formation in the TEM from the perspective of quantum mechanical phase space, here. Firstly, we use two well-known semiclassical approximations, Miller's semiclassical algebra and the frozen Gaussian method, for describing the wave optical generalization of arbitrary geometric aberrations, including nonisoplanatic and slope aberrations. Secondly, we demonstrate that the Wigner function representation of phase space is well suited to also describe incoherent aberrations as well as the ramifications of partial coherence due to the emission process at the electron source. We identify a close relationship between classical phase space and Wigner function distortions due to aberrations as well as classical brightness and quantum mechanical purity. - Highlights: • We discuss several semiclassical approximations to describe image formation in the TEM. • We provide laws how aberrations modify quantum mechanical phase space. • We exhibit the close relation between quantum mechanical purity and axial brightness.
Density functional theory on phase space
Blanchard, Philippe; Várilly, Joseph C
2010-01-01
Forty-five years after the point de d\\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the "divine" energy functional in terms of the electron density [2] still eludes us --and possibly will do so forever [3]. In what follows we examine a formulation in the same spirit with phase-space variables. The validity of Hohenberg-Kohn-Levy-type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase-space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation-exchange functionals on phase space. A new proof of the overbinding property of the Mueller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the T...
Characterizing maximally singular phase-space distributions
Sperling, J.
2016-07-01
Phase-space distributions are widely applied in quantum optics to access the nonclassical features of radiations fields. In particular, the inability to interpret the Glauber-Sudarshan distribution in terms of a classical probability density is the fundamental benchmark for quantum light. However, this phase-space distribution cannot be directly reconstructed for arbitrary states, because of its singular behavior. In this work, we perform a characterization of the Glauber-Sudarshan representation in terms of distribution theory. We address important features of such distributions: (i) the maximal degree of their singularities is studied, (ii) the ambiguity of representation is shown, and (iii) their dual space for nonclassicality tests is specified. In this view, we reconsider the methods for regularizing the Glauber-Sudarshan distribution for verifying its nonclassicality. This treatment is supported with comprehensive examples and counterexamples.
Using the Phase Space to Design Complexity
DEFF Research Database (Denmark)
Heinrich, Mary Katherine; Ayres, Phil
2016-01-01
Architecture that is responsive, adaptive, or interactive can contain active architectural elements or robotic sensor-actuator systems. The consideration of architectural robotic elements that utilize distributed control and distributed communication allows for self-organization, emergence......, and evolution on site in real-time. The potential complexity of behaviors in such architectural robotic systems requires design methodology able to encompass a range of possible outcomes, rather than a single solution. We present an approach of adopting an aspect of complexity science and applying...... it to the realm of computational design in architecture, specifically by considering the phase space and related concepts. We consider the scale and predictability of certain design characteristics, and originate the concept of a formation space extension to the phase space, for design to deal directly...
Thermodynamic Products in the Extended Phase Space
Pradhan, Parthapratim
2016-01-01
We have examined the thermodynamic properties of spherically symmetric charged-AdS black hole, charged AdS BH surrounded by quintessence and charged AdS BH in $f(R)$ gravity in the extended phase-space. Where the cosmological constant should be treated as thermodynamic pressure and its conjugate parameter as thermodynamic volume. Then they should behave as a analog of Van der Waal like systems. In the extended phase space we have calculated the \\emph{entropy product} and \\emph{thermodynamic volume product} of all horizons. The mass(or enthalpy) independent nature of the said products signals they are "universal" quantities. Various types of pictorial diagram of the specific heat is given. The divergence of the specific heat indicates that the second order phase transition occurs under certain condition.
The Quantum Space Phase Transitions for Particles and Force Fields
Chung D.-Y.; Krasnoholovets V.
2006-01-01
We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment spac...
Tailoring Accelerating Beams in Phase Space
Wen, Yuanhui; Zhang, Yanfeng; Chen, Hui; Yu, Siyuan
2016-01-01
An appropriate design of wavefront will enable light fields propagating along arbitrary trajectories thus forming accelerating beams in free space. Previous ways of designing such accelerating beams mainly rely on caustic methods, which start from diffraction integrals and only deal with two-dimensional fields. Here we introduce a new perspective to construct accelerating beams in phase space by designing the corresponding Wigner distribution function (WDF). We find such a WDF-based method is capable of providing both the initial field distribution and the angular spectrum in need by projecting the WDF into the real space and the Fourier space respectively. Moreover, this approach applies to the construction of both two- and three-dimensional fields, greatly generalizing previous caustic methods. It may therefore open up a new route to construct highly-tailored accelerating beams and facilitate applications ranging from particle manipulation and trapping to optical routing as well as material processing.
Wavelet analysis of the nuclear phase space
Energy Technology Data Exchange (ETDEWEB)
Jouault, B.; Sebille, F.; Mota, V. de la
1997-12-31
The description of transport phenomena in nuclear matter is addressed in a new approach based on the mathematical theory of wavelets and the projection methods of statistical physics. The advantage of this framework is to offer the opportunity to use information concepts common to both the formulation of physical properties and the mathematical description. This paper focuses on two features, the extraction of relevant informations using the geometrical properties of the underlying phase space and the optimization of the theoretical and numerical treatments based on convenient choices of the representation spaces. (author). 34 refs.
The Morse oscillator in position space, momentum space, and phase space
DEFF Research Database (Denmark)
Dahl, Jens Peder; Springborg, Michael
1988-01-01
functions are to be calculated. The wave and phase space functions are displayed in a series of curves and contour diagrams. An Appendix discusses the calculation of the modified Bessel functions of real, positive argument and complex order, which is required for calculating the phase space functions...
Computed Tomography of Transverse Phase Space
Energy Technology Data Exchange (ETDEWEB)
Watts, A. [Fermilab; Johnstone, C. [Fermilab; Johnstone, J. [Fermilab
2016-09-19
Two computed tomography techniques are explored to reconstruct beam transverse phase space using both simulated beam and multi-wire profile data in the Fermilab Muon Test Area ("MTA") beamline. Both Filtered Back-Projection ("FBP") and Simultaneous Algebraic Reconstruction Technique ("SART") algorithms [2] are considered and compared. Errors and artifacts are compared as a function of each algorithm’s free parameters, and it is shown through simulation and MTA beamline profiles that SART is advantageous for reconstructions with limited profile data.
Noncanonical Phase-Space Noncommutative Black Holes
Bastos, Catarina; Dias, Nuno; Prata, João
2012-01-01
In this contribution we present a noncanonical phase-space noncommutative (NC) extension of a Kantowski Sachs (KS) cosmological model to describe the interior of a Schwarzschild black hole (BH). We evaluate the thermodynamical quantities inside this NC Schwarzschild BH and compare with the well known quantities. We find that for a NCBH the temperature and entropy have the same mass dependence as the Hawking quantities for a Schwarzschild BH.
Semiclassical TEM image formation in phase space.
Lubk, Axel; Röder, Falk
2015-04-01
Current developments in TEM such as high-resolution imaging at low acceleration voltages and large fields of view, the ever larger capabilities of hardware aberration correction and the systematic shaping of electron beams require accurate descriptions of TEM imaging in terms of wave optics. Since full quantum mechanic solutions have not yet been established for, e.g., the theory of aberrations, we are exploring semiclassical image formation in the TEM from the perspective of quantum mechanical phase space, here. Firstly, we use two well-known semiclassical approximations, Miller's semiclassical algebra and the frozen Gaussian method, for describing the wave optical generalization of arbitrary geometric aberrations, including nonisoplanatic and slope aberrations. Secondly, we demonstrate that the Wigner function representation of phase space is well suited to also describe incoherent aberrations as well as the ramifications of partial coherence due to the emission process at the electron source. We identify a close relationship between classical phase space and Wigner function distortions due to aberrations as well as classical brightness and quantum mechanical purity. Copyright © 2014 Elsevier B.V. All rights reserved.
Periodic orbits and TDHF phase space structure
Energy Technology Data Exchange (ETDEWEB)
Hashimoto, Yukio; Iwasawa, Kazuo [Tsukuba Univ., Ibaraki (Japan). Inst. of Physics; Tsukuma, Hidehiko; Sakata, Fumihiko
1998-03-01
The collective motion of atomic nuclei is closely coupled with the motion of nucleons, therefore, it is nonlinear, and the contents of the motion change largely with the increase of its amplitude. As the framework which describes the collective motion accompanied by the change of internal structure, time-dependent Hurtley Fock (TDHF) method is suitable. At present, the authors try to make the method for studying the large region structure in quantum system by utilizing the features of the TDHF phase space. The studies made so far are briefed. In this report, the correspondence of the large region patterns appearing in the band structure chart of three-level model with the periodic orbit group in the TDHF phase space is described. The Husimi function is made, and it possesses the information on the form of respective corresponding intrinsic state. The method of making the band structure chart is explained. There are three kinds of the tendency in the intrinsic state group. The E-T charts are made for the band structure charts to quantitatively express the large region tendency. The E-T chart and the T{sub r}-T chart are drawn for a selected characteristic orbit group. It became to be known that the large region properties of the quantum intrinsic state group of three-level model can be forecast by examining the properties of the periodic orbit group in the TDHF phase space. (K.I.)
Chirp-driven giant phase space vortices
Trivedi, Pallavi; Ganesh, Rajaraman
2016-06-01
In a collisionless, unbounded, one-dimensional plasma, modelled using periodic boundary conditions, formation of steady state phase space coherent structures or phase space vortices (PSV) is investigated. Using a high resolution one-dimensional Vlasov-Poisson solver based on piecewise-parabolic advection scheme, the formation of giant PSV is addressed numerically. For an infinitesimal external drive amplitude and wavenumber k, we demonstrate the existence of a window of chirped external drive frequency that leads to the formation of giant PSV. The linear, small amplitude, external drive, when chirped, is shown to couple effectively to the plasma and increase both streaming of "untrapped" and "trapped" particle fraction. The steady state attained after the external drive is turned off and is shown to lead to a giant PSV with multiple extrema and phase velocities, with excess density fraction, defined as the deviation from the Maxwellian background, Δ n / n 0 ≃ 20 % - 25 % . It is shown that the process depends on the chirp time duration Δt. The excess density fraction Δn/n0, which contains both trapped and untrapped particle contribution, is also seen to scale with Δt, only inhibited by the gradient of the distribution in velocity space. Both single step drive and multistep chirp processes are shown to lead to steady state giant PSV, with multiple extrema due to embedded holes and clumps, long after the external drive is turned off.
Periodic orbits and TDHF phase space structure
Energy Technology Data Exchange (ETDEWEB)
Hashimoto, Yukio; Iwasawa, Kazuo [Tsukuba Univ., Ibaraki (Japan). Inst. of Physics; Tsukuma, Hidehiko; Sakata, Fumihiko
1998-03-01
The collective motion of atomic nuclei is closely coupled with the motion of nucleons, therefore, it is nonlinear, and the contents of the motion change largely with the increase of its amplitude. As the framework which describes the collective motion accompanied by the change of internal structure, time-dependent Hurtley Fock (TDHF) method is suitable. At present, the authors try to make the method for studying the large region structure in quantum system by utilizing the features of the TDHF phase space. The studies made so far are briefed. In this report, the correspondence of the large region patterns appearing in the band structure chart of three-level model with the periodic orbit group in the TDHF phase space is described. The Husimi function is made, and it possesses the information on the form of respective corresponding intrinsic state. The method of making the band structure chart is explained. There are three kinds of the tendency in the intrinsic state group. The E-T charts are made for the band structure charts to quantitatively express the large region tendency. The E-T chart and the T{sub r}-T chart are drawn for a selected characteristic orbit group. It became to be known that the large region properties of the quantum intrinsic state group of three-level model can be forecast by examining the properties of the periodic orbit group in the TDHF phase space. (K.I.)
Quantum geometry from phase space reduction
Conrady, Florian
2009-01-01
In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly, or equivalently, as an integral over the space of classical tetrahedra. This provides an explicit realization of theorems by Guillemin--Sternberg and Hall that describe the commutation of quantization and reduction. In the final part of the paper, we use our result to express the FK spin foam model as an integral over classical tetrahedra and the asymptotics of the vertex amplitude is determined.
The Extended Relativity Theory in Clifford Spaces
Directory of Open Access Journals (Sweden)
Castro C.
2005-04-01
Full Text Available An introduction to some of the most important features of the Extended Relativity theory in Clifford-spaces (C-spaces is presented whose “point” coordinates are non-commuting Clifford-valued quantities which incorporate lines, areas, volumes, hyper-volumes. . . degrees of freedom associated with the collective particle, string, membrane, p-brane. . . dynamics of p-loops (closed p-branes in target D-dimensional spacetime backgrounds. C-space Relativity naturally incorporates the ideas of an invariant length (Planck scale, maximal acceleration, non-commuting coordinates, supersymmetry, holography, higher derivative gravity with torsion and variable dimensions/signatures. It permits to study the dynamics of all (closed p-branes, for all values of p, on a unified footing. It resolves the ordering ambiguities in QFT, the problem of time in Cosmology and admits superluminal propagation (tachyons without violations of causality. A discussion of the maximal-acceleration Relativity principle in phase-spaces follows and the study of the invariance group of symmetry transformations in phase-space allows to show why Planck areas are invariant under acceleration-boosts transformations. This invariance feature suggests that a maximal-string tension principle may be operating in Nature. We continue by pointing out how the relativity of signatures of the underlying n-dimensional spacetime results from taking different n-dimensional slices through C-space. The conformal group in spacetime emerges as a natural subgroup of the Clifford group and Relativity in C-spaces involves natural scale changes in the sizes of physical objects without the introduction of forces nor Weyl’s gauge field of dilations. We finalize by constructing the generalization of Maxwell theory of Electrodynamics of point charges to a theory in C-spaces that involves extended charges coupled to antisymmetric tensor fields of arbitrary rank. In the concluding remarks we outline briefly
Measurement of Phase Coherence in Space Turbulence
Belmont, G.; Panis, J.; Rezeau, L.; Sahraoui, F.
2008-12-01
In many space plasmas such as Magnetosheath, intense magnetic fluctuations are permanently observed, with power law spectra. Assuming these fluctuations belong to some kind of turbulence, which can legitimately be suspected, spectra are clearly not sufficient to characterize it. Is this turbulence made of non linear "phase-coherent" structures, like in the classical Kolmogorov image, or is it made of incoherent waves as in weak turbulence? Is it homogeneous in space and scales or is it intermittent? " Many methods allow analyzing the statistical properties of turbulence, and the results obtained by tools such as structure functions or wavelets are of course influenced by all these properties, such providing indirect information about them. But few of them are specifically dedicated to the study of phase coherence so that the consequences that can be inferred from them are generally not univocal for this point of view. We will review those few tools existing in the literature that allow measuring more directly the phase coherence and present a new method, called "phase gradient analysis", which we are presently developing for this analysis. Preliminary results of this new tool will be presented.
The symplectic camel and phase space quantization
Energy Technology Data Exchange (ETDEWEB)
Gosson, Maurice de [Blekinge Institute of Technology, Karlskrona (Sweden)
2001-11-30
We show that a result of symplectic topology, Gromov's non-squeezing theorem, also known as the 'principle of the symplectic camel', can be used to quantize phase space in cells. That quantization scheme leads to the correct energy levels for integrable systems and to Maslov quantization of Lagrangian manifolds by purely topological arguments. We finally show that the argument leading to the proof of the non-squeezing theorem leads to a classical form of Heisenberg's inequalities. (author)
Dissipative fragmentation in a phase space approach
Energy Technology Data Exchange (ETDEWEB)
Adorno, A.; Di Toro, M.; Bonasera, A.; Gregoire, C.; Gulminelli, F.
Semi-classical approaches have evidenced the role of one and two-body dissipation in nucleus-nucleus collisions. On the other hand, a substantial energy dissipation and some angular momentum transfer have been observed at moderate energy where a fragmentation process is the dominant reaction mechanism. In order to analyse main features of these reactions, we developed a phenomenological model taking into account phase space constraints. The transition between deep inelastic collisions and abrasion-like fragmentation is described and a general agreement with available data is found.
Experimental Observations of Ion Phase-Space Vortices
DEFF Research Database (Denmark)
Pécseli, Hans; Armstrong, R. J.; Trulsen, J.
1981-01-01
Experimental observations of ion phase-space vortices are reported. The ion phase-space vortices form in the region of heated ions behind electrostatic ion acoustic shocks. The results are in qualitative agreement with numerical and analytic studies....
Space Transportation Engine Program (STEP), phase B
1990-10-01
The Space Transportation Engine Program (STEP) Phase 2 effort includes preliminary design and activities plan preparation that will allow smooth and time transition into a Prototype Phase and then into Phases 3, 4, and 5. A Concurrent Engineering approach using Total Quality Management (TQM) techniques, is being applied to define an oxygen-hydrogen engine. The baseline from Phase 1/1' studies was used as a point of departure for trade studies and analyses. Existing STME system models are being enhanced as more detailed module/component characteristics are determined. Preliminary designs for the open expander, closed expander, and gas generator cycles were prepared, and recommendations for cycle selection made at the Design Concept Review (DCR). As a result of July '90 DCR, and information subsequently supplied to the Technical Review Team, a gas generator cycle was selected. Results of the various Advanced Development Programs (ADP's) for the Advanced Launch Systems (ALS) were contributive to this effort. An active vehicle integration effort is supplying the NASA, Air Force, and vehicle contractors with engine parameters and data, and flowing down appropriate vehicle requirements. Engine design and analysis trade studies are being documented in a data base that was developed and is being used to organize information. To date, seventy four trade studies were input to the data base.
The Quantum Space Phase Transitions for Particles and Force Fields
Directory of Open Access Journals (Sweden)
Chung D.-Y.
2006-07-01
Full Text Available We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment space is miscible to detachment space, and there is no separation between attachment space and detachment spaces. In binary partition space, detachment space and attachment space are in two separat continuous regions. The transition from wavefunction to the collapse of wavefuction under interference becomes the quantum space phase transition from binary lattice space to miscible space. At extremely conditions, the gauge boson force field undergoes a quantum space phase transition to a "hedge boson force field", consisting of a "vacuum" core surrounded by a hedge boson shell, like a bubble with boundary.
Institute of Scientific and Technical Information of China (English)
潘前华; 危韧勇
2009-01-01
The torque ripple caused by diode freewheeling of the inactive phase during non-commutation state of PM brushless DC motor (BLDCM) when using the PWM_ON type of pulse width modulation was analyzed. And the characteris-tics of PWM_ON_PWM type of pulse width modulation was also discussed. Simulation with Matlab indicates that PWM_ON _PWM type is better than other traditional types of PWM in reducing torque ripple during non-commutation state of BLD-CM.%分析了传统的FWM_ON调制方式对无刷直流电动机在非换相期间由于截止相的反并联二极管续流而导致转矩脉动的原因.还分析了PWM_ON_PWM调制方式的运行特性.Matlab仿真表明此种调制方式应用在无刷直流电动机非换相转矩脉动抑制上比传统调制方式具有更好的效果.
Integrable system on phase space with nonplanar metrics
Bogdanov, E I
2001-01-01
The problem on the integrability of the evolution system on the phase spaces with the nonplanar metrics is studied. It is shown that in the case, when the phase space is a sphere, the system Hamiltonians are generated under the action of the Poisson operators on the variations of the phase space geodesic lines and the problem on the evolution system integrability is reduced to the task on the integrability of the repers motion equations on the phase space. The bihamiltonian representation of the evaluation systems is connected with the differential-geometric properties of the phase space
Phase-space networks of geometrically frustrated systems
Han, Yilong
2009-11-01
We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.
Solvable Models on Noncommutative Spaces with Minimal Length Uncertainty Relations
Dey, Sanjib
2014-01-01
Our main focus is to explore different models in noncommutative spaces in higher dimensions. We provide a procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing non-commutative spaces. The representations for the corresponding operators obey algebras whose uncertainty relations lead to minimal length, areas and volumes in phase space, which are in principle natural candidates of many different approaches of quantum gravity. We study some explicit models on these types of noncommutative spaces, first by utilising the perturbation theory, later in an exact manner. In many cases the operators are not Hermitian, therefore we use PT -symmetry and pseudo-Hermiticity property, wherever applicable, to make them self-consistent. Apart from building mathematical models, we focus on the physical implications of noncommutative theories too. We construct Klauder coherent states for the perturbative and nonperturbative noncommutative ha...
Cosmology with Galaxy Cluster Phase Spaces
Stark, Alejo; Huterer, Dragan
2016-01-01
We present a novel approach to constrain accelerating cosmologies with galaxy cluster phase spaces. With the Fisher matrix formalism we forecast constraints on the cosmological parameters that describe the cosmological expansion history. We find that our probe has the potential of providing constraints comparable to, or even stronger than, those from other cosmological probes. More specifically, with 1000 (100) clusters uniformly distributed in redshift between $ 0 \\leq z \\leq 0.8$, after applying a conservative $40\\%$ mass scatter prior on each cluster and marginalizing over all other parameters, we forecast $1\\sigma$ constraints on the dark energy equation of state $w$ and matter density parameter $\\Omega_M$ of $\\sigma_w = 0.161 (0.508)$ and $\\sigma_{\\Omega_M} = 0.001 (0.005)$ in a flat universe. Assuming the same galaxy cluster parameter priors and adding a prior on the Hubble constant we can achieve tight constraints on the CPL parametrization of the dark energy equation of state parameters $w_0$ and $w_a...
Phase Space Cell in Nonextensive Classical Systems
Directory of Open Access Journals (Sweden)
Piero Quarati
2003-06-01
Full Text Available Abstract: We calculate the phase space volume ÃŽÂ© occupied by a nonextensive system of N classical particles described by an equilibrium (or steady-state, or long-term stationary state of a nonequilibrium system distribution function, which slightly deviates from Maxwell-Boltzmann (MB distribution in the high energy tail. We explicitly require that the number of accessible microstates does not change respect to the extensive MB case. We also derive, within a classical scheme, an analytical expression of the elementary cell that can be seen as a macrocell, different from the third power of Planck constant. Thermodynamic quantities like entropy, chemical potential and free energy of a classical ideal gas, depending on elementary cell, are evaluated. Considering the fractional deviation from MB distribution we can deduce a physical meaning of the nonextensive parameter q of the Tsallis nonextensive thermostatistics in terms of particle correlation functions (valid at least in the case, discussed in this work, of small deviations from MB standard case.
Constructing Phase Space Distributions within the Heliosheath
Roelof, E. C.
2014-12-01
The key function in the description of the dynamics of the heliosheath (HS) is the phase space distribution (PSD) of the protons, i.e., how the interaction between the thermal and non-thermal (heated pick-up) proton populations evolves from the termination shock to the heliopause (HP) in this high-beta plasma. Voyager 1 found the heliopause to be essentially a (compound) magnetic separatrix, because the intensity of the non-thermal particle population became undetectably small beyond the HP, whereas the anisotropy characteristics of the galactic cosmic rays were consistent with no re-entry of the magnetic field lines into the HS (at either end). This paper attempts to synthesize in situ observations from Voyagers 1 and 2 (thermal plasma, magnetic field, energetic ions, and cosmic rays) with global ENA images from IBEX and Cassini/INCA into a self-consistent representation of the PSD within the noseward HS from thermal energies to several MeV/nuc. The interpretation of the ENA images requires assumptions on the global behavior of the bulk plasma flow throughout the HS that are self-consistent with all the available data (e.g., the spatial and energy dependence of the IBEX ribbon), because the Compton-Getting effects produced by the flows strongly affect the intensities (and thereby the partial densities and pressures) inferred from the ENA images.
Overview of Phase Space Manipulations of Relativistic Electron Beams
Energy Technology Data Exchange (ETDEWEB)
Xiang, Dao; /SLAC
2012-08-31
Phase space manipulation is a process to rearrange beam's distribution in 6-D phase space. In this paper, we give an overview of the techniques for tailoring beam distribution in 2D, 4D, and 6D phase space to meet the requirements of various applications. These techniques become a new focus of accelerator physics R&D and very likely these advanced concepts will open up new opportunities in advanced accelerators and the science enabled by them.
Wave mechanics in quantum phase space: hydrogen atom
Institute of Scientific and Technical Information of China (English)
LU Jun
2007-01-01
The rigorous sohutions of the stationary Schr(o)dinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The "Fourier-like"projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.
An Extra Phase for Two-Mode Coherent States Displaced in Noncommutative Phase Space
Institute of Scientific and Technical Information of China (English)
YAN Long; FENG Xun-Li; ZHANG Zhi-Ming; LIU Song-Hao
2012-01-01
Using deformed boson algebra,we study the property of two-mode coherent states in noncommutative phase space.When a two-mode field evolves in the noncommutative phase space,it can acquire an extra θ-dependent phase compared to the case of commutative space.This phase is detectable and may be used to test noncommutativity.%Using deformed boson algebra, we study the property of two-mode coherent states in noncommutative phase space. When a two-mode field evolves in the noncommutative phase space, it can acquire an extra 9-dependent phase compared to the case of commutative space. This phase is detectable and may be used to test noncommutativity.
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...
The Bohr-Heisenberg correspondence principle viewed from phase space
DEFF Research Database (Denmark)
Dahl, Jens Peder
2002-01-01
Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can...
Entropic gravity, phase-space noncommutativity and the equivalence principle
Energy Technology Data Exchange (ETDEWEB)
Bastos, Catarina [Instituto de Plasmas e Fusao Nuclear, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Bertolami, Orfeu [Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Dias, Nuno Costa; Prata, Joao Nuno, E-mail: catarina.bastos@ist.utl.pt, E-mail: orfeu.bertolami@fc.up.pt, E-mail: ncdias@meo.pt, E-mail: joao.prata@mail.telepac.pt [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande, 376, 1749-024 Lisboa (Portugal)
2011-06-21
We generalize E Verlinde's entropic gravity reasoning to a phase-space noncommutativity setup. This allows us to impose a bound on the product of the noncommutative parameters based on the equivalence principle. The key feature of our analysis is an effective Planck's constant that naturally arises when accounting for the noncommutative features of the phase-space.
Phase space formalisms of quantum mechanics with singular kernel
Sala, P R; Muga, J G
1997-01-01
The equivalence of the Rivier-Margenau-Hill and Born-Jordan-Shankara phase space formalisms to the conventional operator approach of quantum mechanics is demonstrated. It is shown that in spite of the presence of singular kernels the mappings relating phase space functions and operators back and forth are possible.
Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle
Bastos, Catarina; Dias, Nuno Costa; Prata, João Nuno
2010-01-01
We generalize E. Verlinde's entropic gravity reasoning to a phase-space noncommutativity set-up. This allow us to impose a bound on the product of the noncommutative parameters based on the Equivalence Principle. The key feature of our analysis is an effective Planck's constant that naturally arises when accounting for the noncommutative features of the phase-space.
Wigner function for discrete phase space: exorcising ghost images
Arg"uelles, A; Arg\\"uelles, Arturo; Dittrich, Thomas
2005-01-01
We construct, using simple geometrical arguments, a Wigner function defined on a discrete phase space of arbitrary integer Hilbert-space dimension that is free of redundancies. ``Ghost images'' plaguing other Wigner functions for discrete phase spaces are thus revealed as artifacts. It allows to devise a corresponding phase-space propagator in an unambiguous manner. We apply our definitions to eigenstates and propagator of the quantum baker map. Scars on unstable periodic points of the corresponding classical map become visible with unprecedented resolution.
Quantum Theory of Reactive Scattering in Phase Space
Goussev, Arseni; Waalkens, Holger; Wiggins, Stephen
2010-01-01
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of phase space structure, a {\\em normally hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the phase space structures governing reaction dynamics are built. The quantum normal form theory provides a method for quantizing these phase space structures through the use of the Weyl quantization procedure. We show that this approach provides a solution of the time-independent Schr\\"odinger equation leading to a (local) S-matrix in a neighborhood of the saddle point governing the reaction. It follows easily that the qu...
Noncommutative Spaces and Poincar\\'e Symmetry
Meljanac, Stjepan; Mercati, Flavio; Pikutić, Danijel
2016-01-01
We present a framework which unifies a large class of non-commutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the coordinates, with structure constants depending on the momenta plus terms depending only on the momenta. The possible implementations of the action of Poincar\\'e transformations on these deformed phase spaces are considered, together with the consistency requirements they introduce. It is found that Lorentz transformations in general act nontrivially on tensor products of momenta. In particular, a 'backreaction' effect needs to be considered, which changes in a momentum-dependent way the Lorentz group element which acts on the left and on the right of a composition of two momenta. We conclude with two representative examples, which illustrate the 'backreaction' effect.
Space law information system design, phase 2
Morenoff, J.; Roth, D. L.; Singleton, J. W.
1973-01-01
Design alternatives were defined for the implementation of a Space Law Information System for the Office of the General Counsel, NASA. A thesaurus of space law terms was developed and a selected document sample indexed on the basis of that thesaurus. Abstracts were also prepared for the sample document set.
Cryptanalysis of an information encryption in phase space
Wang, Y.; Quan, C.; Tay, C. J.
2016-10-01
In this paper, we evaluate the security of an information encryption in phase space. We show that the scheme is vulnerable to two kinds of attack, namely, a chosen-ciphertext attack and a known-plaintext attack which is based on an iterative phase-retrieval algorithm using multiple plaintext-ciphertext pairs. The validity of the proposed methods of attack is verified by numerical simulations. The results cast doubts on the present security of information encryption in phase space.
Real-space Berry phases: Skyrmion soccer (invited)
Everschor-Sitte, Karin; Sitte, Matthias
2014-05-01
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.
Real-space Berry phases: Skyrmion soccer (invited)
Energy Technology Data Exchange (ETDEWEB)
Everschor-Sitte, Karin, E-mail: karin@physics.utexas.edu; Sitte, Matthias [The University of Texas at Austin, Department of Physics, 2515 Speedway, Austin, Texas 78712 (United States)
2014-05-07
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.
Tracing the Dark Matter Sheet in Phase Space
Abel, Tom; Kaehler, Ralf
2011-01-01
The primordial dark matter velocity dispersion is small compared to the velocities attained during structure formation. Its initial density distribution is close to uniform and it occupies an initial sheet in phase space that is single valued in velocity space. Because of gravitational forces this three dimensional manifold evolves in phase space without ever tearing, conserving phase-space volume and preserving the connectivity of nearby points. N-body simulations already follow the motion of this sheet in phase space. This fact can be used to extract full fine-grained phase-space-structure information from existing cosmological N-body simulations. Particles are considered as the vertices of an unstructured three dimensional mesh, moving in six dimensional phase-space. On this mesh, mass density and momentum are uniquely defined. We show how to obtain the space density of the fluid, detect caustics, and count the number of streams as well as their individual contributions to any point in configuration-space....
Unequally spaced four levels phase encoding in holographic data storage
Xu, Ke; Huang, Yong; Lin, Xiao; Cheng, Yabin; Li, Xiaotong; Tan, Xiaodi
2016-12-01
Holographic data storage system is a candidate for the information recording due to its large storage capacity and high transfer rate. We propose an unequally spaced four levels phase encoding in the holographic data storage system here. Compared with two levels or three levels phase encoding, four levels phase encoding effectively improves the code rate. While more phase levels can further improve code rate, it also puts higher demand for the camera to differentiate the resulting smaller grayscale difference. Unequally spaced quaternary level phases eliminates the ambiguity of pixels with same phase difference relative to reference light compared to equally spaced quaternary levels. Corresponding encoding pattern design with phase pairs as the data element and decoding method were developed. Our encoding improves the code rate up to 0.875, which is 1.75 times of the conventional amplitude method with an error rate of 0.13 % according to our simulation results.
Codes in W*-Metric Spaces: Theory and Examples
Bumgardner, Christopher J.
2011-01-01
We introduce a "W*"-metric space, which is a particular approach to non-commutative metric spaces where a "quantum metric" is defined on a von Neumann algebra. We generalize the notion of a quantum code and quantum error correction to the setting of finite dimensional "W*"-metric spaces, which includes codes and error correction for classical…
Phase Space Structures of k-threshold Sequential Dynamical Systems
Rani, Raffaele
2011-01-01
Sequential dynamical systems (SDS) are used to model a wide range of processes occurring on graphs or networks. The dynamics of such discrete dynamical systems is completely encoded by their phase space, a directed graph whose vertices and edges represent all possible system configurations and transitions between configurations respectively. Direct calculation of the phase space is in most cases a computationally demanding task. However, for some classes of SDS one can extract information on the connected component structure of phase space from the constituent elements of the SDS, such as its base graph and vertex functions. We present a number of novel results about the connected component structure of the phase space for k-threshold dynamical system with binary state spaces. We establish relations between the structure of the components, the threshold value, and the update sequence. Also fixed-point reachability from garden of eden configurations is investigated and upper bounds for the length of paths in t...
Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
Lukierski, Jerzy
2015-01-01
We consider the general D=4 (10+10)-dimensional kappa-deformed quantum phase space as given by Heisenberg double \\mathcal{H} of D=4 kappa-deformed Poincare-Hopf algebra H. The standard (4+4) -dimensional kappa - deformed covariant quantum phase space spanned by kappa - deformed Minkowski coordinates and commuting momenta generators ({x}_{\\mu },{p}_{\\mu }) is obtained as the subalgebra of \\mathcal{H}. We study further the property that Heisenberg double defines particular quantum spaces with Hopf algebroid structure. We calculate by using purely algebraic methods the explicite Hopf algebroid structure of standard kappa - deformed quantum covariant phase space in Majid-Ruegg bicrossproduct basis. The coproducts for Hopf algebroids are not unique, determined modulo the coproduct gauge freedom. Finally we consider the interpretation of the algebraic description of quantum phase spaces as Hopf bialgebroids.
Phase-space approach to multi-population dynamics
Budko, Neil V
2015-01-01
Simultaneous deterministic dynamics of multiple populations described by a large set of ODE's is considered in the phase space of population sizes and ODE's parameters. The problem is formulated as a multidimensional phase-space conservation law and is solved explicitly for non-interacting multi-population models. Solutions for populations competing for a limited resource and populations with migration are obtained by simple iterative methods. The proposed approach also allows considering phase-space interaction between populations, which is intractable by other methods.
Phase space picture of quantum mechanics group theoretical approach
Kim, Y S
1991-01-01
This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.
Lie algebra type noncommutative phase spaces are Hopf algebroids
Meljanac, Stjepan; Škoda, Zoran; Stojić, Martina
2016-11-01
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way; therefore, obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here, we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.
Lie algebra type noncommutative phase spaces are Hopf algebroids
Meljanac, Stjepan
2014-01-01
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way, therefore obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.
Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II
Directory of Open Access Journals (Sweden)
Peter G. Dodds
2004-01-01
Full Text Available We study local uniform convexity and Kadec-Klee type properties in K-interpolation spaces of Lorentz couples. We show that a wide class of Banach couples of (commutative and non-commutative Lorentz spaces possess the (so-alled (DGL-property originally introduced by Davis, Ghoussoub and Lindenstrauss in the context of renorming order continuous Banach latties. This property is used as a key tool to show that local uniform convexity and certain Kadec-Klee type properties in non-commutative symmetric spaces of measurable operators may be inferred from corresponding properties of the parameter space of the K-interpolation method. Further applications are given to renorming properties of separable symmetric Banach function spaces and their non-commutative counterparts.
The Phase Space Formulation of Time-Symmetric Quantum Mechanics
National Research Council Canada - National Science Library
Charlyne de Gosson; Maurice A. de Gosson
2015-01-01
Time-symmetric quantum mechanics can be described in the Weyl–Wigner–Moyal phase space formalism by using the properties of the cross-terms appearing in the Wigner distribution of a sum of states...
Phase-space geometry of the generalized Langevin equation.
Bartsch, Thomas
2009-09-28
The generalized Langevin equation is widely used to model the influence of a heat bath upon a reactive system. This equation will here be studied from a geometric point of view. A dynamical phase space that represents all possible states of the system will be constructed, the generalized Langevin equation will be formally rewritten as a pair of coupled ordinary differential equations, and the fundamental geometric structures in phase space will be described. It will be shown that the phase space itself and its geometric structure depend critically on the preparation of the system: A system that is assumed to have been in existence forever has a larger phase space with a simpler structure than a system that is prepared at a finite time. These differences persist even in the long-time limit, where one might expect the details of preparation to become irrelevant.
Explaining Gibbsean phase space to second year students
Energy Technology Data Exchange (ETDEWEB)
Vesely, Franz J [Institute of Experimental Physics, University of Vienna (Austria)
2005-03-01
A new approach to teaching introductory statistical physics is presented. We recommend making extensive use of the fact that even systems with a very few degrees of freedom may display chaotic behaviour. This permits a didactic 'bottom-up' approach, starting out with toy systems whose phase space may be depicted on a screen or blackboard, then proceeding to ever higher dimensions in Gibbsean phase space.
Group theoretical construction of planar noncommutative phase spaces
Energy Technology Data Exchange (ETDEWEB)
Ngendakumana, Ancille, E-mail: nancille@yahoo.fr; Todjihoundé, Leonard, E-mail: leonardt@imsp.uac.org [Institut de Mathématiques et des Sciences Physiques (IMSP), Porto-Novo (Benin); Nzotungicimpaye, Joachim, E-mail: kimpaye@kie.ac.rw [Kigali Institute of Education (KIE), Kigali (Rwanda)
2014-01-15
Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.
Kinetic Solvers with Adaptive Mesh in Phase Space
Arslanbekov, Robert R; Frolova, Anna A
2013-01-01
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for solving multi-dimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a tree of trees data structure. The mesh in r-space is automatically generated around embedded boundaries and dynamically adapted to local solution properties. The mesh in v-space is created on-the-fly for each cell in r-space. Mappings between neighboring v-space trees implemented for the advection operator in configuration space. We have developed new algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the full Boltzmann collision integral with dynamically adaptive mesh in velocity space: importance sampling, multi-point projection method, and the variance reduction method. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic...
An extended phase-space SUSY quantum mechanics
Ter-Kazarian, G.
2009-01-01
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N
An extended phase-space SUSY quantum mechanics
Ter-Kazarian, G.
2009-01-01
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N
Elementary particles and emergent phase space
Zenczykowski, Piotr
2014-01-01
The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for ""new physics"". The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space - an arena of events treated in the Standard Model as a classical background - is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers. This bo
Two-Phase Technology at NASA/Johnson Space Center
Ungar, Eugene K.; Nicholson, Leonard S. (Technical Monitor)
1999-01-01
Since the baseline International Space Station (ISS) External Active Thermal Control System (EATCS) was changed from a two-phase mechanically pumped system to a single phase cascade system in the fall of 1993, two-phase EATCS research has continued at a low level at JSC. One of-the lessons of the ISS EATCS selection was that two-phase thermal control systems must have significantly lower power than comparable single phase systems to overcome their larger radiator area, larger line and fluid mass, and perceived higher technical risk. Therefore, research at JSC has concentrated on low power mechanically pumped two-phase EATCSs. In the presentation, the results of a study investigating the trade of single and two-phase mechanically pumped EATCSs for space vehicles will be summarized. The low power two-phase mechanically pumped EATCS system under development at JSC will be described in detail and the current design status of the subscale test unit will be reviewed. Also, performance predictions for a full size EATCS will be presented. In addition to the discussion of two-phase mechanically pumped EATCS development at JSC, two-phase technologies under development for biological water processing will be discussed. These biological water processor technologies are being prepared for a 2001 flight experiment and subsequent usage on the TransHab module on the International Space Station.
Reading Neural Encodings using Phase Space Methods
Abarbanel, Henry D I; Abarbanel, Henry D I; Tumer, Evren C.
2003-01-01
Environmental signals sensed by nervous systems are often represented in spike trains carried from sensory neurons to higher neural functions where decisions and functional actions occur. Information about the environmental stimulus is contained (encoded) in the train of spikes. We show how to "read" the encoding using state space methods of nonlinear dynamics. We create a mapping from spike signals which are output from the neural processing system back to an estimate of the analog input signal. This mapping is realized locally in a reconstructed state space embodying both the dynamics of the source of the sensory signal and the dynamics of the neural circuit doing the processing. We explore this idea using a Hodgkin-Huxley conductance based neuron model and input from a low dimensional dynamical system, the Lorenz system. We show that one may accurately learn the dynamical input/output connection and estimate with high precision the details of the input signals from spike timing output alone. This form of "...
Space power demonstrator engine, phase 1
1987-01-01
The design, analysis, and preliminary test results for a 25 kWe Free-Piston Stirling engine with integral linear alternators are described. The project is conducted by Mechanical Technology under the direction of LeRC as part of the SP-100 Nuclear Space Power Systems Program. The engine/alternator system is designed to demonstrate the following performance: (1) 25 kWe output at a specific weight less than 8 kg/kW; (2) 25 percent efficiency at a temperature ratio of 2.0; (3) low vibration (amplitude less than .003 in); (4) internal gas bearings (no wear, no external pump); and (5) heater temperature/cooler temperature from 630 to 315 K. The design approach to minimize vibration is a two-module engine (12.5 kWe per module) in a linearly-opposed configuration with a common expansion space. The low specific weight is obtained at high helium pressure (150 bar) and high frequency (105 Hz) and by using high magnetic strength (samarium cobalt) alternator magnets. Engine tests began in June 1985; 16 months following initiation of engine and test cell design. Hydrotest and consequent engine testing to date has been intentionally limited to half pressure, and electrical power output is within 15 to 20 percent of design predictions.
Interference Phase of Mass Neutrinos in Kerr Space-Time
Institute of Scientific and Technical Information of China (English)
HUANG Xiu-Ju; WANG Yong-Jiu
2003-01-01
Along the geodesic we calculate the interference phase of the mass neutrinos in some special cases. Because of the rotation of the mass resource which induces the gravitational field, the angular momentum per unit mass, a, has a contribution to the phase, which is different from the case in Schwarzschild space-time.
Exact phase space functional for two-body systems
Gracia-Bondía, José M
2010-01-01
The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently be obtained by minimizing the ground-state energy.
Interference phase of mass neutrino in CM space-time
Institute of Scientific and Technical Information of China (English)
Chen Xia; Wang Yong-Jiu
2009-01-01
In the gravitational field of central mass with electric and magnetic charges and magnetic moment(CM space-time),this paper calculates the interference phase of mass neutrino along geodesic in the radial direction,and discusses the contribution of the electric and magnetic charges and magnetic moment of the central mass to the phase.
On Thermodynamics and Phase Space of Near Horizon Extremal Geometries
Hajian, Kamal
2015-01-01
Near Horizon Extremal Geometries (NHEG), are geometries which may appear in the near horizon region of the extremal black holes. These geometries have $SL(2,\\mathbb{R})\\!\\times\\!U(1)^n$ isometry, and constitute a family of solutions to the theory under consideration. In the first part of this report, their thermodynamic properties are reviewed, and their three universal laws are derived. In addition, at the end of the first part, the role of these laws in black hole thermodynamics is presented. In the second part of this thesis, we review building their classical phase space in the Einstein-Hilbert theory. The elements in the NHEG phase space manifold are built by appropriately chosen coordinate transformations of the original metric. These coordinate transformations are generated by some vector fields, dubbed "symplectic symmetry generators." To fully specify the phase space, we also need to identify the symplectic structure. In order to fix the symplectic structure, we use the formulation of Covariant Phase...
The phase-space density of fermionic dark matter haloes
Shao, Shi; Gao, Liang; Theuns, Tom; Frenk, Carlos S.
2013-04-01
We have performed a series of numerical experiments to investigate how the primordial thermal velocities of fermionic dark matter particles affect the physical and phase-space density profiles of the dark matter haloes into which they collect. The initial particle velocities induce central cores in both profiles, which can be understood in the framework of phase-space density theory. We find that the maximum coarse-grained phase-space density of the simulated haloes (computed in six-dimensional phase space using the ENBID code is very close to the theoretical fine-grained upper bound, while the pseudo-phase-space density, Q ˜ ρ/σ3, overestimates the maximum phase-space density by up to an order of magnitude. The density in the inner regions of the simulated haloes is well described by a `pseudo-isothermal' profile with a core. We have developed a simple model based on this profile which, given the observed surface brightness profile of a galaxy and its central velocity dispersion, accurately predicts its central phase-space density. Applying this model to the dwarf spheroidal satellites of the Milky Way yields values close to 0.5 keV for the mass of a hypothetical thermal warm dark matter particle, assuming that the satellite haloes have cores produced by warm dark matter free streaming. Such a small value is in conflict with the lower limit of 1.2 keV set by the observations of the Lyman α forest. Thus, if the Milky Way dwarf spheroidal satellites have cores, these are likely due to baryonic processes associated with the forming galaxy, perhaps of the kind proposed by Navarro, Eke and Frenk and seen in the recent simulations of galaxy formation in the cold dark matter model.
Evolution of Phase-Space Density in Dark Matter Halos
Hoffman, Yehuda; Shlosman, Isaac; Heller, Clayton
2007-01-01
Evolution of the phase-space density profile in dark matter (DM) halos is investigated by means of constrained simulations, designed to control the merging history of a given DM halo. Halos evolve through a series of quiescent phases of a slow accretion intermitted by violent events of major mergers. In the quiescent phases the density of the halo closely follows the NFW profile and the phase-space density profile, Q(r), is given by the Taylor/Navarro power law, r^{-beta}, where beta ~ 1.9. Expressing the phase-space density by the NFW parameters, Q(r)=Q_s (r/R_s)^{-beta}, the evolution of Q is determined by Q_s. We have found that the effective mass surface density within R_s, Sigma_s = rho_s R_s, remains constant throughout the evolution of a given halo along the main branch of its merging tree. This invariance entails that Q_s ~ R{_s^{-5/2}} and Q(r) ~ Sigma{_s^{-1/2}} R{_s^{-5/2}} (r/R_s)^{-beta}. It follows that the phase-space density remains constant, in the sense of Q_s=const., in the quiescent phases...
Quantum de Finetti theorem in phase-space representation
Leverrier, Anthony; Cerf, Nicolas J.
2009-07-01
The quantum versions of de Finetti’s theorem derived so far express the convergence of n -partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ⊗n . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n -mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Zeeman deceleration beyond periodic phase space stability
Toscano, Jutta; Tauschinsky, Atreju; Dulitz, Katrin; Rennick, Christopher J.; Heazlewood, Brianna R.; Softley, Timothy P.
2017-08-01
In Zeeman deceleration, time-varying spatially inhomogeneous magnetic fields are used to create packets of translationally cold, quantum-state-selected paramagnetic particles with a tuneable forward velocity, which are ideal for cold reaction dynamics studies. Here, the covariance matrix adaptation evolutionary strategy is adopted in order to optimise deceleration switching sequences for the operation of a Zeeman decelerator. Using the optimised sequences, a 40% increase in the number of decelerated particles is observed compared to standard sequences for the same final velocity, imposing the same experimental boundary conditions. Furthermore, we demonstrate that it is possible to remove up to 98% of the initial kinetic energy of particles in the incoming beam, compared to the removal of a maximum of 83% of kinetic energy with standard sequences. Three-dimensional particle trajectory simulations are employed to reproduce the experimental results and to investigate differences in the deceleration mechanism adopted by standard and optimised sequences. It is experimentally verified that the optimal solution uncovered by the evolutionary algorithm is not merely a local optimisation of the experimental parameters—it is a novel mode of operation that goes beyond the standard periodic phase stability approach typically adopted.
Implementation of concurrent engineering to Phase B space system design
Findlay, R.; Braukhane, A.; Schubert, D.; Pedersen, J. F.; Müller, H.; Essmann, O.
2011-12-01
Concurrent engineering (CE) has been in use within the space industry since the mid-1990s for the development of robust, effective design solutions within a reduced period of time; to date, however, such applications have focussed on Phase 0/A feasibility studies, with the potential for application in later phases not yet demonstrated. Applications at the DLR Institute of Space Systems have addressed this gap with practical attempts made on three satellite projects. The use of Phase 0/A CE techniques, such as dedicated CE sessions, online trade-offs, and design iterations and consolidation, was taken and augmented with more novel practices such as online requirements engineering. Underlying these practices was a suite of tools coming from both external and internal sources. While it is noted that the traditional time and cost benefits expected from Phase 0/A use are less likely to be achieved for Phase B applications, the resulting solutions demonstrated an increased robustness and performance.
López-Permouth, Sergio
1990-01-01
The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of injectivitiy, and Cartan matrices.
Non-commutative Hardy inequalities
DEFF Research Database (Denmark)
Hansen, Frank
2009-01-01
We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1 1. Applications to trace functions are given. We introduce the tracial geometric mean...... and generalize Carleman's inequality....
Dimensional reduction over fuzzy coset spaces
Energy Technology Data Exchange (ETDEWEB)
Aschieri, P. E-mail: aschieri@theorie.physik.uni-muenchen.de; Madore, J.; Manousselis, P.; Zoupanos, G
2004-04-01
We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in particular the case of the fuzzy sphere including the dimensional reduction of fermion fields. (author)
Hamilton geometry: Phase space geometry from modified dispersion relations
Barcaroli, Leonardo; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian
2015-01-01
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\\kappa$-Poincar\\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
The Phase Space Elementary Cell in Classical and Generalized Statistics
Directory of Open Access Journals (Sweden)
Piero Quarati
2013-10-01
Full Text Available In the past, the phase-space elementary cell of a non-quantized system was set equal to the third power of the Planck constant; in fact, it is not a necessary assumption. We discuss how the phase space volume, the number of states and the elementary-cell volume of a system of non-interacting N particles, changes when an interaction is switched on and the system becomes or evolves to a system of correlated non-Boltzmann particles and derives the appropriate expressions. Even if we assume that nowadays the volume of the elementary cell is equal to the cube of the Planck constant, h3, at least for quantum systems, we show that there is a correspondence between different values of h in the past, with important and, in principle, measurable cosmological and astrophysical consequences, and systems with an effective smaller (or even larger phase-space volume described by non-extensive generalized statistics.
Phase space view of quantum mechanical systems and Fisher information
Energy Technology Data Exchange (ETDEWEB)
Nagy, Á., E-mail: anagy@madget.atomki.hu
2016-06-17
Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Quantum potential and symmetries in extended phase space
Nasiri, S
2005-01-01
Here, we study the concept of the quantum potential using an extended phase space technique. It seems that, for a given potential, there exist an extended canonical transformation that removes the expression for quantum potential in dynamical equation. The situation, mathematically, is similar to the appearance of centrifugal potential in going from Cartesian to spherical coordinates that changes the physical potential to an effective one. As Examples, the cases of harmonic oscillator, particle in a box and hydrogen atom are worked out, where the quantum potential disappears from the Wigner equation as a possible representation of quantum mechanics in the phase space. This representation that keeps the Hamilton-Jacobi equation form invariant could be obtained by a particular extended canonical transformation on Sobouti-Nasiri equation in extended phase space.
Maximal-acceleration phase space relativity from Clifford algebras
Castro, C
2002-01-01
We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in the spacetime tangent bundle and in phase spaces (cotangent bundle). Crucial in order to establish this link is the use of Clifford algebras in phase spaces. The maximal proper-acceleration bound is a = c^2/ \\Lambda in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. We present the reasons why an Extended Scale Relativity based on Clifford spaces is physically more appealing than those based on kappa-deformed Poincare algebras and the inhomogeneous quantum groups operating in quantum Minkowski spacetimes. The main reason being that the Planck scale should not be taken as a deformation parameter to construct quantum algebras but should exist already as the minimum scale in Clifford spaces.
Grassmann phase space methods for fermions. II. Field theory
Energy Technology Data Exchange (ETDEWEB)
Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)
2017-02-15
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.
Evolution of classical projected phase space density in billiards
Indian Academy of Sciences (India)
Debabrata Biswas
2005-04-01
The classical phase space density projected on to the configuration space offers a means of comparing classical and quantum evolution. In this alternate approach that we adopt here, we show that for billiards, the eigenfunctions of the coarse-grained projected classical evolution operator are identical to a first approximation to the quantum Neumann eigenfunctions. Moreover, there exists a correspondence between the respective eigenvalues although their time evolutions differ.
Uniform approximation from symbol calculus on a spherical phase space
Energy Technology Data Exchange (ETDEWEB)
Yu Liang, E-mail: liangyu@wigner.berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States)
2011-12-16
We use symbol correspondence and quantum normal form theory to develop a more general method for finding uniform asymptotic approximations. We then apply this method to derive a result we announced in an earlier paper, namely the uniform approximation of the 6j-symbol in terms of the rotation matrices. The derivation is based on the Stratonovich-Weyl symbol correspondence between matrix operators and functions on a spherical phase space. The resulting approximation depends on a canonical, or area-preserving, map between two pairs of intersecting level sets on the spherical phase space. (paper)
Quantum phase transition induced by real-space topology
Li, C.; Zhang, G.; Lin, S.; Song, Z.
2016-12-01
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
Quantum phase transition induced by real-space topology.
Li, C; Zhang, G; Lin, S; Song, Z
2016-12-22
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
Adaptive optics and phase diversity imaging for responsive space applications.
Energy Technology Data Exchange (ETDEWEB)
Smith, Mark William; Wick, David Victor
2004-11-01
The combination of phase diversity and adaptive optics offers great flexibility. Phase diverse images can be used to diagnose aberrations and then provide feedback control to the optics to correct the aberrations. Alternatively, phase diversity can be used to partially compensate for aberrations during post-detection image processing. The adaptive optic can produce simple defocus or more complex types of phase diversity. This report presents an analysis, based on numerical simulations, of the efficiency of different modes of phase diversity with respect to compensating for specific aberrations during post-processing. It also comments on the efficiency of post-processing versus direct aberration correction. The construction of a bench top optical system that uses a membrane mirror as an active optic is described. The results of characterization tests performed on the bench top optical system are presented. The work described in this report was conducted to explore the use of adaptive optics and phase diversity imaging for responsive space applications.
Time-Dependent Phase-Space Mapping of Space-Charge-Dominated Beams
Energy Technology Data Exchange (ETDEWEB)
D. Stratakis, R.B. Fiorito, I. Haber, R.A. Kishek, P.G. O' Shea, M. Reiser, J.C.T. Thangaraj, K. Tian
2009-05-01
In this paper we report on a proof of principle experiment for demonstrating the possibility of reconstructing the time resolved-phase-space distribution of a space-charge dominated beam by a tomographic technique which provides us with far more information than a time-sliced emittance. We emphasize that this work describes and demonstrates a new methodology which can be applicable to any beam pulse using imaging methods with the appropriate time resolution for the pulse duration. The combination of a high precision tomographic diagnostic with fast imaging screens and a gated camera are used to produce phase space maps of two beams: one with a parabolic current profile and another with a short perturbation atop a rectangular pulse. The correlations between longitudinal and transverse phase spaces are apparent and their impact on the dynamics is discussed.
Non minimally coupled condensate cosmologies: a phase space analysis
Carloni, Sante; Cianci, Roberto
2014-01-01
We present an analysis of the phase space of cosmological models based on a non minimal coupling between the geometry and a fermionic condensate. We obtain that the strong constraint coming from the Dirac equations allows a detailed design of the cosmology of these models and at the same time guarantees an evolution towards a state indistinguishable from General Relativistic cosmological models. In this light, we show how the use of some specific potentials is able to reproduce naturally two de Sitter phases separated by a power law expansion which could be an interesting model for the unification of an inflationary phase and a dark energy era.
Two Phase Flow and Space-Based Applications
McQuillen, John
1999-01-01
A reduced gravity environment offers the ability to remove the effect of buoyancy on two phase flows whereby density differences that normally would promote relative velocities between the phases and also alter the shape of the interface are removed. However, besides being a potent research tool, there are also many space-based technologies that will either utilize or encounter two-phase flow behavior, and as a consequence, several questions must be addressed. This paper presents some of these technologies missions. Finally, this paper gives a description of web-sites for some funding.
On the Squeezed Number States and their Phase Space Representations
Albano, L; Stephany, J
2002-01-01
We compute the photon number distribution, the Q distribution function and the wave functions in the momentum and position representation for a single mode squeezed number state. We discuss the oscillations which appear in the photon number distribution of squeezed number states for high values of the squeezing parameter. We compare our results with the formalism based on the interference in phase space.
Quantum Theory of Reactive Scattering in Phase Space
Goussev, A.; Schubert, R.; Waalkens, H.; Wiggins, S.; Nicolaides, CA; Brandas, E
2010-01-01
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of Poincare-Birkhoff normal form theory and the perspective of dynamical systems theory. Over the past 10 years the classical normal form theory has provided a met
Entanglement due to noncommutativity in the phase-space
Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno
2013-01-01
The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative (NC) phase-space. The quantum nature and the separability of NC two-mode Gaussian states are examined. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the noncommutative deformation.
Phase space transport in a map of asteroid motion
Institute of Scientific and Technical Information of China (English)
LiyongZHOU; YisuiSUN; JilinZHOU
2000-01-01
We have studied the chaotic transport in a nonlinear model directly applicable to asteroid motion. An exponential and an algebraic diffusion law are observed in different regions of the phase space. We have also investigated the effects of small perturbations and found they can not only accelerate but also decelerate the transport.
Subdivision of phase space for anisotropically interacting water molecules
Epifanov, S. Yu.; Vigasin, A. A.
An efficient numerical algorithm is employed which enables one to perform multidimensional integrations of complicated integrands. Temperature dependence of the second virial coefficient for water is reproduced using the Matsuoka Clementi Yoshimine intermolecular water water potential. Metastable states are shown to occupy significant domain in the water dimer phase space.
An Asymmetrical Space Vector Method for Single Phase Induction Motor
DEFF Research Database (Denmark)
Cui, Yuanhai; Blaabjerg, Frede; Andersen, Gert Karmisholt
2002-01-01
the motor torque performance is not good enough. This paper addresses a new control method, an asymmetrical space vector method with PWM modulation, also a three-phase inverter is used for the main winding and the auxiliary winding. This method with PWM modulation is implemented to control the motor speed...
Wigner Functions for the Bateman System on Noncommutative Phase Space
Institute of Scientific and Technical Information of China (English)
HENG Tai-Hua; LIN Bing-Sheng; JING Si-Cong
2010-01-01
@@ We study an important dissipation system,I.e.the Bateman model on noncommutative phase space.Using the method of deformation quantization,we calculate the Exp functions,and then derive the Wigner functions and the corresponding energy spectra.
Octopus: An Efficient Phase Space Mapping for Light Particles
Kosower, David A.
1992-09-01
I present a generator for relativistic phase space that incorporates much of the effect of typical experimental cuts, and which is suitable for use in Monte Carlo calculations of cross sections for high-energy hadron-hadron or electron-positron scattering experiments.
Deformation quantization: Quantum mechanics lives and works in phase space
Directory of Open Access Journals (Sweden)
Zachos Cosmas K.
2014-01-01
A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002, and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space, (Imperial Press & World Scientific, 2014.
Phase transition in extended thermodynamic phase space and charged Horava-Lifshitz black holes
Poshteh, Mohammad Bagher Jahani
2016-01-01
For charged black holes in Horava-Lifshitz gravity, it is shown that a second order phase transition takes place in extended phase space. We study the behavior of specific heat and free energy at the point of transition in canonical and grand canonical ensembles and show that the black hole falls into a state which is locally and globally stable. We relate the second order nature of phase transition to the fact that the phase transition occurs at a sharp temperature and not over a temperature interval. By taking cosmological constant as thermodynamic pressure for charged black holes, we extend Ehrenfest's equations. We obtain nine equations and show that, all of them are satisfied at the point in which the specific heat diverges. We also apply geometrothermodynamics to extended phase space and show that the scalar curvature of Quevedo metric diverges at the point at which the second order phase transition takes place.
Phase Space Dynamics of Ionization Injection in Plasma Based Accelerators
Xu, X L; Li, F; Zhang, C J; Yan, L X; Du, Y C; Huang, W H; Chen, H B; Tang, C X; Lu, W; Yu, P; An, W; Mori, W B; Joshi, C
2013-01-01
The evolution of beam phase space in ionization-induced injection into plasma wakefields is studied using theory and particle-in-cell (PIC) simulations. The injection process causes special longitudinal and transverse phase mixing leading initially to a rapid emittance growth followed by oscillation, decay, and eventual slow growth to saturation. An analytic theory for this evolution is presented that includes the effects of injection distance (time), acceleration distance, wakefield structure, and nonlinear space charge forces. Formulas for the emittance in the low and high space charge regimes are presented. The theory is verified through PIC simulations and a good agreement is obtained. This work shows how ultra-low emittance beams can be produced using ionization-induced injection.
Dynamic characteristics of an NC table with phase space reconstruction
Institute of Scientific and Technical Information of China (English)
Linhong WANG; Bo WU; Runsheng DU; Shuzi YANG
2009-01-01
The dynamic properties of a numerical control (NC) table directly interfere with the accuracy and surface quality of work pieces machined by a computer numerical control (CNC) machine. Phase space reconstruction is an effective approach for researching dynamic behaviors of a system with measured time series. Based on the theory and method for phase space reconstruction, the correlation dimension, maximum Lyapunov exponent, and dynamic time series measured from the NC table were analyzed. The characteristic quantities such as the power spectrum, phase trajectories, correlation dimension, and maximum Lyapunov exponent are extracted from the measured time series. The chaotic characteristic of the dynamic properties of the NC table is revealed via various approaches.Therefore, an NC table is a nonlinear dynamic system. This research establishes a basis for dynamic system discrimi-nation of a CNC machine.
Driven phase space vortices in plasmas with nonextensive velocity distribution
Trivedi, Pallavi; Ganesh, Rajaraman
2017-03-01
The evolution of chirp-driven electrostatic waves in unmagnetized plasmas is numerically investigated by using a one-dimensional (1D) Vlasov-poisson solver with periodic boundary conditions. The initial velocity distribution of the 1D plasma is assumed to be governed by nonextensive q distribution [C. Tsallis, J. Stat. Phys. 52, 479 (1988)]. For an infinitesimal amplitude of an external drive, we investigate the effects of chirp driven dynamics that leads to the formation of giant phase space vortices (PSV) for both Maxwellian (q = 1) and non-Maxwellian ( q ≠ 1 ) plasmas. For non-Maxwellian plasmas, the formation of giant PSV with multiple extrema and phase velocities is shown to be dependent on the strength of "q". Novel features such as "shark"-like and transient "honeycomb"-like structures in phase space are discussed. Wherever relevant, we compare our results with previous work.
Emittance and Phase Space Tomography for the Fermilab Linac
Energy Technology Data Exchange (ETDEWEB)
Garcia, F.G.G.; Johnstone, C.; Kobilarcik, T.; Koizumi, G.M.; Moore, C.D.; /Fermilab; Newhart, D.L.; /Fermilab
2012-05-01
The Fermilab Linac delivers a variable intensity, 400-MeV beam to the MuCool Test Area experimental hall via a beam line specifically designed to facilitate measurements of the Linac beam emittance and properties. A 10 m, dispersion-free and magnet-free straight utilizes an upstream quadrupole focusing triplet in combination with the necessary in-straight beam diagnostics to fully characterize the transverse beam properties. Since the Linac does not produce a strictly elliptical phase space, tomography must be performed on the profile data to retrieve the actual particle distribution in phase space. This is achieved by rotating the phase space distribution using different waist focusing conditions of the upstream triplet and performing a deconvolution of the profile data. Preliminary measurements using this diagnostic section are reported here. These data represent a first-pass measurement of the Linac emittance based on various techniques. It is clear that the most accurate representation of the emittance is given by the 3-profile approach. Future work will entail minimizing the beam spot size on MW5 to test and possibly improve the accuracy of the 2-profile approach. The 95% emittance is {approx} 18{pi} in the vertical and {approx} 13{pi} in the horizontal, which is especially larger than anticipated - 8-10{pi} was expected. One possible explanation is that the entire Linac pulse is extracted into the MTA beamline and during the first few microseconds, the feed forward and RF regulation are not stable. This may result in a larger net emittance observed versus beam injected into Booster, where the leading part of the Linac beam pulse is chopped. Future studies will clearly entail a measurement of the emittance vs. pulse length. One additional concern is that the Linac phase space is most likely aperture-defined and non-elliptical in nature. A non-elliptical phase-space determination would require a more elaborate analysis and provide another explanation of the
Gravitational phase transitions with an exclusion constraint in position space
Chavanis, Pierre-Henri
2014-01-01
We discuss the statistical mechanics of a system of self-gravitating particles with an exclusion constraint in position space in a space of dimension d. The exclusion constraint puts an upper bound on the density of the system and can stabilize it against gravitational collapse. We plot the caloric curves giving the temperature as a function of the energy and investigate the nature of phase transitions as a function of the size of the system and of the dimension of space in both microcanonical and canonical ensembles. We consider stable and metastable states and emphasize the importance of the latter for systems with long-range interactions. For d ≤ 2, there is no phase transition. For d > 2, phase transitions can take place between a "gaseous" phase unaffected by the exclusion constraint and a "condensed" phase dominated by this constraint. The condensed configurations have a core-halo structure made of a "rocky core" surrounded by an "atmosphere", similar to a giant gaseous planet. For large systems there exist microcanonical and canonical first order phase transitions. For intermediate systems, only canonical first order phase transitions are present. For small systems there is no phase transition at all. As a result, the phase diagram exhibits two critical points, one in each ensemble. There also exist a region of negative specific heats and a situation of ensemble inequivalence for sufficiently large systems. We show that a statistical equilibrium state exists for any values of energy and temperature in any dimension of space. This differs from the case of the self-gravitating Fermi gas for which there is no statistical equilibrium state at low energies and low temperatures when d ≥ 4. By a proper interpretation of the parameters, our results have application for the chemotaxis of bacterial populations in biology described by a generalized Keller-Segel model including an exclusion constraint in position space. They also describe colloids at a fluid
An extended Dirac equation in noncommutative space-time
Mendes, R Vilela
2015-01-01
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed, as well as the effects of coupling the two solutions.
Key-space analysis of double random phase encryption technique
Monaghan, David S.; Gopinathan, Unnikrishnan; Naughton, Thomas J.; Sheridan, John T.
2007-09-01
We perform a numerical analysis on the double random phase encryption/decryption technique. The key-space of an encryption technique is the set of possible keys that can be used to encode data using that technique. In the case of a strong encryption scheme, many keys must be tried in any brute-force attack on that technique. Traditionally, designers of optical image encryption systems demonstrate only how a small number of arbitrary keys cannot decrypt a chosen encrypted image in their system. However, this type of demonstration does not discuss the properties of the key-space nor refute the feasibility of an efficient brute-force attack. To clarify these issues we present a key-space analysis of the technique. For a range of problem instances we plot the distribution of decryption errors in the key-space indicating the lack of feasibility of a simple brute-force attack.
Phase-space Dynamics of Runaway Electrons In Tokamaks
Energy Technology Data Exchange (ETDEWEB)
Xiaoyin Guan, Hong Qin, and Nathaniel J. Fisch
2010-08-31
The phase-space dynamics of runaway electrons is studied, including the influence of loop voltage, radiation damping, and collisions. A theoretical model and a numerical algorithm for the runaway dynamics in phase space are developed. Instead of standard integrators, such as the Runge-Kutta method, a variational symplectic integrator is applied to simulate the long-term dynamics of a runaway electron. The variational symplectic integrator is able to globally bound the numerical error for arbitrary number of time-steps, and thus accurately track the runaway trajectory in phase space. Simulation results show that the circulating orbits of runaway electrons drift outward toward the wall, which is consistent with experimental observations. The physics of the outward drift is analyzed. It is found that the outward drift is caused by the imbalance between the increase of mechanical angular momentum and the input of toroidal angular momentum due to the parallel acceleration. An analytical expression of the outward drift velocity is derived. The knowledge of trajectory of runaway electrons in configuration space sheds light on how the electrons hit the first wall, and thus provides clues for possible remedies.
An extended phase-space SUSY quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ter-Kazarian, G [Byurakan Astrophysical Observatory, Byurakan 378433, Aragatsotn District (Armenia)], E-mail: gago_50@yahoo.com
2009-02-06
In the present paper, we will concern ourselves with the extended phase-space quantum mechanics of particles which have both bosonic and fermionic degrees of freedom, i.e., the quantum field theory in (0 + 1) dimensions in q-(position) and p-(momentum) spaces, exhibiting supersymmetry. We present (N = 2) realization of extended supersymmetry algebra and discuss the vacuum energy and topology of super-potentials. Shape invariance of exactly solvable extended SUSY potentials allows us to obtain analytic expressions for the entire energy spectrum of an extended Hamiltonian with, for example, Scarf potential without ever referring to an underlying differential equation.
TRANSVERSE PHASE SPACE PAINTING FOR SNS ACCUMULATOR RING INJECTION.
Energy Technology Data Exchange (ETDEWEB)
BEEBE-WANG,J.; LEE,Y.Y.; RAPARIA,D.; WEI,J.
1999-03-29
The result of investigation and comparison of a series of transverse phase space painting schemes for the injection of SNS accumulator ring [1] is reported. In this computer simulation study, the focus is on the creation of closed orbit bumps that give desired distributions at the target. Space charge effects such as tune shift, emittance growth and beam losses are considered. The results of pseudo end-to-end simulations from the injection to the target through the accumulator ring and Ring to Target Beam Transfer (RTBT) system [2] are presented and discussed.
Coherent quantum squeezing due to the phase space noncommutativity
Bernardini, Alex E
2015-01-01
The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard billiards is obtained and their components behavior are monitored in time. It is assumed that the independent degrees of freedom are two \\emph{free} 1D harmonic oscillators (HO's), so the system Hamiltonian does not contain interaction terms. Through the noncommutative deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained Hamiltonian represents then two \\emph{interacting} 1D HO's. By assuming that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed...
Identifying phase-space boundaries with Voronoi tessellations
Energy Technology Data Exchange (ETDEWEB)
Debnath, Dipsikha; Matchev, Konstantin T. [University of Florida, Physics Department, Gainesville, FL (United States); Gainer, James S. [University of Hawaii, Department of Physics and Astronomy, Honolulu, HI (United States); Kilic, Can; Yang, Yuan-Pao [The University of Texas at Austin, Theory Group, Department of Physics and Texas Cosmology Center, Austin, TX (United States); Kim, Doojin [University of Florida, Physics Department, Gainesville, FL (United States); CERN, Theory Division, Geneva 23 (Switzerland)
2016-11-15
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis. (orig.)
Phase Space Approach to Laser-driven Electronic Wavepacket Propagation
Takemoto, Norio; Tannor, David J
2012-01-01
We propose a phase space method to propagate a quantum wavepacket driven by a strong external field. The method employs the so-called biorthogonal von Neumann basis recently introduced for the calculation of the energy eigenstates of time-independent quantum systems [A. Shimshovitz and D.J. Tannor, arXiv:1201.2299v1]. While the individual elements in this basis set are time-independent, a small subset is chosen in a time-dependent manner to adapt to the evolution of the wavepacket in phase space. We demonstrate the accuracy and efficiency of the present propagation method by calculating the electronic wavepacket in a one-dimensional soft-core atom interacting with a superposition of an intense, few-cycle, near-infrared laser pulse and an attosecond extreme-ultraviolet laser pulse.
Classical analog of extended phase space SUSY and its breaking
Ter-Kazarian, Gagik
2013-01-01
We derive the classical analog of the extended phase space quantum mechanics of the particle with odd degrees of freedom which gives rise to (N=2)-realization of supersymmetry (SUSY) algebra. By means of an iterative procedure, we find the approximate groundstate solutions to the extended Schr\\"{o}dinger-like equation and use these solutions further to calculate the parameters which measure the breaking of extended SUSY such as the groundstate energy. Consequently, we calculate a more practical measure for the SUSY breaking which is the expectation value of an auxiliary field. We analyze non-perturbative mechanism for extended phase space SUSY breaking in the instanton picture and show that this has resulted from tunneling between the classical vacua of the theory. Particular attention is given to the algebraic properties of shape invariance and spectrum generating algebra.
Geometrical Models of the Phase Space Structures Governing Reaction Dynamics
Waalkens, Holger
2009-01-01
Hamiltonian dynamical systems possessing equilibria of ${saddle} \\times {centre} \\times...\\times {centre}$ stability type display \\emph{reaction-type dynamics} for energies close to the energy of such equilibria; entrance and exit from certain regions of the phase space is only possible via narrow \\emph{bottlenecks} created by the influence of the equilibrium points. In this paper we provide a thorough pedagogical description of the phase space structures that are responsible for controlling transport in these problems. Of central importance is the existence of a \\emph{Normally Hyperbolic Invariant Manifold (NHIM)}, whose \\emph{stable and unstable manifolds} have sufficient dimensionality to act as separatrices, partitioning energy surfaces into regions of qualitatively distinct behavior. This NHIM forms the natural (dynamical) equator of a (spherical) \\emph{dividing surface} which locally divides an energy surface into two components (`reactants' and `products'), one on either side of the bottleneck. This di...
Semiclassical Approximations in Phase Space with Coherent States
Baranger, Michel; de Aguiar, Marcus A. M.; Keck, Frank; Korsch, Hans-Jürgen; Schellhaaß, Bernd
2001-01-01
We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initia...
Liouville`s theorem and phase-space cooling
Energy Technology Data Exchange (ETDEWEB)
Mills, R.L. [Ohio State Univ., Columbus, OH (United States); Sessler, A.M. [Lawrence Berkeley Lab., CA (United States)
1993-09-28
A discussion is presented of Liouville`s theorem and its consequences for conservative dynamical systems. A formal proof of Liouville`s theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur.
Noether-Mei Symmetry of Mechanical System in Phase Space
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui; WANG Peng; DING Ning
2006-01-01
In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a Noether-Mei symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the Mei conserved quantity deduced from the Noether-Mei symmetry of the system are obtained. Finally, two examples are given to illustrate the application of the results.
Classical Analog of Extended Phase Space SUSY and Its Breaking
Gagik Ter-Kazarian
2013-01-01
We derive the classical analog of the extended phase space quantum mechanics of the particle with odd degrees of freedom which gives rise to (N=2)-realization of supersymmetry (SUSY) algebra. By means of an iterative procedure, we find the approximate groundstate solutions to the extended Schr\\"{o}dinger-like equation and use these solutions further to calculate the parameters which measure the breaking of extended SUSY such as the groundstate energy. Consequently, we calculate a more practic...
Quantum and Classical Phase Space Separability and Entanglement
Patwardhan, A
2002-01-01
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The correspondence between the classical and the quantum criterion of separability for the system is obtained in terms of these functions. Entanglement is generic and separability is special. Some applications are discussed in commonly occuring examples and possibly in exotic systems.
Torus as phase space: Weyl quantization, dequantization, and Wigner formalism
Energy Technology Data Exchange (ETDEWEB)
Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it [Dipartimento di Matematica, Università di Bari, I-70125 Bari (Italy)
2016-08-15
The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.
Phase space analysis of some interacting Chaplygin gas models
Energy Technology Data Exchange (ETDEWEB)
Khurshudyan, M. [Academy of Sciences of Armenia, Institute for Physical Research, Ashtarak (Armenia); Tomsk State University of Control Systems and Radioelectronics, Laboratory for Theoretical Cosmology, Tomsk (Russian Federation); Tomsk State Pedagogical University, Department of Theoretical Physics, Tomsk (Russian Federation); Myrzakulov, R. [Eurasian National University, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan)
2017-02-15
In this paper we discuss a phase space analysis of various interacting Chaplygin gas models in general relativity. Linear and nonlinear sign changeable interactions are considered. For each case appropriate late time attractors of field equations are found. The Chaplygin gas is one of the dark fluids actively considered in modern cosmology due to the fact that it is a joint model of dark energy and dark matter. (orig.)
Experimental phase-space-based optical amplification of scar modes
Michel, Claire; Doya, Valerie; Aschieri, Pierre; Blanc, Wilfried; Legrand, Olivier; Mortessagne, Fabrice
2012-01-01
Waves billiard which are chaotic in the geometrical limit are known to support non-generic spatially localized modes called scar modes. The interaction of the scar modes with gain has been recently investigated in optics in micro-cavity lasers and vertically-cavity surface-emitting lasers. Exploiting the localization properties of scar modes in their wave analogous phase space representation, we report experimental results of scar modes selection by gain in a doped D-shaped optical fiber.
On-line phase space measurement with kicker excitation
Dietrich, J.; Maier, R.; Mohos, I.
1998-12-01
A new method for on-line phase space measurements with kicker excitation at COSY was developed. The position data were measured using the analog output of two beam position monitors (BPMs) and directly monitored on a digital storage oscilloscope with an external clock (bunch-synchronous sampling). Nonlinear behavior of the proton beam was visible as well as were resonance islands. Typical measurements are presented.
Kinetic derivation of generalized phase space Chern-Simons theory
Hayata, Tomoya
2016-01-01
We study a kinetic theory in $2d$ phase space when all abelian Berry curvatures are nonzero. We derive the complete form of the Poisson brackets, and calculate transports induced by Berry curvatures. Then we construct the low-energy effective theory to reproduce the transports. Such an effective theory is given by the Chern-Simons theory in $1+2d$ dimensions. Some implications of the Chern-Simons theory are also discussed.
Phase space representation of spatially partially coherent imaging.
Castaneda, Roman
2008-08-01
The phase space representation of imaging with optical fields in any state of spatial coherence is developed by using spatial coherence wavelets. It leads to new functions for describing the optical transfer and response of imaging systems when the field is represented by Wigner distribution functions. Specific imaging cases are analyzed in this context, and special attention is devoted to the imaging of two point sources.
Hawking radiation and classical tunneling: A ray phase space approach
Tracy, E. R.; Zhigunov, D.
2016-01-01
Acoustic waves in fluids undergoing the transition from sub- to supersonic flow satisfy governing equations similar to those for light waves in the immediate vicinity of a black hole event horizon. This acoustic analogy has been used by Unruh and others as a conceptual model for "Hawking radiation." Here, we use variational methods, originally introduced by Brizard for the study of linearized MHD, and ray phase space methods, to analyze linearized acoustics in the presence of background flows. The variational formulation endows the evolution equations with natural Hermitian and symplectic structures that prove useful for later analysis. We derive a 2 × 2 normal form governing the wave evolution in the vicinity of the "event horizon." This shows that the acoustic model can be reduced locally (in ray phase space) to a standard (scalar) tunneling process weakly coupled to a unidirectional non-dispersive wave (the "incoming wave"). Given the normal form, the Hawking "thermal spectrum" can be derived by invoking standard tunneling theory, but only by ignoring the coupling to the incoming wave. Deriving the normal form requires a novel extension of the modular ray-based theory used previously to study tunneling and mode conversion in plasmas. We also discuss how ray phase space methods can be used to change representation, which brings the problem into a form where the wave functions are less singular than in the usual formulation, a fact that might prove useful in numerical studies.
Prediction of Tropical Rainfall by Local Phase Space Reconstruction.
Waelbroeck, H.; López-Pea, R.; Morales, T.; Zertuche, F.
1994-11-01
The authors propose a weather prediction model based on a local reconstruction of the dynamics in phase space, using an 11-year dataset from Tlaxcala, Mexico. A vector in phase space corresponds to T consecutive days of data; the best predictions are found for T = 14. The prediction for the next day, x0 fL(x0), is based on a local reconstruction of the dynamical map f in an ball centered at x0. The high dimensionality of the phase space implies a large optimal value of , so that the number of points in an ball is sufficient to reconstruct the local map. The local approximation fL f is therefore not very good and the prediction skill drops off quickly at first, with a timescale of 2 days. On the other hand, the authors find useful skill in the prediction of 10-day rainfall accumulations, which reflects the persistence of weather patterns. The mean-squared error in the prediction of the rainfall anomaly for the year 1992 was 64% of the variance, and the early beginning of the rain season was correctly predicted.
A phase-space model for Pleistocene ice volume
Imbrie, John Z; Lisiecki, Lorraine E
2011-01-01
We present a phase-space model that simulates Pleistocene ice volume changes based on Earth's orbital parameters. Terminations in the model are triggered by a combination of ice volume and orbital forcing and agree well with age estimates for Late Pleistocene terminations. The average phase at which model terminations begin is approximately 90 +/- 90 degrees before the maxima in all three orbital cycles. The large variability in phase is likely caused by interactions between the three cycles and ice volume. Unlike previous ice volume models, this model produces an orbitally driven increase in 100-kyr power during the mid-Pleistocene transition without any change in model parameters. This supports the hypothesis that Pleistocene variations in the 100-kyr power of glacial cycles could be caused, at least in part, by changes in Earth's orbital parameters, such as amplitude modulation of the 100-kyr eccentricity cycle, rather than changes within the climate system.
Characteristic Functions over C*-Probability Spaces
Institute of Scientific and Technical Information of China (English)
王勤; 李绍宽
2003-01-01
Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.
The Geometry of Noncommutative Space-Time
Mendes, R. Vilela
2016-10-01
Stabilization, by deformation, of the Poincaré-Heisenberg algebra requires both the introduction of a fundamental lentgh and the noncommutativity of translations which is associated to the gravitational field. The noncommutative geometry structure that follows from the deformed algebra is studied both for the non-commutative tangent space and the full space with gravity. The contact points of this approach with the work of David Finkelstein are emphasized.
Grassmann phase space methods for fermions. I. Mode theory
Dalton, B. J.; Jeffers, J.; Barnett, S. M.
2016-07-01
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggest the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. The theory of Grassmann phase space methods for fermions based on separate modes is developed, showing how the distribution function is defined and used to determine quantum correlation functions, Fock state populations and coherences via Grassmann phase space integrals, how the Fokker-Planck equations are obtained and then converted into equivalent Ito equations for stochastic Grassmann variables. The fermion distribution function is an even Grassmann function, and is unique. The number of c-number Wiener increments involved is 2n2, if there are n modes. The situation is somewhat different to the bosonic c-number case where only 2 n Wiener increments are involved, the sign of the drift term in the Ito equation is reversed and the diffusion matrix in the Fokker-Planck equation is anti-symmetric rather than symmetric. The un-normalised B distribution is of particular importance for determining Fock state populations and coherences, and as pointed out by Plimak, Collett and Olsen, the drift vector in its Fokker-Planck equation only depends linearly on the Grassmann variables. Using this key feature we show how the Ito stochastic equations can be solved numerically for finite times in terms of c-number stochastic
Harmonic analysis on triple spaces
DEFF Research Database (Denmark)
Danielsen, Thomas Hjortgaard
In this thesis we study examples of triple spaces, both their structure theory, their invariant differential operators as well as analysis on them. The first major results provide us with some examples of triple spaces which are strongly spherical, i.e. satisfy some conditions reminiscent...... of properties of symmetric spaces. The algebras of invariant differential operators for these spaces are studied and the conclusion is that most of them are non-commutative. Finally, we restrict our attention to a single triple space, giving a specific polar decomposition and corresponding integration formula......, and studying the relations between open orbits of parabolic subgroups, multiplicities and distribution vectors....
Linearization of the longitudinal phase space without higher harmonic field
Directory of Open Access Journals (Sweden)
Benno Zeitler
2015-12-01
Full Text Available Accelerator applications like free-electron lasers, time-resolved electron diffraction, and advanced accelerator concepts like plasma acceleration desire bunches of ever shorter longitudinal extent. However, apart from space charge repulsion, the internal bunch structure and its development along the beam line can limit the achievable compression due to nonlinear phase space correlations. In order to improve such a limited longitudinal focus, a correction by properly linearizing the phase space is required. At large scale facilities like Flash at Desy or the European Xfel, a higher harmonic cavity is installed for this purpose. In this paper, another method is described and evaluated: Expanding the beam after the electron source enables a higher order correction of the longitudinal focus by a subsequent accelerating cavity which is operated at the same frequency as the electron gun. The elaboration of this idea presented here is based on a ballistic bunching scheme, but can be extended to bunch compression based on magnetic chicanes. The core of this article is an analytic model describing this approach, which is verified by simulations, predicting possible bunch length below 1 fs at low bunch charge. Minimizing the energy spread down to σ_{E}/E<10^{-5} while keeping the bunch long is another interesting possibility, which finds applications, e.g., in time resolved transmission electron microscopy concepts.
Space-time mechanics: Quantum causal structure and expansive force
Valenzuela, Mauricio
2015-01-01
Combining twistor space and phase space formulation of quantum mechanics we propose a new framework of quantization of geometries which incorporates Wigner functions for geometrical observables. Quantizing the light-cone in 2+1D and 3+1D results in one-sheet "quantum hyperboloids". We propose that the latter rule the causal structure of the space-time, yielding uncertainty of positions and space-time curvature. The quantum hyperboloid predicts accelerated propagation of signals and effective space expansion. These effects are noticeable at scales of the quantization parameter in twistor space and negligible at much larger scales since the hyperboloid is asymptotic to the light-cone. Due to space-time non-commutativity it is necessary to introduce notions of observers which are able to determine distances in specific directions. Thus, in the perspective of a time-observer, time and radius of spatial sections of the quantum hyperboloid become discrete and bounded from below. Hence the time is quantized and punc...
Acceleration of Classical Mechanics by Phase Space Constraints.
Martínez-Núñez, Emilio; Shalashilin, Dmitrii V
2006-07-01
In this article phase space constrained classical mechanics (PSCCM), a version of accelerated dynamics, is suggested to speed up classical trajectory simulations of slow chemical processes. The approach is based on introducing constraints which lock trajectories in the region of the phase space close to the dividing surface, which separates reactants and products. This results in substantial (up to more than 2 orders of magnitude) speeding up of the trajectory simulation. Actual microcanonical rates are calculated by introducing a correction factor equal to the fraction of the phase volume which is allowed by the constraints. The constraints can be more complex than previously used boosting potentials. The approach has its origin in Intramolecular Dynamics Diffusion Theory, which shows that the majority of nonstatistical effects are localized near the transition state. An excellent agreement with standard trajectory simulation at high energies and Monte Carlo Transition State Theory at low energies is demonstrated for the unimolecular dissociation of methyl nitrite, proving that PSCCM works both in statistical and nonstatistical regimes.
Tomographic measurement of the phase space distribution of a space-charge-dominated beam
Stratakis, Diktys
Many applications of accelerators, such as free electron lasers, pulsed neutron sources, and heavy ion fusion, require a good quality beam with high intensity. In practice, the achievable intensity is often limited by the dynamics at the low-energy, space-charge dominated end of the machine. Because low-energy beams can have complex distribution functions, a good understanding of their detailed evolution is needed. To address this issue, we have developed a simple and accurate tomographic method to map the beam phase using quadrupole magnets, which includes the effects from space charge. We extend this technique to use also solenoidal magnets which are commonly used at low energies, especially in photoinjectors, thus making the diagnostic applicable to most machines. We simulate our technique using a particle in cell code (PIC), to ascertain accuracy of the reconstruction. Using this diagnostic we report a number of experiments to study and optimize injection, transport and acceleration of intense space charge dominated beams. We examine phase mixing, by studying the phase-space evolution of an intense beam with a transversely nonuniform initial density distribution. Experimental measurements, theoretical predictions and PIC simulations are in good agreement each other. Finally, we generate a parabolic beam pulse to model those beams from photoinjectors, and combine tomography with fast imaging techniques to investigate the time-sliced parameters of beam current, size, energy spread and transverse emittance. We found significant differences between the slice emittance profiles and slice orientation as the beam propagates downstream. The combined effect of longitudinal nonuniform profiles and fast imaging of the transverse phase space provided us with information about correlations between longitudinal and transverse dynamics that we report within this dissertation.
Multimegawatt space nuclear power supply, Phase 1 Final report
Energy Technology Data Exchange (ETDEWEB)
1989-02-17
This Specification establishes the performance, design, development, and test requirements for the Boeing Multimegawatt Space Nuclear Power System (MSNPS). The Boeing Multimegawatt Space Power System is part of the DOE/SDIO Multimegawatt Space Nuclear Power Program. The purpose of this program is to provide a space-based nuclear power system to meet the needs of SDIO missions. The Boeing MSNPS is a category 1 concept which is capable of delivering 10's of MW(e) for 100's of seconds with effluent permitted. A design goal is for the system to have growth or downscale capability for other power system concepts. The growth objective is to meet the category 3 capability of 100's of MW(e) for 100's of seconds, also with effluent permitted. The purpose of this preliminary document is to guide the conceptual design effort throughout the Phase 1 study effort. This document will be updated through out the study. It will thus result in a record of the development of the design effort.
A concise treatise on quantum mechanics in phase space
Curtright, Thomas L; Zachos, Cosmas K
2014-01-01
This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions density -- matrices in a special Weyl representation -- and star products are the cornerstones of the formalism. The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. In this logically complete and self-standing formula...
A gauge theory of gravity in curved phase-spaces
Castro, Carlos
2016-06-01
After a cursory introduction of the basic ideas behind Born’s Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain nonholonomic modifications of Riemann-Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the 8D cotangent bundle T∗M of spacetime is explicitly constructed and based on the gauge group SO(6, 2) ×sR8 which acts on the tangent space to the cotangent bundle T(x,p)T∗M at each point (x,p). Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase-spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, quantum field theory (QFT) in accelerated frames, T-duality, double field theory, and generalized geometry.
Lyapunov exponent in quantum mechanics A phase-space approach
Man'ko, V I
2000-01-01
Using the symplectic tomography map, both for the probability distributionsin classical phase space and for the Wigner functions of its quantumcounterpart, we discuss a notion of Lyapunov exponent for quantum dynamics.Because the marginal distributions, obtained by the tomography map, are alwayswell defined probabilities, the correspondence between classical and quantumnotions is very clear. Then we also obtain the corresponding expressions inHilbert space. Some examples are worked out. Classical and quantum exponentsare seen to coincide for local and non-local time-dependent quadraticpotentials. For non-quadratic potentials classical and quantum exponents aredifferent and some insight is obtained on the taming effect of quantummechanics on classical chaos. A detailed analysis is made for the standard map.Providing an unambiguous extension of the notion of Lyapunov exponent toquantum mechnics, the method that is developed is also computationallyefficient in obtaining analytical results for the Lyapunov expone...
Quantum information processing in phase space: A modular variables approach
Ketterer, A.; Keller, A.; Walborn, S. P.; Coudreau, T.; Milman, P.
2016-08-01
Binary quantum information can be fault-tolerantly encoded in states defined in infinite-dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular variables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.
Origami: Delineating Cosmic Structures with Phase-Space Folds
Neyrinck, Mark C.; Falck, Bridget L.; Szalay, Alex S.
2015-01-01
Structures like galaxies and filaments of galaxies in the Universe come about from the origami-like folding of an initially flat three-dimensional manifold in 6D phase space. The ORIGAMI method identifies these structures in a cosmological simulation, delineating the structures according to their outer folds. Structure identification is a crucial step in comparing cosmological simulations to observed maps of the Universe. The ORIGAMI definition is objective, dynamical and geometric: filament, wall and void particles are classified according to the number of orthogonal axes along which dark-matter streams have crossed. Here, we briefly review these ideas, and speculate on how ORIGAMI might be useful to find cosmic voids.
Phase space view of quantum mechanical systems and Fisher information
Nagy, Á.
2016-06-01
Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini-Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Values of the phase space factors for double beta decay
Energy Technology Data Exchange (ETDEWEB)
Stoica, Sabin, E-mail: stoica@theory.nipne.ro; Mirea, Mihai [Horia Hulubei Foundation, 407, Atomistilor street, P.O. Box MG12, 077125 Magurele (Romania); Horia Hulubei National Institute of Physics and Nuclear Engineering, 30 Reactorului street, P.O. Box MG6, Magurele (Romania)
2015-10-28
We report an up-date list of the experimentally most interesting phase space factors for double beta decay (DBD). The electron/positron wave functions are obtained by solving the Dirac equations with a Coulomb potential derived from a realistic proton density distribution in nucleus and with inclusion of the finite nuclear size (FNS) and electron screening (ES) effects. We build up new numerical routines which allow us a good control of the accuracy of calculations. We found several notable differences as compared with previous results reported in literature and possible sources of these discrepancies are discussed.
Entanglement and separability in the noncommutative phase-space scenario
Bernardini, Alex E; Bertolami, Orfeu; Dias, Nuno C; Prata, João N
2014-01-01
Quantumness and separability criteria for continuous variable systems are discussed for the case of a noncommutative (NC) phase-space. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are examined. Two families of covariance matrices describing standard quantum mechanics (QM) separable states are deformed into a NC QM configuration and then investigated through the positive partial transpose criterium for identifying quantum entanglement. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the NC deformation. Extensions of some preliminary results are presented.
Quantum dynamics via a time propagator in Wigner's phase space
DEFF Research Database (Denmark)
Grønager, Michael; Henriksen, Niels Engholm
1995-01-01
that the simple classical deterministic motion breaks down surprisingly fast in an anharmonic potential. Finally, we discuss the possibility of using the scheme as a useful approach to quantum dynamics in many dimensions. To that end we present a Monte Carlo integration scheme using the norm of the propagator......We derive an expression for a short-time phase space propagator. We use it in a new propagation scheme and demonstrate that it works for a Morse potential. The propagation scheme is used to propagate classical distributions which do not obey the Heisenberg uncertainty principle. It is shown...
The Phase Space Formulation of Time-Symmetric Quantum Mechanics
Directory of Open Access Journals (Sweden)
Charlyne de Gosson
2015-11-01
Full Text Available Time-symmetric quantum mechanics can be described in the Weyl–Wigner–Moyal phase space formalism by using the properties of the cross-terms appearing in the Wigner distribution of a sum of states. These properties show the appearance of a strongly oscillating interference between the pre-selected and post-selected states. It is interesting to note that the knowledge of this interference term is sufficient to reconstruct both states.Quanta 2015; 4: 27–34.
Capture into resonance and phase space dynamics in optical centrifuge
Armon, Tsafrir
2016-01-01
The process of capture of a molecular enesemble into rotational resonance in the optical centrifuge is investigated. The adiabaticity and phase space incompressibility are used to find the resonant capture probability in terms of two dimensionless parameters P1,P2 characterising the driving strength and the nonlinearity, and related to three characteristic time scales in the problem. The analysis is based on the transformation to action-angle variables and the single resonance approximation, yielding reduction of the three-dimensional rotation problem to one degree of freedom. The analytic results for capture probability are in a good agreement with simulations. The existing experiments satisfy the validity conditions of the theory.
Phase space reduction and vortex statistics: An anyon quantization ambiguity
Energy Technology Data Exchange (ETDEWEB)
Allen, T.J.; Bordner, A.J.; Crossley, D.B. (Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706 (United States))
1994-06-15
We examine the quantization of the motion of two charged vortices in a Ginzburg-Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be implemented either in the reduced phase space or Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics, we show that these two ways of implementing the constraints are inequivalent unless the vortices are quantized with conventional statistics, either fermionic or bosonic.
Plane Pendulum and Beyond by Phase Space Geometry
Klee, Bradley
2016-01-01
By careful analysis, the simple harmonic approximation leads to a wildly inaccurate prediction for the period of a simple plane pendulum. We make a perturbation ansatz for the phase space trajectory of a one-dimensional, anharmonic oscillator and apply conservation of energy to set undetermined functions. Iteration of the algorithm yields, to arbitrary precision, a solution to the equations of motion and the period of oscillation. Comparison with Jacobian elliptic functions leads to multidimensional applications such as the construction of approximate Seiffert spirals. Throughout we develop a quantum/classical analogy for the purpose of comparing time-independent perturbation theories.
Phase Space of Anisotropic $R^n$ Cosmologies
Leon, Genly
2014-01-01
We construct general anisotropic cosmological scenarios governed by an $f(R)=R^n$ gravitational sector. Focusing then on some specific geometries, and modelling the matter content as a perfect fluid, we perform a phase-space analysis. We analyze the possibility of accelerating expansion at late times, and additionally, we determine conditions for the parameter $n$ for the existence of phantom behavior, contracting solutions as well as of cyclic cosmology. Furthermore, we analyze if the universe evolves towards the future isotropization without relying on a cosmic no-hair theorem. Our results indicate that anisotropic geometries in modified gravitational frameworks present radically different cosmological behaviors compared to the simple isotropic scenarios.
ORIGAMI: Delineating Cosmic Structures with Phase-Space Folds
Neyrinck, Mark C; Szalay, Alex S
2013-01-01
Structures like galaxies and filaments of galaxies in the Universe come about from the origami-like folding of an initially flat three-dimensional manifold in 6D phase space. The ORIGAMI method identifies these structures in a cosmological simulation, delineating the structures according to their outer folds. Structure identification is a crucial step in comparing cosmological simulations to observed maps of the Universe. The ORIGAMI definition is objective, dynamical and geometric: filament, wall and void particles are classified according to the number of orthogonal axes along which dark-matter streams have crossed. Here, we briefly review these ideas, and speculate on how ORIGAMI might be useful to find cosmic voids.
The phase-space analysis of modified gravity (MOG)
Jamali, Sara; Roshan, Mahmood
2016-09-01
We investigate the cosmological consequences of a scalar-vector-tensor theory of gravity known as modified gravity (MOG). In MOG, in addition to metric tensor, there are two scalar fields G( x) and μ (x), and one vector field φ _{α }(x). Using the phase space analysis, we explore the cosmological consequences of a model of MOG and find some new interesting features which are absent in Λ CDM model. More specifically we study the possibility that if the extra fields of this theory behave like dark energy to explain the cosmic speedup. More interestingly, with or without cosmological constant, a strongly phantom crossing occurs. Also we find that this theory in its original form (Λ ≠ 0) possesses a true sequence of cosmological epochs. However, we show that, surprisingly, there are two radiation-dominated epochs, f_5 and f_6, two matter-dominated phases, f_3 and f_4, and two late time accelerated eras, f_{12} and f7. Depending on the initial conditions the universe will realize only three of these six eras. However, the matter-dominated phases are dramatically different from the standard matter-dominated epoch. In these phases the cosmic scale factor grows as a(t)˜ t^{0.46} and t^{0.52}, respectively, which are slower than the standard case, i.e. a(t)˜ t^{2/3}. Considering these results we discuss the cosmological viability of MOG.
On Schwarzschild black holes in a D-dimensional noncommutative space
Chabab, M; Sedra, M B
2012-01-01
This work aims to implement the idea of noncommutativity in the subject of black holes. Its principal contents deal with a study of Schwarzschild black holes in a D-dimensional noncommutative space. Various aspects related to the non commutative extension are discussed and some non trivial results are derived.
On coherent-state representations of quantum mechanics: Wave mechanics in phase space
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Jørgensen, Thomas Godsk; Torres-Vega, Gabino
1997-01-01
one wants to solve the stationary Schrodinger equation in phase space and we devise two schemes for the removal of these ambiguities. The physical interpretation of the phase-space wave functions is discussed and a procedure for computing expectation values as integrals over phase space is presented...
Experimental Characterizations of 4-D Transverse Phase-Space of a Compressed Beam
Zhou, Feng; Andonian, Gerard; Ben-Zvi, Ilan; Cline, David B; Murokh, Alex; Rosenzweig, James E; Yakimenko, Vitaly
2005-01-01
Coherent synchrotron radiation can significantly distort beam phase spaces in longitudinal direction and bending plane through a bunch compressor. A tomography technique is used to reconstruct transverse phase space of electron beam. Transverse 4-D phase spaces are systematically measured at UCLA/ATF compressor and their characteristics with different bunch compression conditions are analyzed.
Phase Space Velocy Correlation and Degrees of Freedom
Mattingly, Sean; Berumen, Jorge; Chu, Feng; Hood, Ryan; Skiff, Fred
2016-10-01
We measure the phase space distribution function's velocity correlation function C(v ,v' , τ) = t in a cylindrical axially magnetized laboratory plasma (n 109 ,Te 5eV ,Ti 0.08eV) generated with an inductively coupled RF source. We use Laser Induced Fluorescence (LIF) with two lasers that each have their own atomic transition scheme and collection optics to simultaneously measure distinct ion subpopulations at differing velocities v and v'. A separately mounted antenna facilitates the velocity correlation measurement through either single mode excitation with a sinusoidal signal or broadband excitation with white noise. LIF photon acquisition is synchronized with digitizer sampling of the signal driving the fluctuation excitation antenna. With this we explore phase space degrees of freedom in v and v' with either monochromatic or broadband excitation. Finally, driving a sinusoidal wave near the ion cyclotron frequency causes linear wave - particle resonance ω - nΩci =k| |(ω) v| | that results in a tunable ion resonance velocity located within the Doppler broadened IVDF - making it measureable by LIF. NSF DOE Grant DE-FG02-99ER54543.
Quantization as Asymptotics of Diffusion Processes in the Phase Space
Beniaminov, E M
2008-01-01
This work is an extended version of the paper arXiv:0803.2669v1[math-ph], in which the main results were announced. We consider certain classical diffusion process for a wave function on the phase space. It is shown that at the time of order $10^{-11}$ {\\it sec} this process converges to a process considered by quantum mechanics and described by the Schrodinger equation. This model studies the probability distributions in the phase space corresponding to the wave functions of quantum mechanics. We estimate the parameters of the model using the Lamb--Retherford experimental data on shift in the spectrum of hydrogen atom and the assumption on the heat reason of the considered diffusion process. In the paper it is shown that the quantum mechanical description of the processes can arise as an approximate description of more exact models. For the model considered in this paper, this approximation arises when the Hamilton function changes slowly under deviations of coordinates, momenta, and time on intervals whose ...
Removing phase-space restrictions in factorized cross sections
Feige, Ilya; Yan, Kai
2015-01-01
Factorization in gauge theories holds at the amplitude or amplitude-squared level for states of given soft or collinear momenta. When performing phase-space integrals over such states, one would generally like to avoid putting in explicit cuts to separate soft from collinear momenta. Removing these cuts induces an overcounting of the soft-collinear region and adds new infrared-ultraviolet divergences in the collinear region. In this paper, we first present a regulator-independent subtraction algorithm for removing soft-collinear overlap at the amplitude level which may be useful in pertubative QCD. We then discuss how both the soft-collinear and infrared-ultraviolet overlap can be undone for certain observables in a way which respects factorization. Our discussion clarifies some of the subtleties in phase-space subtractions and includes a proof of the infrared finiteness of a suitably subtracted jet function. These results complete the connection between factorized QCD and Soft-Collinear Effective Theory.
Coherent quantum squeezing due to the phase space noncommutativity
Bernardini, Alex E.; Mizrahi, Salomon S.
2015-06-01
The effects of general noncommutativity of operators on producing deformed coherent squeezed states is examined in phase space. A two-dimensional noncommutative (NC) quantum system supported by a deformed mathematical structure, similar to that of Hadamard billiard, is obtained and the components behaviour is monitored in time. It is assumed that the independent degrees of freedom are two free 1D harmonic oscillators (HOs), so the system Hamiltonian does not contain interaction terms. Through the NC deformation parameterized by a Seiberg-Witten transform on the original canonical variables, one gets the standard commutation relations for the new ones, such that the obtained, new, Hamiltonian represents two interacting 1D HOs. By admitting that one HO is inverted relatively to the other, we show that their effective interaction induces a squeezing dynamics for initial coherent states imaged in the phase space. A suitable pattern of logarithmic spirals is obtained and some relevant properties are discussed in terms of Wigner functions, which are essential to put in evidence the effects of the noncommutativity.
What is the phase space of the last glacial inception?
Bahadory, Taimaz; Tarasov, Lev
2017-04-01
Would the ice and climate pattern of glacial inception changed much with small tweaks to the initial Eemian climate state? Given the very limited available geological constraints, what is the range of potential spatio-temporal patterns of ice sheet inception and associated climate? What positive and negative feedbacks between ice, atmospheric and ocean circulation, and vegetation dominate glacial inception? As a step towards answering these questions, we examine the phase space of glacial inception in response to a subset of uncertainties in a coupled 3D model through an ensemble of simulations. The coupled model consists of the GSM (Glacial Systems Model) and LOVECLIM earth systems model of intermediate complexity. The former includes a 3D ice sheet model, asynchronously coupled glacio isostatic adjustment, surface drainage solver, and permafrost resolving bed thermal model. The latter includes an ocean GCM, atmospheric component, dynamic/thermodynamic seaice, and simplified dynamical vegetation. Our phase space exploration probes uncertainties in: initial conditions, downscaling and upscaling, the radiative effect of clouds, snow and ice albedo, precipitation parameterization, and freshwater discharge. The probe is constrained by model fit to present day climate and LGM climate.
Dynamical tunneling in systems with a mixed phase space
Energy Technology Data Exchange (ETDEWEB)
Loeck, Steffen
2010-04-22
Tunneling is one of the most prominent features of quantum mechanics. While the tunneling process in one-dimensional integrable systems is well understood, its quantitative prediction for systems with a mixed phase space is a long-standing open challenge. In such systems regions of regular and chaotic dynamics coexist in phase space, which are classically separated but quantum mechanically coupled by the process of dynamical tunneling. We derive a prediction of dynamical tunneling rates which describe the decay of states localized inside the regular region towards the so-called chaotic sea. This approach uses a fictitious integrable system which mimics the dynamics inside the regular domain and extends it into the chaotic region. Excellent agreement with numerical data is found for kicked systems, billiards, and optical microcavities, if nonlinear resonances are negligible. Semiclassically, however, such nonlinear resonance chains dominate the tunneling process. Hence, we combine our approach with an improved resonance-assisted tunneling theory and derive a unified prediction which is valid from the quantum to the semiclassical regime. We obtain results which show a drastically improved accuracy of several orders of magnitude compared to previous studies. (orig.)
Tomography of the electron beam transverse phase space at PITZ
Energy Technology Data Exchange (ETDEWEB)
Asova, Galina
2013-09-15
The operation of a Free Elector Laser, FEL, requires high energy, high peak current electron beams with small transverse emittance. In the contemporary FELs, the electron beam is passed through a periodic magnetic structure - an undulator - which modifies the straight beam trajectory into a sinusoidal one, where FEL light is generated at each bend. According to the energy, the transverse emittance and the peak current of the beam and the parameters of the undulator, FEL radiation with wavelength in the range of nano- to micrometers can be generated. Studies and development of FELs are done all over the world. The Free electron LASer in Hamburg, FLASH, and the international European X-ray FEL, XFEL, in Hamburg, Germany, are two leading projects of the Deutsches Elektronen SYnchrotron, DESY. Part of the research program on FELs in DESY is realized in Zeuthen within the project Photo-Injector Test Facility at DESY in Zeuthen, PITZ. PITZ is an international collaboration including Germany, Russia, Italy, France, Bulgaria, Thailand, United Kingdom. The Institute of Nuclear Research and Nuclear Energy, INRNE, at the Bulgarian Academy of Sciences participates from bulgarian side. PITZ studies and optimizes the photo-injectors for FLASH and the XFEL. The research program emphasizes on detailed measurements of the transverse phase-space density distribution. Until 2010 the single slit scan technique has been used to measure the beam transverse distributions. At the end of 2010 a module for tomographic diagnostics has been installed which extends the possibilities of PITZ to measure simultaneously the two transverse planes of a single micropulse with improved signal-to-noise ratio. The difficult conditions of low emittance for high bunch charge and low energy make the operation of the module challenging. This thesis presents the design considerations for the tomography module, a number of reconstruction algorithms and their applicability to limited data sets, the influence
Torre, Amalia
2005-01-01
Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner f
L2 Orthogonal Space Time Code for Continuous Phase Modulation
Hesse, Matthias; Deneire, Luc
2008-01-01
To combine the high power efficiency of Continuous Phase Modulation (CPM) with either high spectral efficiency or enhanced performance in low Signal to Noise conditions, some authors have proposed to introduce CPM in a MIMO frame, by using Space Time Codes (STC). In this paper, we address the code design problem of Space Time Block Codes combined with CPM and introduce a new design criterion based on L2 orthogonality. This L2 orthogonality condition, with the help of simplifying assumption, leads, in the 2x2 case, to a new family of codes. These codes generalize the Wang and Xia code, which was based on pointwise orthogonality. Simulations indicate that the new codes achieve full diversity and a slightly better coding gain. Moreover, one of the codes can be interpreted as two antennas fed by two conventional CPMs using the same data but with different alphabet sets. Inspection of these alphabet sets lead also to a simple explanation of the (small) spectrum broadening of Space Time Coded CPM.
A phase-space beam position monitor for synchrotron radiation
Energy Technology Data Exchange (ETDEWEB)
Samadi, Nazanin, E-mail: nazanin.samadi@usask.ca [University of Saskatchewan, 107 Wiggins Road, Saskatoon, SK (Canada); Bassey, Bassey; Martinson, Mercedes [University of Saskatchewan, 116 Science Place, Saskatoon, SK (Canada); Belev, George; Dallin, Les; Jong, Mark de [Canadian Light Source, 44 Innovation Boulevard, Saskatoon, SK (Canada); Chapman, Dean [University of Saskatchewan, 107 Wiggins Road, Saskatoon, SK (Canada)
2015-06-25
A system has been developed to measure the vertical position and angle of the electron beam at a single location from a synchrotron source. The system uses a monochromator tuned to the absorption edge of a contrast material and has a sensitivity comparable with other beam position monitors. The stability of the photon beam position on synchrotron beamlines is critical for most if not all synchrotron radiation experiments. The position of the beam at the experiment or optical element location is set by the position and angle of the electron beam source as it traverses the magnetic field of the bend-magnet or insertion device. Thus an ideal photon beam monitor would be able to simultaneously measure the photon beam’s position and angle, and thus infer the electron beam’s position in phase space. X-ray diffraction is commonly used to prepare monochromatic beams on X-ray beamlines usually in the form of a double-crystal monochromator. Diffraction couples the photon wavelength or energy to the incident angle on the lattice planes within the crystal. The beam from such a monochromator will contain a spread of energies due to the vertical divergence of the photon beam from the source. This range of energies can easily cover the absorption edge of a filter element such as iodine at 33.17 keV. A vertical profile measurement of the photon beam footprint with and without the filter can be used to determine the vertical centroid position and angle of the photon beam. In the measurements described here an imaging detector is used to measure these vertical profiles with an iodine filter that horizontally covers part of the monochromatic beam. The goal was to investigate the use of a combined monochromator, filter and detector as a phase-space beam position monitor. The system was tested for sensitivity to position and angle under a number of synchrotron operating conditions, such as normal operations and special operating modes where the photon beam is intentionally altered
The phase-space analysis of modified gravity (MOG)
Energy Technology Data Exchange (ETDEWEB)
Jamali, Sara; Roshan, Mahmood [Ferdowsi University of Mashhad, Department of Physics, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)
2016-09-15
We investigate the cosmological consequences of a scalar-vector-tensor theory of gravity known as modified gravity (MOG). In MOG, in addition to metric tensor, there are two scalar fields G(x) and μ(x), and one vector field φ{sub α}(x). Using the phase space analysis, we explore the cosmological consequences of a model of MOG and find some new interesting features which are absent in ΛCDM model. More specifically we study the possibility that if the extra fields of this theory behave like dark energy to explain the cosmic speedup. More interestingly, with or without cosmological constant, a strongly phantom crossing occurs. Also we find that this theory in its original form (Λ ≠ 0) possesses a true sequence of cosmological epochs. However, we show that, surprisingly, there are two radiation-dominated epochs, f{sub 5} and f{sub 6}, two matter-dominated phases, f{sub 3} and f{sub 4}, and two late time accelerated eras, f{sub 12} and f{sub 7}. Depending on the initial conditions the universe will realize only three of these six eras. However, the matter-dominated phases are dramatically different from the standard matter-dominated epoch. In these phases the cosmic scale factor grows as a(t) ∝ t{sup 0.46} and t{sup 0.52}, respectively, which are slower than the standard case, i.e. a(t) ∝ t{sup 2/3}. Considering these results we discuss the cosmological viability of MOG. (orig.)
Semiclassical approximations in phase space with coherent states
Energy Technology Data Exchange (ETDEWEB)
Baranger, M. [Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA (United States); De Aguiar, M.A.M. [Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA (United States); Instituto de Fisica ' Gleb Wataghin' , Universidade Estadual de Campinas, Campinas (Brazil); Keck, F.; Korsch, H.J.; Schellhaass, B. [FB Physik, Universitaet Kaiserslautern, Kaiserslautern (Germany)
2001-09-14
We present a complete derivation of the semiclassical limit of the coherent-state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial-value representation for the semiclassical propagator, based on an initial Gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed Gaussian approximation. It is very different from the Herman-Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent-state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states. (author)
Semiclassical approximations in phase space with coherent states
Baranger, M.; de Aguiar, M. A. M.; Keck, F.; Korsch, H. J.; Schellhaaß, B.
2001-09-01
We present a complete derivation of the semiclassical limit of the coherent-state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial-value representation for the semiclassical propagator, based on an initial Gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed Gaussian approximation. It is very different from the Herman-Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent-state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.
Tailoring phase-space in neutron beam extraction
Energy Technology Data Exchange (ETDEWEB)
Weichselbaumer, S. [Heinz Maier-Leibnitz Zentrum und Physik-Department E21, Technische Universität München, Lichtenbergstr. 1, D-85748 Garching (Germany); Brandl, G. [Heinz Maier-Leibnitz Zentrum und Physik-Department E21, Technische Universität München, Lichtenbergstr. 1, D-85748 Garching (Germany); Physik-Department E21, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany); Georgii, R., E-mail: Robert.Georgii@frm2.tum.de [Heinz Maier-Leibnitz Zentrum und Physik-Department E21, Technische Universität München, Lichtenbergstr. 1, D-85748 Garching (Germany); Physik-Department E21, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany); Stahn, J. [Laboratory for Neutron Scattering, Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Panzner, T. [Material Science and Simulations, Neutrons and Muons, Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Böni, P. [Physik-Department E21, Technische Universität München, James-Franck-Str. 1, D-85748 Garching (Germany)
2015-09-01
In view of the trend towards smaller samples and experiments under extreme conditions it is important to deliver small and homogeneous neutron beams to the sample area. For this purpose, elliptic and/or Montel mirrors are ideally suited as the phase space of the neutrons can be defined far away from the sample. Therefore, only the useful neutrons will arrive at the sample position leading to a very low background. We demonstrate the ease of designing neutron transport systems using simple numeric tools, which are verified using Monte-Carlo simulations that allow taking into account effects of gravity and finite beam size. It is shown that a significant part of the brilliance can be transferred from the moderator to the sample. Our results may have a serious impact on the design of instruments at spallation sources such as the European Spallation Source (ESS) in Lund, Sweden.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
DIÓGENES CAMPOS
2017-03-01
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.
The Harari Shupe preon model and nonrelativistic quantum phase space
Żenczykowski, P.
2008-03-01
We propose that the whole algebraic structure of the Harari-Shupe rishon model originates via a Dirac-like linearization of quadratic form x2 +p2, with position and momentum satisfying standard commutation relations. The scheme does not invoke the concept of preons as spin-1/2 subparticles, thus evading the problem of preon confinement, while fully explaining all symmetries emboded in the Harari-Shupe model. Furthermore, the concept of quark colour is naturally linked to the ordering of rishons. Our scheme leads to group U (1) ⊗ SU (3) combined with SU (2), with two of the SU (2) generators not commuting with reflections. An interpretation of intra-generation quark-lepton transformations in terms of genuine rotations and reflections in phase space is proposed.
Searching for fractal phenomena in multidimensional phase-spaces
Blažek, Mikuláš
2000-07-01
A unified point of view on the fractal analysis in d-dimensional phase-spaces is presented. It is applicable to the data coming from the counting experiments. Explicit expressions are formulated for the fundamental types of factorial moments characterizing the presence of the fractal phenomena, their number being given by (2 d+1 - 1), as well as for a variety of associated statistical moments; special attention is paid to two and three dimensions. In particular, it is found that scaling properties of the modified dispersion moments are directly related with the presence of empty bins in the corresponding distributions. As to the high-energy experiments, those expressions can be applied to the data presently available, e.g. from LEP, as well as to the data arising in the near future from heavy-ion collisions performed at the CERN collider and from the pp collisions observed at the Tevatron, Fermilab.
Phase-space noncommutative formulation of Ozawa's uncertainty principle
Bastos, Catarina; Bernardini, Alex E.; Bertolami, Orfeu; Costa Dias, Nuno; Prata, João Nuno
2014-08-01
Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature amplifiers and for noiseless quadrature transducers. Several distinctive features appear as a consequence of the noncommutative extension: measurement interactions which are noiseless, and observables which are undisturbed by a measurement, or of independent intervention in ordinary quantum mechanics, may acquire noise, become disturbed by the measurement, or no longer be an independent intervention in noncommutative quantum mechanics. It is also found that there can be states which violate Ozawa's universal noise-disturbance trade-off relation, but verify its noncommutative deformation.
The phase space analysis of modified gravity (MOG)
Jamali, Sara
2016-01-01
We investigate the cosmological consequences of a scalar-vector-tensor theory of gravity known as MOG. In MOG, in addition to metric tensor, there are two scalar fields $G(x)$ and $\\mu(x)$, and one vector field $\\phi_{\\alpha}(x)$. Using the phase space analysis, we explore the cosmological consequences of a model of MOG and find some new interesting features which are absent in $\\Lambda$CDM model. More specifically we study the possibility that if the extra fields of this theory behave like dark energy to explain the cosmic speedup. More interestingly, with or without cosmological constant, strongly phantom crossing happens. Also we find that this theory in its original form ($\\Lambda\
Charting the invisible in phase space (Abstract only)
Indian Academy of Sciences (India)
Alvaro de Rujula
2012-06-01
One challenge in particle physics is that not all the momenta relevant to many processes are observable. Some particles are nearly invisible (neutrinos and hypothetical neutralinos), others escape undetected down the beam pipes of colliders. One faces the task of extracting the maximum information (e.g. on the mass of the unobserved particles) from a set of more unknowns than constraining energy–momentum conservation equations. We study the simplest realistic case of current interest: single- production at a hadron collider, followed by its leptonic decay. We derive and discuss the statistically-optimal ‘singularity variable’ relevant to the measurement of the mass. In spite of its simplicity, this process is fairly non-trivial and constitutes a good ‘training’ example for the scrutiny of phenomena involving invisible objects. Our graphical analysis of the phase space is akin to that of a Dalitz plot, extended to such processes.
Aspects of Phase-Space Noncommutative Quantum Mechanics
Bertolami, O
2015-01-01
In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM) are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In particular, the issues related with gauge invariance of the electromagnetic field and the weak equivalence principle (WEP) in the context of the gravitational quantum well (GQW) are considered. The question of the Lorentz symmetry and the associated dispersion relation is also examined. Constraints are set on the relevant noncommutative parameters so that gauge invariance and Lorentz invariance holds. In opposition, the WEP is verified to hold in the noncommutative set up, and it is only possible to observe a violation through an anisotropy of the noncommutative parameters.
A study on quantum similarity in the phase space
Sellier, J. M.; Ivanova, D. Y.; Dimov, I.
2016-10-01
Quantum similarity represents an important concept in the context of many applied disciplines such as physical and quantum chemistry. Nowadays, two definitions exist based, respectively, on the real and the phase spaces. In this paper, we focus on the second one, which was presented recently, and investigate it. In particular, being its mathematical definition dependent on a given integer s, we study the influence of this parameter on the similarity between two systems. To keep this investigation comprehensible, while still meaningful, we focus on a very simple quantum system represented by a hydrogen atom in the ground and excited states corresponding to the quantum numbers (n , l , m) =(1 , 0 , 0) and (n , l , m) =(2 , 0 , 0) .
ORIGAMI: Delineating Halos using Phase-Space Folds
Falck, Bridget L; Szalay, Alexander S
2012-01-01
We present the ORIGAMI method of identifying structures, particularly halos, in cosmological N-body simulations. Structure formation can be thought of as the folding of an initially flat three-dimensional manifold in six-dimensional phase space. ORIGAMI finds the outer folds that delineate these structures. Halo particles are identified as those that have undergone shell-crossing along 3 orthogonal axes, providing a dynamical definition of halo regions that is independent of density. ORIGAMI also identifies other morphological structures: particles that have undergone shell-crossing along 2, 1, or 0 orthogonal axes correspond to filaments, walls, and voids respectively. We compare this method to a standard Friends-of-Friends halo-finding algorithm and find that ORIGAMI halos are somewhat larger, more diffuse, and less spherical, though the global properties of ORIGAMI halos are in good agreement with other modern halo-finding algorithms.
ORIGAMI: DELINEATING HALOS USING PHASE-SPACE FOLDS
Energy Technology Data Exchange (ETDEWEB)
Falck, Bridget L.; Neyrinck, Mark C.; Szalay, Alexander S. [Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218 (United States)
2012-08-01
We present the ORIGAMI method of identifying structures, particularly halos, in cosmological N-body simulations. Structure formation can be thought of as the folding of an initially flat three-dimensional manifold in six-dimensional phase space. ORIGAMI finds the outer folds that delineate these structures. Halo particles are identified as those that have undergone shell-crossing along three orthogonal axes, providing a dynamical definition of halo regions that is independent of density. ORIGAMI also identifies other morphological structures: particles that have undergone shell-crossing along 2, 1, or 0 orthogonal axes correspond to filaments, walls, and voids, respectively. We compare this method to a standard friends-of-friends halo-finding algorithm and find that ORIGAMI halos are somewhat larger, more diffuse, and less spherical, though the global properties of ORIGAMI halos are in good agreement with other modern halo-finding algorithms.
Semi-classical Scar functions in phase space
Rivas, A M F
2006-01-01
We develop a semi-classical approximation for the scar function in the Weyl-Wigner representation in the neighborhood of a classically unstable periodic orbit of chaotic two dimensional systems. The prediction of hyperbolic fringes, asymptotic to the stable and unstable manifolds, is verified computationally for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus. Characteristic fringe patterns can be distinguished even for quasi-energies where the fixed point is not Bohr-quantized. Also the patterns are highly localized in the neighborhood of the periodic orbit and along its stable and unstable manifolds without any long distance patterns that appears for the case of the spectral Wigner function.
Aspects of phase-space noncommutative quantum mechanics
Directory of Open Access Journals (Sweden)
O. Bertolami
2015-11-01
Full Text Available In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In particular, the issues related with gauge invariance of the electromagnetic field and the weak equivalence principle (WEP in the context of the gravitational quantum well (GQW are considered. The question of the Lorentz symmetry and the associated dispersion relation is also examined. Constraints are set on the relevant noncommutative parameters so that gauge invariance and Lorentz invariance holds. In opposition, the WEP is verified to hold in the noncommutative setup, and it is only possible to observe a violation through an anisotropy of the noncommutative parameters.
Generalizing the Boltzmann equation in complex phase space.
Zadehgol, Abed
2016-08-01
In this work, a generalized form of the BGK-Boltzmann equation is proposed, where the velocity, position, and time can be represented by real or complex variables. The real representation leads to the conventional BGK-Boltzmann equation, which can recover the continuity and Navier-Stokes equations. We show that the complex representation yields a different set of equations, and it can also recover the conservation and Navier-Stokes equations, at low Mach numbers, provided that the imaginary component of the macroscopic mass can be neglected. We briefly review the Constant Speed Kinetic Model (CSKM), which was introduced in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)JCTPAH0021-999110.1016/j.jcp.2014.06.053] and Zadehgol [Phys. Rev. E 91, 063311 (2015)PLEEE81539-375510.1103/PhysRevE.91.063311]. The CSKM is then used as a basis to show that the complex-valued equilibrium distribution function of the present model can be identified with a simple singularity in the complex phase space. The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the "branes," in the complex phase space, do not affect the local kinetic states. This property of the new model, which is referred to as the "apparent jumps" in the present work, is used to construct new models. The theoretical findings have been tested by simulating three benchmark flows. The results of the present simulations are in excellent agreement with the previous results reported by others.
Wigner phase space distribution via classical adiabatic switching
Energy Technology Data Exchange (ETDEWEB)
Bose, Amartya [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Makri, Nancy [Department of Chemistry, University of Illinois, 600 S. Goodwin Avenue, Urbana, Illinois 61801 (United States); Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801 (United States)
2015-09-21
Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if the perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.
Generalizing the Boltzmann equation in complex phase space
Zadehgol, Abed
2016-08-01
In this work, a generalized form of the BGK-Boltzmann equation is proposed, where the velocity, position, and time can be represented by real or complex variables. The real representation leads to the conventional BGK-Boltzmann equation, which can recover the continuity and Navier-Stokes equations. We show that the complex representation yields a different set of equations, and it can also recover the conservation and Navier-Stokes equations, at low Mach numbers, provided that the imaginary component of the macroscopic mass can be neglected. We briefly review the Constant Speed Kinetic Model (CSKM), which was introduced in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014), 10.1016/j.jcp.2014.06.053] and Zadehgol [Phys. Rev. E 91, 063311 (2015), 10.1103/PhysRevE.91.063311]. The CSKM is then used as a basis to show that the complex-valued equilibrium distribution function of the present model can be identified with a simple singularity in the complex phase space. The virtual particles, in the present work, are concentrated on virtual "branes" which surround the computational nodes. Employing the Cauchy integral formula, it is shown that certain variations of the "branes," in the complex phase space, do not affect the local kinetic states. This property of the new model, which is referred to as the "apparent jumps" in the present work, is used to construct new models. The theoretical findings have been tested by simulating three benchmark flows. The results of the present simulations are in excellent agreement with the previous results reported by others.
On Quantum Mechanics on Noncommutative Quantum Phase Space
Institute of Scientific and Technical Information of China (English)
A.E.F. DjemaI; H. Smail
2004-01-01
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM),characterized by a space noncommutativity matrix parameter θ =∈k ijθk and a momentum noncommutativity matrix parameter βij = ∈k ijβk, is shown to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two parameters θ and β possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that noncommutativity is represented by a unique parameter which may play the role of a fundamental constant characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results,we discover a new phenomenon which consists of a free particle on NCQPS viewed as equivalent to a harmonic oscillator with Larmor frequency depending on β, representing the same particle in presence ofa magnetic field B = q-1 β. For the other examples, additional correction terms depending onβ appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively feeled with opposite sign.
Phase-Space Structure & Substructure of Dark Halos
Arad, A D I
2004-01-01
A method is presented for computing the 6-D phase-space density f(x,v) and its PDF v(f) in an N-body system. It is based on Delaunay tessellation, yielding v(f) with a fixed smoothing window over a wide f range, independent of the sampling resolution. It is found that in a gravitationally relaxed halo built by hierarchical clustering, v(f) is a robust power law, v(f) f^{-2.5 \\pm 0.05}, over more than 4 decades in f, from its virial level to the current resolution limit. This is valid for halos of different sizes in the LCDM cosmology, indicating insensitivity to the initial-fluctuation power spectrum as long as the small-scale fluctuations were not completely suppressed. By mapping f in position space, we find that the high-f contributions to v(f) come from the "cold" subhalos within the parent halo rather than the halo central region and its global spherical profile. The f in subhalos near the halo virial radius is more than 100 times higher than at the halo center, and it decreases gradually with decreasing...
Nonlinear Landau-Zener tunneling in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Trimborn, F [Institut fuer theoretische Physik, Leibniz Universitaet Hannover, D-30167 Hannover (Germany); Witthaut, D [QUANTOP, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen (Denmark); Kegel, V; Korsch, H J, E-mail: friederike.trimborn@itp.uni-hannover.d [Fachbereich Physik, TU Kaiserslautern, D-67663 Kaiserslautern (Germany)
2010-05-15
We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focusing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity and thus fundamentally alters the dynamics. It is shown that essentially all the features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase-space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility of exploiting Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analyzed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive yet readily implementable probe for decoherence, since the noise has significant effect on the transition rate for slow parameter variations.
Nonlinear Landau-Zener tunneling in quantum phase space
Trimborn, F; Kegel, V; Korsch, H J; 10.1088/1367-2630/12/5/053010
2010-01-01
We present a detailed analysis of the Landau-Zener problem for an interacting Bose-Einstein condensate in a time-varying double-well trap, especially focussing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity condition and thus fundamentally alters the dynamics. It is shown that essentially all features of the Landau-Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility to exploit Landau-Zener sweeps to generate squeezed states for spectroscopic tasks is analysed in detail. Moreover, we study the influence of phase noise and propose a Landau-Zener sweep as a sensitive, yet readily implementable probe for decoherence, since this has a significant effec...
A Phase Space Approach to the Gravitational Arrow of Time
Rothman, T; Rothman, Tony; Anninos, Peter
1997-01-01
We attempt to find a function that characterizes gravitational clumping= and that increases monotonically as inhomogeneity increases. We choose $S =3D ln\\Omega$ as the candidate ``gravitational entropy'' function, where $\\Om= ega$ is the phase-space volume below the Hamiltonian H of the system under consideration. We compute $\\Omega$ for transverse electromagnetic waves a= nd for gravitational wave, radiation and density perturbations in an expanding F= LRW universe. These calculations are carried out in the linear regime under t= he assumption that the phases of the oscillators comprising the system are r= andom. Entropy is thus attributed to the lack of knowledge of the exact field configuration. We find that $\\Omega$, and hence $ln\\Omega$ behaves as required. We also carry out calculations for Bianchi IX cosmological mode= ls and find that, even in this homogeneous case, the function can be interpreted sensibly. We compare our results with Penrose's C^2 hypothesis. Because S is defined to resemble the fund...
Sherkatghanad, Zeinab; Mirzaeyan, Zahra; Mansoori, Seyed Ali Hosseini
2014-01-01
We consider the critical behaviors and phase transitions of Gauss Bonnet-Born Infeld-AdS black holes (GB-BI-AdS) for $d=5,6$ and the extended phase space. We assume the cosmological constant, $\\Lambda$, the coupling coefficient $\\alpha$, and the BI parameter $\\beta$ to be thermodynamic pressures of the system. Having made these assumptions, the critical behaviors are then studied in the two canonical and grand canonical ensembles. We find "reentrant and triple point phase transitions" (RPT-TP) and "multiple reentrant phase transitions" (multiple RPT) with increasing pressure of the system for specific values of the coupling coefficient $\\alpha$ in the canonical ensemble. Also, we observe a reentrant phase transition (RPT) of GB-BI-AdS black holes in the grand canonical ensemble and for $d=6$. These calculations are then expanded to the critical behavior of Born-Infeld-AdS (BI-AdS) black holes in the third order of Lovelock gravity and in the grand canonical ensemble to find a Van der Waals behavior for $d=7$ ...
Kurien, Binoy G.; Ashcom, Jonathan B.; Shah, Vinay N.; Rachlin, Yaron; Tarokh, Vahid
2016-09-01
Atmospheric turbulence presents a fundamental challenge to Fourier phase recovery in optical interferometry. Typical reconstruction algorithms employ Bayesian inference techniques which rely on prior knowledge of the scene under observation. In contrast, Redundant Spacing Calibration (RSC) algorithms employ redundancy in the baselines of the interferometric array to directly expose the contribution of turbulence, thereby enabling phase recovery for targets of arbitrary and unknown complexity. Traditionally RSC algorithms have been applied directly to single-exposure measurements, which are reliable only at high photon flux in general. In scenarios of low photon flux, such as those arising in the observation of dim objects in space, one must instead rely on time-averaged, atmosphere-invariant quantities such as the bispectrum. In this paper, we develop a novel RSC-based algorithm for prior-less phase recovery in which we generalize the bispectrum to higher-order atmosphere-invariants (n-spectra) for improved sensitivity. We provide a strategy for selection of a high-SNR set of n-spectra using the graph-theoretic notion of the minimum cycle basis. We also discuss a key property of this set (wrap-invariance), which then enables reliable application of standard linear estimation techniques to recover the Fourier phases from the 2π-wrapped n-spectra phases. For validation, we analyze the expected shot-noise-limited performance of our algorithm for both pairwise and Fizeau interferometric architectures, and corroborate this analysis with simulation results showing performance near an atmosphere-oracle Cramer-Rao bound. Lastly, we apply techniques from the field of compressed sensing to perform image reconstruction from the estimated complex visibilities.
Phase transition and entropy inequality of noncommutative black holes in a new extended phase space
Miao, Yan-Gang
2016-01-01
We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as {\\em the noncommutative pressure}. In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former takes a UV effect while the latter does an IR effect, respectively. In addition, by means of the reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.
Exploring phase space using smartphone acceleration and rotation sensors simultaneously
Monteiro, Martín; Cabeza, Cecilia; Martí, Arturo C.
2014-07-01
A paradigmatic physical system as the physical pendulum is experimentally studied using the acceleration and rotation (gyroscope) sensors available on smartphones and other devices such as iPads and tablets. A smartphone is fixed to the outside of a bicycle wheel whose axis is kept horizontal and fixed. The compound system, wheel plus smartphone, defines a physical pendulum which can rotate, giving full turns in one direction, or oscillate about the equilibrium position (performing either small or large oscillations). Measurements of the radial and tangential acceleration and the angular velocity obtained with smartphone sensors allow a deep insight into the dynamics of the system to be gained. In addition, thanks to the simultaneous use of the acceleration and rotation sensors, trajectories in the phase space are directly obtained. The coherence of the measures obtained with the different sensors and by traditional methods is remarkable. Indeed, due to their low cost and increasing availability, smartphone sensors are valuable tools that can be used in most undergraduate laboratories.
f(R,T) Dark Energy Models in Phase Space
Shabani, Hamid
2013-01-01
We investigate cosmological solutions of f(R,T) modified theories of gravity for a perfect fluid in a spatially homogeneous and isotropic background through phase space analysis, where R is Ricci scalar and T denotes trace of energy-momentum tensor of matter content. The theory is explored for minimal case f(R,T)=g(R)+h(T), pure non-minimal case f(R,T)=g(R)h(T), and f(R,T)=g(R)+g(R)h(T). For first case, the acceptable cosmological solutions which contain long enough matter dominated era followed by a late-time accelerated expansion are found. We classify solutions in six classes which demonstrate more acceptable solutions than the f(R) gravity. In background of f(R,T) gravity, cosmological behavior of some function g(R) is explored theoretically and is shown that the models $aR^{-\\beta}$ for $-1.43\\leq\\beta0$, $R [\\log{(\\alpha R)}]^{q}$ for two values $q=\\pm1$ with $\\alpha>0$, $R^{p}\\exp{(qR)}$ for $p\\rightarrow 1^{+}$ with $q>0$, $R+\\alpha R^{-n}$ for $n\\rightarrow-1^{+}$ with $\\alpha0$ and $R^{p}\\exp{(q/R)}...
Phase space of modified Gauss-Bonnet gravity.
Carloni, Sante; Mimoso, José P
2017-01-01
We investigate the evolution of non-vacuum Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f(R) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations.
Characterization of informational completeness for covariant phase space observables
Kiukas, J.; Lahti, P.; Schultz, J.; Werner, R. F.
2012-10-01
In the nonrelativistic setting with finitely many canonical degrees of freedom, a shift-covariant phase space observable is uniquely characterized by a positive operator of trace one and, in turn, by the Fourier-Weyl transform of this operator. We study three properties of such observables, and characterize them in terms of the zero set of this transform. The first is informational completeness, for which it is necessary and sufficient that the zero set has dense complement. The second is a version of informational completeness for the Hilbert-Schmidt class, equivalent to the zero set being of measure zero, and the third, known as regularity, is equivalent to the zero set being empty. We give examples demonstrating that all three conditions are distinct. The three conditions are the special cases for p = 1, 2, ∞ of a more general notion of p-regularity defined as the norm density of the span of translates of the operator in the Schatten-p class. We show that the relation between zero sets and p-regularity can be mapped completely to the corresponding relation for functions in classical harmonic analysis.
Simple procedure for phase-space measurement and entanglement validation
Rundle, R. P.; Mills, P. W.; Tilma, Todd; Samson, J. H.; Everitt, M. J.
2017-08-01
It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasiprobability distribution (Wigner function) [Phys. Rev. Lett. 117, 180401 (2016), 10.1103/PhysRevLett.117.180401]. Such functions take the form of expectation values of an observable that has a direct analogy to displaced parity operators. In this work we give a procedure for the measurement of the Wigner function that should be applicable to any quantum system. We have applied our procedure to IBM's Quantum Experience five-qubit quantum processor to demonstrate that we can measure and generate the Wigner functions of two different Bell states as well as the five-qubit Greenberger-Horne-Zeilinger state. Because Wigner functions for spin systems are not unique, we define, compare, and contrast two distinct examples. We show how the use of these Wigner functions leads to an optimal method for quantum state analysis especially in the situation where specific characteristic features are of particular interest (such as for spin Schrödinger cat states). Furthermore we show that this analysis leads to straightforward, and potentially very efficient, entanglement test and state characterization methods.
Phase Space Dissimilarity Measures for Structural Health Monitoring
Energy Technology Data Exchange (ETDEWEB)
Bubacz, Jacob A [ORNL; Chmielewski, Hana T [ORNL; Pape, Alexander E [ORNL; Depersio, Andrew J [ORNL; Hively, Lee M [ORNL; Abercrombie, Robert K [ORNL; Boone, Shane [ORNL
2011-11-01
A novel method for structural health monitoring (SHM), known as the Phase Space Dissimilarity Measures (PSDM) approach, is proposed and developed. The patented PSDM approach has already been developed and demonstrated for a variety of equipment and biomedical applications. Here, we investigate SHM of bridges via analysis of time serial accelerometer measurements. This work has four aspects. The first is algorithm scalability, which was found to scale linearly from one processing core to four cores. Second, the same data are analyzed to determine how the use of the PSDM approach affects sensor placement. We found that a relatively low-density placement sufficiently captures the dynamics of the structure. Third, the same data are analyzed by unique combinations of accelerometer axes (vertical, longitudinal, and lateral with respect to the bridge) to determine how the choice of axes affects the analysis. The vertical axis is found to provide satisfactory SHM data. Fourth, statistical methods were investigated to validate the PSDM approach for this application, yielding statistically significant results.
Sherkatghanad, Zeinab; Mirza, Behrouz; Mirzaiyan, Zahra; Mansoori, Seyed Ali Hosseini
We consider the critical behaviors and phase transitions of Gauss-Bonnet-Born-Infeld-AdS black holes (GB-BI-AdS) for d = 5, 6 and the extended phase space. We assume the cosmological constant, Λ, the coupling coefficient α, and the BI parameter β to be thermodynamic pressures of the system. Having made these assumptions, the critical behaviors are then studied in the two canonical and grand canonical ensembles. We find “reentrant and triple point phase transitions” (RPT-TP) and “multiple reentrant phase transitions” (multiple RPT) with increasing pressure of the system for specific values of the coupling coefficient α in the canonical ensemble. Also, we observe a reentrant phase transition (RPT) of GB-BI-AdS black holes in the grand canonical ensemble and for d = 6. These calculations are then expanded to the critical behavior of Born-Infeld-AdS (BI-AdS) black holes in the third-order of Lovelock gravity and in the grand canonical ensemble to find a van der Waals (vdW) behavior for d = 7 and a RPT for d = 8 for specific values of potential ϕ in the grand canonical ensemble. Furthermore, we obtain a similar behavior for the limit of β →∞, i.e. charged-AdS black holes in the third-order of the Lovelock gravity. Thus, it is shown that the critical behaviors of these black holes are independent of the parameter β in the grand canonical ensemble.
An effective method to accurately calculate the phase space factors for $\\beta^- \\beta^-$ decay
Neacsu, Andrei
2015-01-01
Accurate calculations of the electron phase space factors are necessary for reliable predictions of double-beta decay rates, and for the analysis of the associated electron angular and energy distributions. We present an effective method to calculate these phase space factors that takes into account the distorted Coulomb field of the daughter nucleus, yet allows one to easily calculate the phase space factors with good accuracy relative to the most exact methods available in the recent literature.
Phase-space dissimilarity measures for industrial and biomedical applications
Protopopescu, V. A.; Hively, L. M.
2005-12-01
One of the most important problems in time-series analysis is the suitable characterization of the dynamics for timely, accurate, and robust condition assessment of the underlying system. Machine and physiological processes display complex, non-stationary behaviors that are affected by noise and may range from (quasi-)periodic to completely irregular (chaotic) regimes. Nevertheless, extensive experimental evidence indicates that even when the systems behave very irregularly (e.g., severe tool chatter or cardiac fibrillation), one may assume that - for all practical purposes - the dynamics are confined to low dimensional manifolds. As a result, the behavior of these systems can be described via traditional nonlinear measures (TNM), such as Lyapunov exponents, Kolmogorov entropy, and correlation dimension. While these measures are adequate for discriminating between clear-cut regular and chaotic dynamics, they are not sufficiently sensitive to distinguish between slightly different irregular (chaotic) regimes, especially when data are noisy and/or limited. Both machine and physiological dynamics usually fall into this latter category, creating a massive stumbling block to prognostication of abnormal regimes. We present here a recently developed approach that captures more efficiently changes in the underlying dynamics. We start with process-indicative, time-serial data that are checked for quality and discarded if inadequate. Acceptable data are filtered to remove confounding artifacts (e.g., sinusoidal variation in three-phase electrical signals or eye-blinks and muscular activity in EEG). The artifact-filtered data are then used to recover the essential features of the underlying dynamics via standard time-delay, phase-space reconstruction. One of the main results of this reconstruction is a discrete approximation of the distribution function (DF) on the attractor. Unaltered dynamics yield an unchanging geometry of the attractor and the visitation frequencies of
High Performance Ka-band Phase Shifters for Space Telecommunications Project
National Aeronautics and Space Administration — We propose a novel MEMS-based digital phase shifter targeted for Ka-band operation, but scalable down to X-band and up to W-band. This novel phase shifter will...
National Aeronautics and Space Administration — In this SBIR Phase 1 we propose to develop a novel microscope by integrating Fourier phase contrast microscopy (FPCM) and epi-fluorescence microscopy. In FPCM, the...
Multi-phases in gauge theories on non-simply connected spaces
Hatanaka, H; Sakamoto, M; Takenaga, K; Hatanaka, Hisaki; Ohnishi, Katsuhiko; Sakamoto, Makoto; Takenaga, Kazunori
2002-01-01
It is pointed out that phase structures of gauge theories compactified on non-simply connected spaces are quite nontrivial. As a demonstration, an SU(2) gauge model on M^3 x S^1 is studied and is shown to possess three phases: Hosotani, Higgs and coexisting phases. A general discussion about phase structures for small and large scales of compactified spaces is given. The nontriviality of phase structures suggests a GUT scenario in which the hierarchy problem may dynamically be solved if there exists a mechanism that a radius of a compactified space is stabilized in close vicinity to a critical radius.
The Spatial Equivalence Between Wavelet Decomposition and Phase Space Embedding of EEG
Institute of Scientific and Technical Information of China (English)
YOU Rong-yi; HUANG Xiao-jing
2008-01-01
Using both the wavelet decomposition and the phase space embedding, the phase trajectories of electroencephalogram (EEG) is described. It is illustrated based on the present work,that is,the wavelet decomposition of EEG is essentially a projection of EEG chaotic attractor onto the wavelet space opened by wavelet filter vectors, which is in correspondence with the phase space embedding of the same EEG. In other words, wavelet decomposition and phase space embedding are equivalent in methodology. Our experimental results show that in both the wavelet space and the embedded space the structure of phase trajectory of EEG is similar to each other. These results demonstrate that wavelet decomposition is effective on characterizing EEG time series.
Generalised partition functions: inferences on phase space distributions
Treumann, Rudolf A.; Baumjohann, Wolfgang
2016-06-01
It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q - 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.
Deformed phase space Kaluza–Klein cosmology and late time acceleration
Energy Technology Data Exchange (ETDEWEB)
Sabido, M., E-mail: msabido@fisica.ugto.mx [Departamento de Física de la Universidad de Guanajuato, A.P. E-143, C.P. 37150, León, Guanajuato (Mexico); Yee-Romero, C., E-mail: carlos.yee@uabc.edu.mx [Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Baja California, Ensenada, Baja California (Mexico)
2016-06-10
The effects of phase space deformations on Kaluza–Klein cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables. In the deformed model, we find an accelerating scale factor and therefore infer the existence of an effective cosmological constant from the phase space deformation parameter β.
Deformed phase space for 3d loop gravity and hyperbolic discrete geometries
Bonzom, Valentin; Girelli, Florian; Livine, Etera R
2014-01-01
We revisit the loop gravity space phase for 3D Riemannian gravity by algebraically constructing the phase space $T^*\\mathrm{SU}(2)\\sim\\mathrm{ISO}(3)$ as the Heisenberg double of the Lie group $\\mathrm{SO}(3)$ provided with the trivial cocyle. Tackling the issue of accounting for a non-vanishing cosmological constraint $\\Lambda \
Deformed phase space Kaluza-Klein cosmology and late time acceleration
Sabido, M.; Yee-Romero, C.
2016-06-01
The effects of phase space deformations on Kaluza-Klein cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables. In the deformed model, we find an accelerating scale factor and therefore infer the existence of an effective cosmological constant from the phase space deformation parameter β.
Variational principle and phase space measure in non-canonical coordinates
Directory of Open Access Journals (Sweden)
Sergi, A
2005-11-01
Full Text Available Non-canonical equations of motion are derived from a variational principle written in symplectic form. The invariant measure of phase space and the covariant expression for the entropy are derived from non-canonical transformations of coordinates. This shows that the geometry of non-canonical phase space is non trivial even if dynamics has no compressibility.
Discrete phase space - II: The second quantization of free relativistic wave fields
Das, A
2008-01-01
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential equations in the arena of discrete phase space and continuous time. The scalar field and electromagnetic fields are quantized with commutation relations. The spin-1/2 field is quantized with anti-commutation relations. Moreover, the total momentum, energy and charge of these free relativisitic quantized fields in the discrete phase space and continuous time are computed exactly. The results agree completely with those computed from the relativisitic fields defned on the space-time continuum.
Bazarov, Ivan V; Gulliford, Colwyn; Li, Yulin; Liu, Xianghong; Sinclair, Charles K; Soong, Ken; Hannon, Fay
2008-01-01
We present a comparison between space charge calculations and direct measurements of the transverse phase space for space charge dominated electron bunches after a high voltage photoemission DC gun followed by an emittance compensation solenoid magnet. The measurements were performed using a double-slit setup for a set of parameters such as charge per bunch and the solenoid current. The data is compared with detailed simulations using 3D space charge codes GPT and Parmela3D with initial particle distributions created from the measured transverse and temporal laser profiles. Beam brightness as a function of beam fraction is calculated for the measured phase space maps and found to approach the theoretical maximum set by the thermal energy and accelerating field at the photocathode.
Directory of Open Access Journals (Sweden)
Ivan V. Bazarov
2008-10-01
Full Text Available We present a comparison between space charge calculations and direct measurements of the transverse phase space of space charge dominated electron bunches from a high voltage dc photoemission gun followed by an emittance compensation solenoid magnet. The measurements were performed using a double-slit emittance measurement system over a range of bunch charge and solenoid current values. The data are compared with detailed simulations using the 3D space charge codes GPT and Parmela3D. The initial particle distributions were generated from measured transverse and temporal laser beam profiles at the photocathode. The beam brightness as a function of beam fraction is calculated for the measured phase space maps and found to approach within a factor of 2 the theoretical maximum set by the thermal energy and the accelerating field at the photocathode.
Operator space structures and the split property, 2
Fidaleo, F
1997-01-01
in \\cite{B1,B2} and studied in \\cite{F}. The split property for a Quantum Field Theory is characterized by equivalent conditions relative to the non-commutative embeddings $\\F_i$, $i=1,2$, constructed by the modular Hamiltonian of a privileged faithful state such as e.g. the vacuum state. The above characterization would be also useful for theories on a curved space-time where there exists no a-priori privileged state.
New space vector modulation technique for single-phase multilevel converters
León Galván, José Ignacio; Portillo Guisado, Ramón Carlos; García Franquelo, Leopoldo; Vázquez Pérez, Sergio; Carrasco Solís, Juan Manuel; Domínguez, E
2007-01-01
Single-phase multilevel converters are suitable for medium power applications as photovoltaic systems and switched reluctance machines. An overview of possible modulation methods including carrier-based pulse width modulation and space vector modulation techniques for multilevel single-phase converters is presented. A new space vector modulation for this type of converters is proposed. This space vector modulation method is very simple presenting low computational cost. Different solutions fo...
Semi-classical mechanics in phase space: the quantum target of minimal strings
Energy Technology Data Exchange (ETDEWEB)
Gomez, Cesar [Instituto de Fisica Teorica CSIC/UAM, C-XVI Universidad Autonoma, E-28049 Madrid (Spain); Montanez, Sergio [Instituto de Fisica Teorica CSIC/UAM, C-XVI Universidad Autonoma, E-28049 Madrid (Spain); Resco, Pedro [Instituto de Fisica Teorica CSIC/UAM, C-XVI Universidad Autonoma, E-28049 Madrid (Spain)
2005-11-15
The target space M{sub p,q} of (p,q) minimal strings is embedded into the phase space of an associated integrable classical mechanical model. This map is derived from the matrix model representation of minimal strings. Quantum effects on the target space are obtained from the semiclassical mechanics in phase space as described by the Wigner function. In the classical limit the target space is a fold catastrophe of the Wigner function that is smoothed out by quantum effects. Double scaling limit is obtained by resolving the singularity of the Wigner function. The quantization rules for backgrounds with ZZ branes are also derived.
Semi-Classical Mechanics in Phase Space: The Quantum Target of Minimal Strings
Gómez, C; Resco, P; Gomez, Cesar; Montanez, Sergio; Resco, Pedro
2005-01-01
The target space $M_{p,q}$ of $(p,q)$ minimal strings is embedded into the phase space of an associated integrable classical mechanical model. This map is derived from the matrix model representation of minimal strings. Quantum effects on the target space are obtained from the semiclassical mechanics in phase space as described by the Wigner function. In the classical limit the target space is a fold catastrophe of the Wigner function that is smoothed out by quantum effects. Double scaling limit is obtained by resolving the singularity of the Wigner function. The quantization rules for backgrounds with ZZ branes are also derived.
Space station gas compressor technology study program, phase 1
Hafele, B. W.; Rapozo, R. R.
1989-01-01
The objectives were to identify the space station waste gases and their characteristics, and to investigate compressor and dryer types, as well as transport and storage requirements with tradeoffs leading to a preliminary system definition.
Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation
Zenczykowski, Piotr
2009-01-01
According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space ...
Space-Time Uncertainty and Approaches to D-Brane Field Theory
Yoneya, Tamiaki
2007-01-01
In connection with the space-time uncertainty principle which gives a simple qualitative characterization of non-local or non-commutative nature of short-distance space-time structure in string theory, author's recent approaches toward field theories for D-branes are briefly outlined, putting emphasis on some key ideas lying in the background. The final section of the present report is devoted partially to a tribute to Yukawa on the occasion of the centennial of his birth.
Energy content of stormtime ring current from phase space mapping simulations
Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.
1993-01-01
We perform a phase space mapping study to estimate the enhancement in energy content that results from stormtime particle transport in the equatorial magnetosphere. Our pre-storm phase space distribution is based on a steady-state transport model. Using results from guiding-center simulations of ion transport during model storms having main phases of 3 hr, 6 hr, and 12 hr, we map phase space distributions of ring current protons from the pre-storm distribution in accordance with Liouville's theorem. We find that transport can account for the entire ten to twenty-fold increase in magnetospheric particle energy content typical of a major storm if a realistic stormtime enhancement of the phase space density f is imposed at the nightside tail plasma sheet (represented by an enhancement of f at the neutral line in our model).
Multimegawatt space nuclear power supply: Phase 1, Final report
Energy Technology Data Exchange (ETDEWEB)
1989-02-17
The Phase 2 program objectives are to (1) demonstrate concept feasibility, (2) develop a preliminary design, and (3) complete Phase 3 engineering development and ground test plans. The approach to accomplish these objectives is to prove technical feasibility of our baseline design early in the program while maintaining flexibility to easily respond to changing requirements and advances in technology. This approach recognizes that technology is advancing rapidly while the operational phase MSNPS is 15 to 20 years in the future. This plan further recognizes that the weapons platform and Advanced Launch System (ALS) are in very early program definition stages; consequently, their requirements, interfaces, and technological basis will evolve. This document outlines the Phase 2 plan along with task scheduling of the various program aspects.
Efficient molecular quantum dynamics in coordinate and phase space using pruned bases
Larsson, Henrik R; Tannor, David J
2016-01-01
We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized Gaussians (Weylets) to create a new basis, projected Weylets, that takes the best from both methods. We benchmark pruned dynamics using phase-space-localized PvB, projected Weylets, and coordinate-space-localized DVR bases, with real-world examples in up to six dimensions. We show that coordinate-space localization is most important for efficient pruning and that pruned dynamics is much faster compared to unpruned, exact dynamics. Phase-space localization is useful for more demanding dynamics where many basis functions are required. There, projected Weylets offer a more compact representation than pruned DVR bases.
Efficient molecular quantum dynamics in coordinate and phase space using pruned bases
Larsson, H. R.; Hartke, B.; Tannor, D. J.
2016-11-01
We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized Gaussians (Weylets) to create a new basis, projected Weylets, that takes the best from both methods. We benchmark pruned time-dependent dynamics using phase-space-localized PvB, projected Weylets, and coordinate-space-localized DVR bases, with real-world examples in up to six dimensions. For the examples studied, coordinate-space localization is the most important factor for efficient pruning and the pruned dynamics is much faster than the unpruned, exact dynamics. Phase-space localization is useful for more demanding dynamics where many basis functions are required. There, projected Weylets offer a more compact representation than pruned DVR bases.
On the energy-momentum tensor in Moyal space
Energy Technology Data Exchange (ETDEWEB)
Balasin, Herbert; Schweda, Manfred [Vienna University of Technology, Institute for Theoretical Physics, Vienna (Austria); Blaschke, Daniel N. [Los Alamos National Laboratory, Theory Division, Los Alamos, NM (United States); Gieres, Francois [Universite de Lyon, Universite Claude Bernard Lyon 1 et CNRS/IN2P3, Institut de Physique Nucleaire de Lyon, Villeurbanne (France)
2015-06-15
We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line. (orig.)
Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space
DEFF Research Database (Denmark)
Heim, D.M.; Schleich, W.P.; Alsing, P.M.
2013-01-01
We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function...... of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function....
κ-Poincaré–Hopf algebra and Hopf algebroid structure of phase space from twist
Energy Technology Data Exchange (ETDEWEB)
Jurić, Tajron, E-mail: Tajron.Juric@irb.hr [Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb (Croatia); Meljanac, Stjepan, E-mail: meljanac@irb.hr [Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb (Croatia); Štrajn, Rina, E-mail: r.strajn@jacobs-university.de [Jacobs University Bremen, 28759 Bremen (Germany)
2013-11-15
We unify κ-Poincaré algebra and κ-Minkowski spacetime by embedding them into quantum phase space. The quantum phase space has Hopf algebroid structure to which we apply the twist in order to get κ-deformed Hopf algebroid structure and κ-deformed Heisenberg algebra. We explicitly construct κ-Poincaré–Hopf algebra and κ-Minkowski spacetime from twist. It is outlined how this construction can be extended to κ-deformed super-algebra including exterior derivative and forms. Our results are relevant for constructing physical theories on noncommutative spacetime by twisting Hopf algebroid phase space structure.
Space station contamination control study: Internal combustion, phase 1
Ruggeri, Robert T.
1987-01-01
Contamination inside Space Station modules was studied to determine the best methods of controlling contamination. The work was conducted in five tasks that identified existing contamination control requirements, analyzed contamination levels, developed outgassing specification for materials, wrote a contamination control plan, and evaluated current materials of offgassing tests used by NASA. It is concluded that current contamination control methods can be made to function on the Space Station for up to 1000 days, but that current methods are deficient for periods longer than about 1000 days.
Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation
Directory of Open Access Journals (Sweden)
Tai-fu Li
2013-01-01
Full Text Available The chaotic time series can be expanded to the multidimensional space by phase space reconstruction, in order to reconstruct the dynamic characteristics of the original system. It is difficult to obtain complete phase space for chaotic time series, as a result of the inconsistency of phase space reconstruction. This paper presents an idea of subspace approximation. The chaotic time series prediction based on the phase space reconstruction can be considered as the subspace approximation problem in different neighborhood at different time. The common static neural network approximation is suitable for a trained neighborhood, but it cannot ensure its generalization performance in other untrained neighborhood. The subspace approximation of neural network based on the nonlinear extended Kalman filtering (EKF is a dynamic evolution approximation from one neighborhood to another. Therefore, in view of incomplete phase space, due to the chaos phase space reconstruction, we put forward subspace adaptive evolution approximation method based on nonlinear Kalman filtering. This method is verified by multiple sets of wind speed prediction experiments in Wulong city, and the results demonstrate that it possesses higher chaotic prediction accuracy.
A novel PWM scheme to eliminate the diode freewheeling In the Inactive phase in BLDC motor
Institute of Scientific and Technical Information of China (English)
WEI Kun; HU Chang-sheng; ZHANG Zhong-chao
2006-01-01
The brushless DC motor (BLDCM) with trapezoidal electromotive force (back-EMF) waveform is used widely.In principle,when the motor runs in the 120°conduction mode,two of the three phases are active while the other phase is inactive at all times.However,a ripple current occurs in the inactive phase due to the diode freewheeling during the non-commutation period in the traditional pulse width modulation (PWM) methods,which aggravates the torque ripples.A new PWM method is proposed in this paper to eliminate the diode freewheeling during the non-commutation period in the inactive phase.As a result,the torque ripple is suppressed using the proposed method.The simulation and experimental results are demonstrated to verify the validity of the proposed PWM method.
An Asymmetrical Space Vector Method for Single Phase Induction Motor
DEFF Research Database (Denmark)
Cui, Yuanhai; Blaabjerg, Frede; Andersen, Gert Karmisholt
2002-01-01
Single phase induction motors are the workhorses in low-power applications in the world, and also the variable speed is necessary. Normally it is achieved either by the mechanical method or by controlling the capacitor connected with the auxiliary winding. Any above method has some drawback which...
Non-Commutative Geometry from Strings
Chu, Chong-Sun
2005-01-01
Comment: 26 pages, no figures. To appear in the Elsevier Encyclopedia of Mathematical Physics. This web version has a more comprehensive list of references. Comments and corrections welcome. v2: Typos corrected, references and some comments added. v3: 27 pages. more references and Comments added. v4: references added. Final version
Wormhole inspired by non-commutative geometry
Energy Technology Data Exchange (ETDEWEB)
Rahaman, Farook, E-mail: rahaman@iucaa.ernet.in [Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal (India); Karmakar, Sreya, E-mail: sreya.karmakar@gmail.com [Department of Physics, Calcutta Institute of Engineering and Management, Kolkata 700040, West Bengal (India); Karar, Indrani, E-mail: indrani.karar08@gmail.com [Department of Mathematics, Saroj Mohan Institute of Technology, Guptipara, West Bengal (India); Ray, Saibal, E-mail: saibal@iucaa.ernet.in [Department of Physics, Government College of Engineering & Ceramic Technology, Kolkata 700010, West Bengal (India)
2015-06-30
In the present Letter we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV). A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this letter is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist in this Lorentzian distribution with viable physical properties.
Wormhole inspired by non-commutative geometry
Directory of Open Access Journals (Sweden)
Farook Rahaman
2015-06-01
Full Text Available In the present Letter we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV. A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this letter is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist in this Lorentzian distribution with viable physical properties.
Phase space investigation of the lithium amide halides
Energy Technology Data Exchange (ETDEWEB)
Davies, Rosalind A. [Hydrogen Storage Chemistry Group, School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom); Hydrogen and Fuel Cell Group, School of Chemical Engineering, University of Birmingham, Edgbaston B15 2TT (United Kingdom); Hewett, David R.; Korkiakoski, Emma [Hydrogen Storage Chemistry Group, School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom); Thompson, Stephen P. [Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0QX (United Kingdom); Anderson, Paul A., E-mail: p.a.anderson@bham.ac.uk [Hydrogen Storage Chemistry Group, School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom)
2015-10-05
Highlights: • The lower limits of halide incorporation in lithium amide have been investigated. • The only amide iodide stoichiometry observed was Li{sub 3}(NH{sub 2}){sub 2}I. • Solid solutions were observed in both the amide chloride and amide bromide systems. • A 46% reduction in chloride content resulted in a new phase: Li{sub 7}(NH{sub 2}){sub 6}Cl. • New low-chloride phase maintained improved H{sub 2} desorption properties of Li{sub 4}(NH{sub 2}){sub 3}Cl. - Abstract: An investigation has been carried out into the lower limits of halide incorporation in lithium amide (LiNH{sub 2}). It was found that the lithium amide iodide Li{sub 3}(NH{sub 2}){sub 2}I was unable to accommodate any variation in stoichiometry. In contrast, some variation in stoichiometry was accommodated in Li{sub 7}(NH{sub 2}){sub 6}Br, as shown by a decrease in unit cell volume when the bromide content was reduced. The amide chloride Li{sub 4}(NH{sub 2}){sub 3}Cl was found to adopt either a rhombohedral or a cubic structure depending on the reaction conditions. Reduction in chloride content generally resulted in a mixture of phases, but a new rhombohedral phase with the stoichiometry Li{sub 7}(NH{sub 2}){sub 6}Cl was observed. In comparison to LiNH{sub 2}, this new low-chloride phase exhibited similar improved hydrogen desorption properties as Li{sub 4}(NH{sub 2}){sub 3}Cl but with a much reduced weight penalty through addition of chloride. Attempts to dope lithium amide with fluoride ions have so far proved unsuccessful.
Phase-space dynamics of runaway electrons in magnetic fields
Guo, Zehua; McDevitt, Christopher J.; Tang, Xian-Zhu
2017-04-01
Dynamics of runaway electrons in magnetic fields are governed by the competition of three dominant physics: parallel electric field acceleration, Coulomb collision, and synchrotron radiation. Examination of the energy and pitch-angle flows reveals that the presence of local vortex structure and global circulation is crucial to the saturation of primary runaway electrons. Models for the vortex structure, which has an O-point to X-point connection, and the bump of runaway electron distribution in energy space have been developed and compared against the simulation data. Identification of these velocity-space structures opens a new venue to re-examine the conventional understanding of runaway electron dynamics in magnetic fields.
Phase Space of Rolling Solutions of the Tippe Top
Directory of Open Access Journals (Sweden)
S. Torkel Glad
2007-03-01
Full Text Available Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and quadratic in momenta. In the Euler angle variables (θ,φ,ψ these integrals give separation equations that have the same structure as the equations of the Lagrange top. It makes it possible to describe the whole space of solutions by representing them in the space of parameters (D,λ,E being constant values of the integrals of motion.
Longitudinal phase space of multiparticle final states in high energy hadron-hadron collisions
Institute of Scientific and Technical Information of China (English)
吴元芳; 刘连寿
1995-01-01
The highly anisotropic phase space (known as longitudinal phase space) of multipartide final states in high energy hh collisions is studied in detail. It is pointed out that the anisotropy of phase space should manifest itself not only in the dramatic difference in magnitude between the average transverse and longitudinal momenta, but also in the anisotropy of dynamical fluctuations in the two directions. It means that the particle distribution in phase space has the property of selfaffine fractal. A method for experimentally testing the selfaffine fractality and measuring its cbaracteristic parameterHurst exponent is given. In addition, the correlation between the degree of longitudinal fractality and the magnitude of average transverse momentum is discussed. A new characteristic quantity--average transverse momentum per event--for de scribing the dynamical property of an event (hard, soft or ultrasoft) is proposed. A comparison of the results with experimental data is given.
Phase-space diffusion in turbulent plasmas: The random acceleration problem revisited
DEFF Research Database (Denmark)
Pécseli, H.L.; Trulsen, J.
1991-01-01
Phase-space diffusion of test particles in turbulent plasmas is studied by an approach based on a conditional statistical analysis of fluctuating electrostatic fields. Analytical relations between relevant conditional averages and higher-order correlations, , and triple...
Directory of Open Access Journals (Sweden)
Fang Liu
2016-01-01
Full Text Available Feature extraction from vibration signal is still a challenge in the area of fault diagnosis and remaining useful life (RUL estimation of rotary machine. In this paper, a novel feature called phase space similarity (PSS is introduced for health condition monitoring of bearings. Firstly, the acquired signal is transformed to the phase space through the phase space reconstruction (PSR. The similar vibration always exists in the phase space due to the comparable evolution of the dynamics that are characteristic of the system state. Secondly, the normalized cross-correlation (NCC is employed to calculate the PSS between bearing data with different states. Based on the PSS, a fault pattern recognition algorithm, a bearing fault size prediction algorithm, and a RUL estimation algorithm are introduced to analyze the experimental signal. Results have shown the effectiveness of the PSS as it can better grasp the nature and regularity of the signals.
Selection of Phase Space Reconstruction Parameters for EMG Signals of the Uterus
Directory of Open Access Journals (Sweden)
Brzozowska Ewelina
2016-12-01
Full Text Available Biological time series have a finite number of samples with noise included in them. Because of this fact, it is not possible to reconstruct phase space in an ideal manner. One kind of biomedical signals are electrohisterographical (EHG datasets, which represent uterine muscle contractile activity. In the process of phase space reconstruction, the most important thing is suitable choice of the method for calculating the time delay τ and embedding dimension d, which will reliably reconstruct the original signal. The parameters used in digital signal processing are key to arranging adequate parameters of the analysed attractor embedded in the phase space. The aim of this paper is to present a method employed for phase space reconstruction for EHG signals that will make it possible for their further analysis to be carried out.
Kull, A.; R. A. Treumann; Böhringer, Hans
1997-01-01
The statistical mechanical investigation of Violent Relaxation of phase space elements of different densities first derived by Lynden-Bell (1967) is re-examined. It is found that the mass independence of the equations of motion of Violent Relaxation calls for a constraint on the volume of the phase space elements used to formulate the statistical mechanical description of Violent Relaxation. In agreement with observations of astrophysical objects believed to have been subject to Violent Relax...
Phase-Space Explorations in Time-Dependent Density Functional Theory
Rajam, Arun K.; Hessler, Paul; Gaun, Christian; Maitra, Neepa T.
2009-01-01
We discuss two problems which are particularly challenging for approximations in time-dependent density functional theory (TDDFT) to capture: momentum-distributions in ionization processes, and memory-dependence in real-time dynamics. We propose an extension of TDDFT to phase-space densities, discuss some formal aspects of such a "phase-space density functional theory" and explain why it could ameliorate the problems in both cases. For each problem, a two-electron model system is exactly nume...
Subpicosecond electron bunch train production using a phase-space exchange technique
Energy Technology Data Exchange (ETDEWEB)
Sun, Y.-E.; /Fermilab; Piot, P.; /Fermilab /Northern Illinois U.; Johnson, A.S.; Lumpkin, A.H.; /Fermilab; Maxwell, T.J.; /Fermilab /Northern Illinois U.; Ruan, J.; Thurman-Keup, R.M.; /Fermilab
2011-03-01
Our recent experimental demonstration of a photoinjector electron bunch train with sub-picosecond structures is reported in this paper. The experiment is accomplished by converting an initially horizontal beam intensity modulation into a longitudinal phase space modulation, via a beamline capable of exchanging phase-space coordinates between the horizontal and longitudinal degrees of freedom. The initial transverse modulation is produced by intercepting the beam with a multislit mask prior to the exchange. We also compare our experimental results with numerical simulations.