Quantitative wave-particle duality
Qureshi, Tabish
2016-07-01
The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is here described not just as two extreme cases of wave and particle characteristics, but in terms of quantitative measures of these characteristics, known to follow a duality relation. A very simple and intuitive derivation of a closely related duality relation is presented, which should be understandable to the introductory student.
On the analogy of quantum wave-particle duality with bouncing droplets
Richardson, Chris D; Martin, John; Vandewalle, Nicolas; Bastin, Thierry
2014-01-01
We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm interpretation of quantum mechanics. Through numerical means we obtain single-slit diffraction and double-slit interference patterns that strongly resemble those reported in experiment and that reflect a striking resemblance to quantum diffraction and interference on a phenomenological level. We, however, identify evident differences from quantum mechanics which arise from the governing equations at the fundamental level.
Cheong, Yong Wook; Song, Jinwoong
2014-01-01
There is no consensus on the genuine meaning of wave-particle duality and the interpretation of quantum theory. How can we teach duality and quantum theory despite this lack of consensus? This study attempts to answer this question. This research argues that reality issues are at the core of both the endless debates concerning the interpretation…
Cheong, Yong Wook; Song, Jinwoong
2014-01-01
There is no consensus on the genuine meaning of wave-particle duality and the interpretation of quantum theory. How can we teach duality and quantum theory despite this lack of consensus? This study attempts to answer this question. This research argues that reality issues are at the core of both the endless debates concerning the interpretation…
Putz, Mihai V.
2010-01-01
Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR) is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor 1-n2, in terms of magnitude n∈[0,1]. of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function. PMID:21152325
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2010-10-01
Full Text Available Within the path integral Feynman formulation of quantum mechanics, the fundamental Heisenberg Uncertainty Relationship (HUR is analyzed in terms of the quantum fluctuation influence on coordinate and momentum estimations. While introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic HUR is recovered in a close analytical manner for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor √1-n2, in terms of magnitude n ε [0,1] of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence. The practical implications of the present particle-to-wave ratio as well as of the free-evolution quantum picture are discussed for experimental implementation, broken symmetry and the electronic localization function.
Wave-Particle Duality in Classical Mechanics
Davydov, Alexander Y
2012-01-01
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after surprising discovery of "walkers" - droplets that bounce on a vertically vibrating bath of the same fluid and can form wave-particle symbiotic structures with the surface waves they generate. Macroscopic walkers were shown experimentally to exhibit particle and wave properties simultaneously. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to walkers, no constant inflow of energy is required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show that such quantum phenomena as p...
Tunneling time distribution by means of Nelson’s quantum mechanics and wave-particle duality
Indian Academy of Sciences (India)
Koh'Ichiro Hara; Ichiro Ohba
2002-08-01
We construct a tunneling time distribution by means of Nelson’s quantum mechanics and investigate statistical properties of the tunneling time distribution. As a result, we ﬁnd that the relationship between the average and the variance of the tunneling time shows ‘wave-particle duality’.
Wave-particle duality in classical mechanics
Davydov, Alexander Y.
2012-05-01
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in a strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propel via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, an observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may emerge as approximation from a more profound theory on a deeper level.
Directory of Open Access Journals (Sweden)
Malek A.
2014-10-01
Full Text Available A hypothesis based on the exchange and the inter-conversion of the “real” and the equiv- alent “virtual” particles of the quantum vacuum can resolve the contradiction of wave- particle duality, the “spookiness” and the other conflicting properties of the quantum particles. It can be shown using simple mathematics that the extent of the wave or the particle nature of a quantum particle depends on the rate of t his “real / virtual” particle exchange, the velocity and the rest mass of the exchanging “real” particle.
Rauch, Helmut
2015-01-01
The quantum interference of de Broglie matter waves is probably one of the most startling and fundamental aspects of quantum mechanics. It continues to tax our imaginations and leads us to new experimental windows on nature. Quantum interference phenomena are vividly displayed in the wide assembly of neutron interferometry experiments, which have been carried out since the first demonstration of a perfect silicon crystal interferometer in 1974. Since the neutron experiences all four fundamental forces of nature (strong, weak, electromagnetic, and gravitational), interferometry with neutrons provides a fertile testing ground for theory and precision measurements. Many Gedanken experiments of quantum mechanics have become real due to neutron interferometry. Quantum mechanics is a part of physics where experiment and theory are inseparably intertwined. This general theme permeates the second edition of this book. It discusses more than 40 neutron interferometry experiments along with their theoretical motivation...
Ayene, Mengesha; Kriek, Jeanne; Damtie, Baylie
2011-01-01
Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students' depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an…
Deciphering the Enigma of Wave-Particle Duality
Bhaumik, Mani
2016-01-01
A satisfactory explanation of the confounding wave-particle duality of matter is presented in terms of the reality of the wave nature of a particle. In this view a quantum particle is an objectively real wave packet consisting of irregular disturbances of underlying quantum fields. It travels holistically as a unit and thereby acts as a particle. Only the totality of the entire wave packet at any instance embodies all the conserved quantities, for example the energy-momentum, rest mass, and charge of the particle, and as such must be acquired all at once during detection. On this basis, many of the bizarre behaviors observed in the quantum domain, such as wave function collapse, the limitation of prediction to only a probability rather than an actuality, the apparent simultaneous existence of a particle in more than one place, and the inherent uncertainty can be reasonably comprehended. The necessity of acquiring the wave function in its entirety for detection, as evinced by the appearance of collapse of the ...
Wave-particle duality in a Raman atom interferometer
Jia, Ai-Ai; Yang, Jun; Yan, Shu-Hua; Hu, Qing-Qing; Luo, Yu-Kun; Zhu, Shi-Yao
2015-08-01
We theoretically investigate the wave-particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach-Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the φ - π - π/2 type of atom interferometer, we find that the visibility (V) and predictability (P) still satisfy the duality relation, P2 + V2 ≤ 1. Project supported by the National Natural Science Foundation of China (Grant No. 51275523) and the Special Research Found for the Doctoral Program of Higher Education, China (Grant No. 20134307110009).
The wave-particle duality in the Weyl-Dirac theory
Agop, M.; Nica, P.
2000-09-01
The solution of a static two-dimensional wave equation in the Gauss-Mainardi-Codazzi formalism of Weyl-Dirac theory is obtained in terms of the elliptic function with a complex argument. In particular, by double degenerating the elliptic function, wave-particle duality results. Associating a superconducting behaviour to matter, by means of the duality, we find some superconducting parameters: Bc2, the average carrier density, the gap energy and the pair-breaking time. The discontinuities of these parameters for sequences (1/3), (1/5), (1/7),... imply that the quantum spacetime is Cantorian.
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this article,we make a review on the development of a newly proposed quantum computer,duality computer,or the duality quantum computer and the duality mode of quantum computers.The duality computer is based on the particle-wave duality principle of quantum mechanics.Compared to an ordinary quantum computer,the duality quantum computer is a quantum computer on the move and passing through a multi-slit.It offers more computing operations than is possible with an ordinary quantum computer.The most two distinct operations are:the quantum division operation and the quantum combiner operation.The division operation divides the wave function of a quantum computer into many attenuated,and identical parts.The combiner operation combines the wave functions in different parts into a single part.The duality mode is a way in which a quantum computer with some extra qubit resource simulates a duality computer.The main structure of duality quantum computer and duality mode,the duality mode,their mathematical description and algorithm designs are reviewed.
Wave-Particle Duality in the Elastodynamics of the Spacetime Continuum (STCED
Directory of Open Access Journals (Sweden)
Millette P. A.
2014-10-01
Full Text Available We examine the nature of the wave-particle duality in the Elastodynamics of the Space- time Continuum (STCED, due to the propagation of deformations in the STC by lon- gitudinal dilatation and transverse distortion wave displacements. We first consider the special case of Electromagnetism which consists of transverse waves only, and use the photon wavefunction to demonstrate that | Ψ | 2 represents a physical energy density, not a probability density. However, normalization by the system energy allows use of the probabilistic formulation of quantum theory. In the STCED l ongitudinal and transverse wave equations, the transverse wave is the source of the interference pattern in double slit experiments, influencing the location of the longitudinal wave, as observed experi- mentally. We note the similarity of STCEDwave-particle duality and Louis de Broglie’s “double solution”.
Ayene, Mengesha; Kriek, Jeanne; Damtie, Baylie
2011-12-01
Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students’ depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an understanding of quantum mechanics. A phenomenographic study was carried out to categorize a picture of students’ descriptions of these key quantum concepts. Data for this study were obtained from a semistructured in-depth interview conducted with undergraduate physics students (N=25) from Bahir Dar, Ethiopia. The phenomenographic data analysis revealed that it is possible to construct three qualitatively different categories to map students’ depictions of the concept wave-particle duality, namely, (1) classical description, (2) mixed classical-quantum description, and (3) quasiquantum description. Similarly, it is proposed that students’ depictions of the concept uncertainty can be described with four different categories of description, which are (1) uncertainty as an extrinsic property of measurement, (2) uncertainty principle as measurement error or uncertainty, (3) uncertainty as measurement disturbance, and (4) uncertainty as a quantum mechanics uncertainty principle. Overall, we found students are more likely to prefer a classical picture of interpretations of quantum mechanics. However, few students in the quasiquantum category applied typical wave phenomena such as interference and diffraction that cannot be explained within the framework classical physics for depicting the wavelike properties of quantum entities. Despite inhospitable conceptions of the uncertainty principle and wave- and particlelike properties of quantum entities in our investigation, the findings presented in this paper are highly consistent with those reported in previous studies. New findings and some implications for instruction and the
Directory of Open Access Journals (Sweden)
Mengesha Ayene1
2011-11-01
Full Text Available Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students’ depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an understanding of quantum mechanics. A phenomenographic study was carried out to categorize a picture of students’ descriptions of these key quantum concepts. Data for this study were obtained from a semistructured in-depth interview conducted with undergraduate physics students (N=25 from Bahir Dar, Ethiopia. The phenomenographic data analysis revealed that it is possible to construct three qualitatively different categories to map students’ depictions of the concept wave-particle duality, namely, (1 classical description, (2 mixed classical-quantum description, and (3 quasiquantum description. Similarly, it is proposed that students’ depictions of the concept uncertainty can be described with four different categories of description, which are (1 uncertainty as an extrinsic property of measurement, (2 uncertainty principle as measurement error or uncertainty, (3 uncertainty as measurement disturbance, and (4 uncertainty as a quantum mechanics uncertainty principle. Overall, we found students are more likely to prefer a classical picture of interpretations of quantum mechanics. However, few students in the quasiquantum category applied typical wave phenomena such as interference and diffraction that cannot be explained within the framework classical physics for depicting the wavelike properties of quantum entities. Despite inhospitable conceptions of the uncertainty principle and wave- and particlelike properties of quantum entities in our investigation, the findings presented in this paper are highly consistent with those reported in previous studies. New findings and some implications for instruction
The GRA Beam-Splitter Experiment and Wave-Particle Duality of Light
Kaloyerou, P N
2005-01-01
Grangier, Roger and Aspect (GRA) performed a beam-splitter experiment to demonstrate particle behaviour of light and a Mach-Zehnder interferometer experiment to demonstrate wave behaviour of light. The distinguishing feature of these experiments is the use of a gating system to produce near ideal single photon states. With the demonstration of both wave and particle behaviour (in the two mutually exclusive experiments) they claim to have demonstrated the dual wave-particle behaviour of light, and hence, to have confirmed Bohr's Principle of complementarity. The demonstration of the wave behaviour of light is not in dispute. But, we want to demonstrate, contrary to the claims of GRA, that their beam-splitter experiment does not conclusively confirm the particle behaviour of light, and hence does not confirm particle-wave duality, nor, more generally, is complementarity confirmed. Our demonstration consists of providing a detailed model based on the Causal Interpretation of Quantum Fields (CIEM), which does not...
Duality Computing in Quantum Computers
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; LIU Yang
2008-01-01
In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.
Theoretical photon origin, a didactic introduction to the wave particle duality
L., Paco H Talero
2016-01-01
In modern physics courses the idea of photon has been teaching through from the einsteinian formulation based on the photoelectric effect. Einstein's photon concept allow the quantization of the electromagnetic field, but does not dwell on the idea of photon as particle. The objective of this paper was to demonstrate that the photon has its origin essentially in the special relativity, the electromagnetic theory and in the symmetry between the Lorentz's transformations associated flat monochromatic electromagnetic waves and particles with zero rest mass. This approach allows to understand the wave-particle duality of photon and allows to propose an alternative teaching focused on this duality to develop the course of modern physics.
Wave-particle duality of C(60) molecules.
Arndt, M; Nairz, O; Vos-Andreae, J; Keller, C; van der Zouw, G; Zeilinger, A
1999-10-14
Quantum superposition lies at the heart of quantum mechanics and gives rise to many of its paradoxes. Superposition of de Broglie matter waves' has been observed for massive particles such as electrons, atoms and dimers, small van der Waals clusters, and neutrons. But matter wave interferometry with larger objects has remained experimentally challenging, despite the development of powerful atom interferometric techniques for experiments in fundamental quantum mechanics, metrology and lithography. Here we report the observation of de Broglie wave interference of C(60) molecules by diffraction at a material absorption grating. This molecule is the most massive and complex object in which wave behaviour has been observed. Of particular interest is the fact that C(60) is almost a classical body, because of its many excited internal degrees of freedom and their possible couplings to the environment. Such couplings are essential for the appearance of decoherence, suggesting that interference experiments with large molecules should facilitate detailed studies of this process.
Wave-Particle Duality and the Hamilton-Jacobi Equation
Sivashinsky, Gregory I
2009-01-01
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behavior. The de Broglie wave thus acquires a clear deterministic meaning of a wave-like excitation of the classical action function. The problem of quantization in terms of the breathing action function and the double-slit experiment are discussed.
Physics of the Blues: Music, Fourier and Wave - Particle Duality
Energy Technology Data Exchange (ETDEWEB)
Gibson, J. Murray (ANL)
2003-10-15
Art and science are intimately connected. There is probably no art that reveals this more than music. Music can be used as a tool to teach physics and engineering to non-scientists, illustrating such diverse concepts as Fourier analysis and quantum mechanics. This colloquium is aimed in reverse, to explain some interesting aspects of music to physicists. Topics include: What determines the frequency of notes on a musical scale? What is harmony and why would Fourier care? Where did the blues come from? (We' re talking the 'physics of the blues', and not 'the blues of physics' - that's another colloquium). Is there a musical particle? The presentation will be accompanied by live keyboard demonstrations. The presenter will attempt to draw tenuous connections between the subject of his talk and his day job as Director of the Advanced Photon Source at Argonne National Laboratory.
Wave-particle duality: suggestion for an experiment
Sen, R N
2012-01-01
Feynman contended that the double-slit experiment contained the `only mystery' in quantum mechanics. The mystery was that electrons traverse the interferometer as waves, but are detected as particles. This note was motivated by the question whether single electrons can be detected as waves. It suggests a double-slit interferometry experiment with atoms of noble gases in which it may be possible to detect an individual atom as a probability wave, using a detector which can execute two different types of simple harmonic motion: as a simple pendulum, and as a torsion pendulum. In the experiment, a torsional oscillation will never be induced by the impact of a probability wave, but will always be induced by the impact of a particle. Detection as a wave is contingent on the atom interacting much more strongly with the macroscopic detector as a whole than with its microscopic constituents. This requirement may be more difficult to meet with electrons, protons, neutrons or photons than with atoms.
Sleutel, Pascal; Dietrich, Erik; Van Der Veen, Jan T.; Van Joolingen, Wouter R.
2016-01-01
This study brings a recently discovered macroscopic phenomenon with wave-particle characteristics into the classroom. The system consists of a liquid droplet levitating over a vertically shaken liquid pool. The droplets allow visualization of a wave-particle system in a directly observable way. We
Sleutel, Pascal; Dietrich, Erik; Van der Veen, Jan T.; van Joolingen, Wouter R.
2016-09-01
This study brings a recently discovered macroscopic phenomenon with wave-particle characteristics into the classroom. The system consists of a liquid droplet levitating over a vertically shaken liquid pool. The droplets allow visualization of a wave-particle system in a directly observable way. We show how to interpret this macroscopic phenomenon and how to set up and carry out this experiment. A class of students performed single slit diffraction experiments with droplets. By scoring individual droplet trajectories students find a diffraction pattern. This pilot application in the classroom shows that students can study and discuss the wave-particle nature of the bouncing droplet experiment. The experiment therefore provides a useful opportunity to show wave-particle behavior on the macroscopic level.
Duality quantum algorithm efficiently simulates open quantum systems
Shi-Jie Wei; Dong Ruan; Gui-Lu Long
2016-01-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the op...
General Quantum Interference Principle and Duality Computer
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu
2006-01-01
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of thesub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer,the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer,it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented:the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
Directory of Open Access Journals (Sweden)
Héctor Torres-Silva
2008-11-01
Full Text Available In this paper we study the energy conversion laws of the macroscopic harmonic LC oscillator, the electromagnetic wave (photon and the hydrogen atom. As our analysis indicates, the energies of these apparently different systems obey exactly the same energy conversion law. Based on our results and the wave-particle duality of electrons, we find that the hydrogen atom is, in fact, a natural chiral microscopic LC oscillator. In the framework of classical electromagnetic field theory we analytically obtain, for the hydrogen atom, the quantized electron orbit radius , and quantized energy , (n = 1, 2, 3, · · ·, where is the Bohr radius and is the Rydberg constant. Without the adaptation of any other fundamental principles of quantum mechanics, we present a reasonable explanation of the polarization of photon, selection rules and Pauli exclusion principle. Our results also reveal an essential connection between electron spin and the intrinsic helical movement of electrons and indicate that the spin itself is the effect of quantum confinement.En este trabajo se presenta un estudio de las leyes macroscópicas de conversión de energía del oscilador armónico LC, la onda electromagnética (fotones y el átomo de hidrógeno. Como nuestro análisis indica, las energías de estos aparentemente diferentes sistemas obedecen exactamente la misma ley de conversión de la energía. Sobre la base de nuestros resultados y de la dualidad onda-partícula del electrón, nos encontramos con que el átomo de Hidrógeno, de hecho, es un oscilador LC microscópico naturalmente quiral. En el marco de la teoría clásica de campos electromagnéticos se obtiene analíticamente, para el átomo de hidrógeno, el radio cuantizado de la órbita electrónica , y la energía cuantizada , (n=1, 2, 3.., donde es el radio de Bohr, y es la constante de Rydberg. Sin la adaptación de otros principios fundamentales de la mecánica cuántica, se presenta una explicación razonable de
Duality quantum algorithm efficiently simulates open quantum systems.
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-28
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d(3)) in contrast to O(d(4)) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Duality quantum algorithm efficiently simulates open quantum systems
Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu
2016-07-01
Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
Double Solution with Chaos Dynamic Redundance and Causal Wave-Particle Duality
Kirilyuk, A P
1999-01-01
A system of two interacting, physically real, initially homogeneous fields is considered as the simplest basis for the world construction in which one of them, a 'protofield' of electromagnetic nature, is attracted to another protofield, or medium, responsible for the eventually emerging gravitational effects. The interaction process is analysed within the generalised 'effective (optical) potential method' in which we avoid any usual perturbative reduction. It then appears that for generic system parameters the protofields, instead of simply 'falling' one onto another and forming a fixed 'bound state', are engaged in a self-sustained process of nonlinear pulsation, or 'quantum beat', consisting in unceasing cycles of self-amplified auto-squeeze, or 'collapse' ('reduction'), of a portion of the extended protofields to a small volume followed by the inverse phase of extension. Centres of consecutive reductions form the physical 'points' of thus emerging, intrinsically discrete space, and each of them is 'select...
Macroscopic realism, wave-particle duality and the superposition principle for entangled states
Chuprikov, N L
2006-01-01
On the basis of our model of a one-dimensional (1D) completed scattering (Russian Physics, 49, p.119 and p.314 (2006)) we argue that the linear formalism of quantum mechanics (QM) respects the principles of the macroscopic realism (J. Phys.: Condens. Matter, 14, R415-R451 (2002)). In QM one has to distinguish two kinds of pure ensembles: pure unentangled ensembles to be macroscopically inseparable, and pure entangled ones to be macroscopically separable. A pure entangled ensemble is an intermediate link between a pure unentangled ensemble and classical mixture. Like the former it strictly respects the linear formalism of QM. Like the latter it is decomposable into macroscopically distinct subensembles, in spite of interference between them; our new model exemplifies how to perform such a decomposition in the case of a 1D completed scattering. To respect macroscopic realism, the superposition principle must be reformulated: it must forbid introducing observables for entangled states.
Lawrence, I.
1996-01-01
Discusses a teaching strategy for introducing quantum ideas into the school classroom using modern devices. Develops the concepts of quantization, wave-particle duality, nonlocality, and tunneling. (JRH)
Gauss decomposition for quantum groups and duality
Damaskinsky, E V; Lyakhovsky, V D; Sokolov, M A
1995-01-01
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality aspects of the Gauss decomposition are also touched. For clarity of exposition a few simple examples are considered in some details.
Grothendieck-Verdier duality patterns in quantum algebra
Manin, Yu I.
2017-08-01
After a brief survey of the basic definitions of Grothendieck-Verdier categories and dualities, I consider in this context dualities introduced earlier in the categories of quadratic algebras and operads, largely motivated by the theory of quantum groups. Finally, I argue that Dubrovin's `almost duality' in the theory of Frobenius manifolds and quantum cohomology must also fit a (possibly extended) version of Grothendieck-Verdier duality.
Hadamard states for quantum Abelian duality
Benini, Marco; Dappiaggi, Claudio
2016-01-01
Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C$^*$-algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states to such algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three C$^*$-algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors we obtain a state for the full theory, providing ultimately a unitary implementation of Abelian duality.
Constructing Dualities from Quantum State Manifolds
van Zyl, H J R
2015-01-01
The thesis develops a systematic procedure to construct semi-classical gravitational duals from quantum state manifolds. Though the systems investigated are simple quantum mechanical systems without gauge symmetry many familiar concepts from the conventional gauge/gravity duality come about in a very natural way. The investigation of the low-dimensional manifolds link existing results in the $AdS_2/CFT_1$ literature. We are able to extend these in various ways and provide an explicit dictionary. The higher dimensional investigation is also concluded with a simple dictionary, but this dictionary requires the inclusion of many bulk coordinates. Consequently further work is needed to relate these results to existing literature. Possible ways to achieve this are discussed.
Critical Assessment of Wave-Particle Complementarity via Derivation from Quantum Mechanics
Herbut, Fedor
2009-01-01
After introducing sketchily Bohr's wave-particle complementarity principle in his own words, a derivation of an extended form of the principle from standard quantum mechanics is performed. Reality-evaluation of each step is given. The derived theory is applied to simple examples and the extended entities are illustrated in a thought experiment. Assessment of the approach of Bohr and of this article is taken up again with a rather negative conclusion as far as reflecting reality is concerned. The paper ends with selected incisive opinions on Bohr's dogmatic attitude and with some comments by the present author.
Quantum Poisson-Lie T-duality and WZNW model
Alekseev, A Yu; Tseytlin, Arkady A
1996-01-01
A pair of conformal sigma models related by Poisson-Lie T-duality is constructed by starting with the O(2,2) Drinfeld double. The duality relates the standard SL(2,R) WZNW model to a constrained sigma model defined on SL(2,R) group space. The quantum equivalence of the models is established by using a path integral argument.
Directory of Open Access Journals (Sweden)
Horst Koch
2013-03-01
Full Text Available The high speed of biological processes such as photosynthesis, enzymatic reactions or neuronal activity cannot completely be explained on the basis of classic physical approaches. Different quantum biology effects such as tunnelling have been postulated. We hypothetically admit that deceleration of electron velocity based on light-particle duality of electrons leads to time acceleration. Deceleration from the status of light towards a status of a particle may therefore speed up biochemical or biophysical reactions in the atomic or molecular dimension. Electrophysiological and biological phenomena are discussed on the basis of the hypothesis
Brambila, Danilo
2012-05-01
Quantum chaos has emerged in the half of the last century with the notorious problem of scattering of heavy nuclei. Since then, theoreticians have developed powerful techniques to approach disordered quantum systems. In the late 70\\'s, Casati and Chirikov initiated a new field of research by studying the quantum counterpart of classical problems that are known to exhibit chaos. Among the several quantum-classical chaotic systems studied, the kicked rotor stimulated a lot of enthusiasm in the scientific community due to its equivalence to the Anderson tight binding model. This equivalence allows one to map the random Anderson model into a set of fully deterministic equations, making the theoretical analysis of Anderson localization considerably simpler. In the one-dimensional linear regime, it is known that Anderson localization always prevents the diffusion of the momentum. On the other hand, for higher dimensions it was demonstrated that for certain conditions of the disorder parameter, Anderson localized modes can be inhibited, allowing then a phase transition from localized (insulating) to delocalized (metallic) states. In this thesis we will numerically and theoretically investigate the properties of a multidimensional quantum kicked rotor in a nonlinear medium. The presence of nonlinearity is particularly interesting as it raises the possibility of having soliton waves as eigenfunctions of the systems. We keep the generality of our approach by using an adjustable diffusive nonlinearity, which can describe several physical phenomena. By means of Variational Calculus we develop a chaotic map which fully describes the soliton dynamics. The analysis of such a map shows a rich physical scenario that evidences the wave-particle behavior of a soliton. Through the nonlinearity, we trace a correspondence between quantum and classical mechanics, which has no equivalent in linearized systems. Matter waves experiments provide an ideal environment for studying Anderson
Trigonometric version of quantum-classical duality in integrable systems
Beketov, M; Zabrodin, A; Zotov, A
2015-01-01
We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars-Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars-Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit correspondin...
New Insights into Quantum Gravity from Gauge/gravity Duality
Engelhardt, Netta
2016-01-01
Using gauge/gravity duality, we deduce several nontrivial consequences of quantum gravity from simple properties of the dual field theory. These include: (1) a version of cosmic censorship, (2) restrictions on evolution through black hole singularities, and (3) the exclusion of certain cosmological bounces. In the classical limit, the latter implies a new singularity theorem.
New insights into quantum gravity from gauge/gravity duality
Engelhardt, Netta; Horowitz, Gary T.
2016-06-01
Using gauge/gravity duality, we deduce several nontrivial consequences of quantum gravity from simple properties of the dual field theory. These include: (1) a version of cosmic censorship, (2) restrictions on evolution through black hole singularities, and (3) the exclusion of certain cosmological bounces. In the classical limit, the latter implies a new singularity theorem.
Geometric Langlands Program and Dualities in Quantum Physics
2009-04-30
systems, such as the KdV hier- archy, to an affine analogue of the Langlands duality. We have conjectured that common eigenvalues of the mutually...the spectra of the quantum KdV Hamiltonians. (5) In the joint papers [2, 3] with B. Feigin and L. Rybnikov, we have studied the spectra of the
Algebra of Observables and States for Quantum Abelian Duality
Capoferri, Matteo
2016-01-01
The study of dualities is a central issue in several modern approaches to quantum field theory, as they have broad consequences on the structure and on the properties of the theory itself. We call Abelian duality the generalisation to arbitrary spacetime dimension of the duality between electric and magnetic field in Maxwell theory. In the present thesis, in the framework of algebraic quantum field theory, the Abelian duality for quantum field theory on globally hyperbolic spacetime with compact Cauchy surface is tackled. Fistly, the algebra of observables is constructed. It is shown that it can be presented as the direct sum of three pre-symplectic Abelian groups, each corresponding to a different sector of the theory. As a consequence, it is possible to provide quantum states for the theory by building separate states on each direct summand. In particular, explicit examples in two and four dimensions are discussed thoroughly; a ground Hadamard state in a suitable sense is proved to exist for both of them. L...
Spectrum of a duality-twisted Ising quantum chain
Grimm, U
2002-01-01
The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function.
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Energy Technology Data Exchange (ETDEWEB)
Abłamowicz, Rafał, E-mail: rablamowicz@tntech.edu [Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville, Tennessee 38505 (United States); Gonçalves, Icaro, E-mail: icaro.goncalves@ufabc.edu.br [Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP (Brazil); Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy)
2014-10-15
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Quantum Fluctuations of Light A Modern Perspective on Wave\\/Particle Duality
Carmichael, H J
2001-01-01
We review studies of the fluctuations of light made accessible by the invention of the laser and the strong interactions realized in cavity QED experiments. Photon antibunching advocating the discrete (particles), is contrasted with amplitude squeezing which speaks of the continuous (waves). The tension between particles and waves is demonstrated by a recent experiment which combines the measurement strategies used to observe these nonclassical behaviors of light [Phys. Rev. Lett. 85, 3149 (2000)].
Elementary Concepts of Quantum Theory
Warren, J. W.
1974-01-01
Discusses the importance and difficulties of teaching basic quantum theory. Presents a discussion of wave-particle duality, indeterminacy, the nature of a quantized state of a system, and the exclusion principle. (MLH)
Trigonometric version of quantum-classical duality in integrable systems
Beketov, M.; Liashyk, A.; Zabrodin, A.; Zotov, A.
2016-02-01
We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars-Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars-Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit corresponding to the classical Calogero-Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.
An N/4 fixed-point duality quantum search algorithm
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Here a fixed-point duality quantum search algorithm is proposed.This algorithm uses iteratively non-unitary operations and measurements to search an unsorted database.Once the marked item is found,the algorithm stops automatically.This algorithm uses a constant non-unitary operator,and requires N/4 steps on average(N is the number of data from the database) to locate the marked state.The implementation of this algorithm in a usual quantum computer is also demonstrated.
Duality constructions from quantum state manifolds
Kriel, J N; Scholtz, F G
2015-01-01
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS_2/CFT_1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et. al. the corresponding state manifol...
Duality constructions from quantum state manifolds
Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.
2015-11-01
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.
Duality in the quantum Hall system
Lütken, C. A.; Ross, G. G.
1992-05-01
We suggest that a unified description of the integer and fractional phases of the quantum Hall system may be possible if the scaling diagram of transport coefficients is invariant under linear fractional (modular) transformations. In this model the hierarchy of states, as well as the observed universality of critical exponents, are consequences of a discrete SL(2,openZ) symmetry acting on the parameter space of an effective quantum-field theory. Available scaling data on the position of delocalization fixed points in the integer case and the position of mobility fixed points in the fractional case agree with the model within experimental accuracy.
Quantum state reduction and conditional time evolution of wave-particle correlations in cavity QED.
Foster, G T; Orozco, L A; Castro-Beltran, H M; Carmichael, H J
2000-10-09
We report measurements in cavity QED of a wave-particle correlation function which records the conditional time evolution of the field of a fraction of a photon. Detection of a photon prepares a state of well-defined phase that evolves back to equilibrium via a damped vacuum Rabi oscillation. We record the regression of the field amplitude. The recorded correlation function is nonclassical and provides an efficiency independent path to the spectrum of squeezing. Nonclassicality is observed even when the intensity fluctuations are classical.
Duality in adiabatic level crossing Quantum coherence and complete reflection
Fujikawa, K; Fujikawa, Kazuo; Suzuki, Hiroshi
1997-01-01
A field dependent su(2) gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) level crossing problem. It is pointed out that weak and strong level crossing interactions are interchanged under this transformation, and thus realizing a naive strong and weak duality. A reliable perturbation theory is thus formulated in the both limits of weak and strong interactions. Main characteristics of the level crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-described by simple perturbation theory without referring to Stokes phenomena. We also show that quantum coherence in a double well potential is generally suppressed by the effect of level crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.
Adams, Allan; Schaefer, Thomas; Steinberg, Peter; Thomas, John E
2012-01-01
Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical, and that do not have a simple description in terms of weakly interacting quasi-particles. Two systems that have recently attracted a great deal of interest are the quark-gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by more than 20 orders of magnitude in temperature, but they were shown to exhibit very similar hydrodynamic flow. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection between these fields, and it also serves as an introduction to the Focus Issue of N...
SU(2) Yang-Mills Theory: Waves, Particles, and Quantum Thermodynamics
Hofmann, Ralf
2016-01-01
We elucidate how Quantum Thermodynamics at temperature $T$ emerges from pure and classical SU(2) Yang-Mills theory on a four-dimensional Euclidean spacetime slice $S_1\\times {\\bf R}^3$. The concept of a (deconfining) thermal ground state, composed of certain solutions to the fundamental, classical Yang-Mills equation, allows for a unified addressation of both (classical) wave- and (quantum) particle-like excitations thereof.
Adams, Allan; Carr, Lincoln D.; Schäfer, Thomas; Steinberg, Peter; Thomas, John E.
2012-11-01
Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical and that do not have a simple description in terms of weakly interacting quasiparticles. Two systems that have recently attracted a great deal of interest are the quark-gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by 19 orders of magnitude in temperature, but were shown to exhibit very similar hydrodynamic flows. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio, which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection between these fields, and also serves as an introduction to the focus issue of New Journal of Physics on ‘Strongly Correlated Quantum Fluids: From Ultracold Quantum Gases to Quantum Chromodynamic Plasmas’. The presentation is accessible to the general physics reader and includes discussions of the latest research developments in all three areas.
Duality, Confinement and Supersymmetry in Restricted Quantum Chromodynamics (rcd)
Rana, J. M. S.
Electromagnetic duality has been utilized to study the isocolor charge-dyon interactions in Restricted Quantum Chromodynamics (RCD),in terms of current-current correlation (in magnetic gauge)using dielectric and permeability parameters of the associated vacuum. In the state of dyonic superconductivity, it has been shown that the dual propagators behave as 1/k4 (for small k2), which in analogy with superconductivity (dual superconductivity) leads to the confinement of colored fluxes associated with dyonic quarks vide generalized Meissner effect. Based on semi-quantitative analysis of vortex solutions of RCD and by calculating the masses for the massive collective modes of the condensed vacuum, the expressions for the London penetration depth, coherence length and the associated flux energy functions for the type I and type II superconducting media have been obtained. It has further been demonstrated that in the type I medium, vortices tend to coalesce and hence are attractive, while the energy function supports repulsive forces between vortices in the type II superconducting medium. The RCD has been supersymmetrized in N=1 limit and the supersymmetric dyonic solutions have been obtained. In the dyonic background gauge one-loop quantum corrections to the dyonic mass have been calculated and it has been shown that the one-loop quantum corrections lead no change in classical mass of the dyon.
Duality, Phase Structures and Dilemmas in Symmetric Quantum Games
Ichikawa, T; Ichikawa, Tsubasa; Tsutsui, Izumi
2006-01-01
Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games exemplified by the familiar games, the Battle of the Sexes (BoS) and the Prisoners' Dilemma (PD). These two types of symmetric games are shown to be related by a duality map, which ensures that they share common phase structures with respect to the equilibria of the strategies. We find eight distinct phase structures possible for the symmetric games, which are determined by the classical payoff matrices from which the quantum games are defined. We also discuss the possibility of resolving the dilemmas in the classical BoS, PD and the Stag Hunt (SH) game based on the phase structures obtained in the quantum games. It is observed that quantization cannot resolve the dilemma fully for the BoS, while it generically can for the PD and SH if appropriate correlations for the strategies of...
Superconformal quantum field theories in string. Gauge theory dualities
Energy Technology Data Exchange (ETDEWEB)
Wiegandt, Konstantin
2012-08-14
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
SU(2 Yang–Mills Theory: Waves, Particles, and Quantum Thermodynamics
Directory of Open Access Journals (Sweden)
Ralf Hofmann
2016-08-01
Full Text Available We elucidate how Quantum Thermodynamics at temperature T emerges from pure and classical S U ( 2 Yang–Mills theory on a four-dimensional Euclidean spacetime slice S 1 × R 3 . The concept of a (deconfining thermal ground state, composed of certain solutions to the fundamental, classical Yang–Mills equation, allows for a unified addressation of both (classical wave- and (quantum particle-like excitations thereof. More definitely, the thermal ground state represents the interplay between nonpropagating, periodic configurations which are electric-magnetically (antiselfdual in a non-trivial way and possess topological charge modulus unity. Their trivial-holonomy versions—Harrington–Shepard (HS (anticalorons—yield an accurate a priori estimate of the thermal ground state in terms of spatially coarse-grained centers, each containing one quantum of action ℏ localized at its inmost spacetime point, which induce an inert adjoint scalar field ϕ ( | ϕ | spatio-temporally constant. The field ϕ , in turn, implies an effective pure-gauge configuration, a μ gs , accurately describing HS (anticaloron overlap. Spatial homogeneity of the thermal ground-state estimate ϕ , a μ gs demands that (anticaloron centers are densely packed, thus representing a collective departure from (antiselfduality. Effectively, such a “nervous” microscopic situation gives rise to two static phenomena: finite ground-state energy density ρ gs and pressure P gs with ρ gs = − P gs as well as the (adjoint Higgs mechanism. The peripheries of HS (anticalorons are static and resemble (antiselfdual dipole fields whose apparent dipole moments are determined by | ϕ | and T, protecting them against deformation potentially caused by overlap. Such a protection extends to the spatial density of HS (anticaloron centers. Thus the vacuum electric permittivity ϵ 0 and magnetic permeability μ 0 , supporting the propagation of wave-like disturbances in the U ( 1 Cartan
On duality between quantum maps and quantum states
Zyczkowski, K; Zyczkowski, Karol; Bengtsson, Ingemar
2004-01-01
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is defined and analyzed. Using the concept of the dynamical matrix and the Jamiolkowski isomorphism we explore the relation between the set of quantum operations (dynamics) and the set of density matrices acting on an extended Hilbert space (kinematics). An analogous relation is established between the classical maps and an extended space of the discrete probability distributions.
Gauge/gravity duality. Exploring universal features in quantum matter
Energy Technology Data Exchange (ETDEWEB)
Klug, Steffen
2013-07-09
In this dissertation strongly correlated quantum states of matter are explored with the help of the gauge/gravity duality, relating strongly coupled gauge theories to weakly curved gravitational theories. The main focus of the present work is on applications to condensed matter systems, in particular high temperature superconductors and quantum matter close to criticality at zero temperature. The gauge/gravity duality originates from string theory and is a particular realization of the holographic principle. Therefore, a brief overview of the conceptual ideas behind string theory and the ramifications of the holographic principle are given. Along the way, supersymmetry and supersymmetric field theories needed to understand the low energy effective field theories of superstring theory will be discussed. Armed with the string theory background, the double life of D-branes, extended object where open strings end, is explained as massive solitonic solutions to the type II supergravity equations of motion and their role in generating supersymmetric Yang-Mills theories. Connecting these two different pictures of D-branes will give an explicit construction of a gauge/gravity duality, the AdS{sub 5}/CFT{sub 4} correspondence between N=4 supersymmetric SU(N{sub c}) Yang-Mills theory in four dimensions with vanishing β-function to all orders, describing a true CFT, and type IIB supergravity in ten-dimensional AdS{sub 5} x S{sup 5} spacetime. Furthermore, the precise dictionary relating operators of the conformal field theory to fields in the gravitational theory is established. More precisely, the partitions functions of the strongly coupled N=4 supersymmetric Yang-Mills theory in the large N{sub c} limit is equal to the on-shell supergravity partition evaluated at the boundary of the AdS space. Applying the knowledge of perturbative quantum field theory and its relation to the quantum partition function the dictionary may be extended to finite temperature and finite
Mross, David F.; Alicea, Jason; Motrunich, Olexei I.
2016-07-01
We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2 +1 ) dimensions (QED3 ) with N =1 fermion flavors. The duality proceeds via an exact, nonlocal mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED3 scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and N =2 QED3 .
Wave Particle Duality and the Afshar Experiment
Directory of Open Access Journals (Sweden)
Drezet A.
2011-01-01
Full Text Available We analyze the experiment realized in 2003-2004 by S. Afshar et al. in order to refute the principle of complementarity. We discuss the general meaning of this principle and show that contrarily to the claim of the authors Bohr's complementarity is not in danger in this experiment.
Wave Particle Duality and the Afshar Experiment
Directory of Open Access Journals (Sweden)
Drezet A.
2011-01-01
Full Text Available We analyze the experiment realized in 2003-2004 by S. Afshar et al. [1] in order to refute the principle of complementarity. We discuss the general meaning of this principle and show that contrarily to the claim of the authors Bohr’s complementarity is not in danger in this experiment.
Symmetry and Degeneracy in Quantum Mechanics. Self-Duality in Finite Spin Systems
Osacar, C.; Pacheco, A. F.
2009-01-01
The symmetry of self-duality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…
Symmetry and Degeneracy in Quantum Mechanics. Self-Duality in Finite Spin Systems
Osacar, C.; Pacheco, A. F.
2009-01-01
The symmetry of self-duality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…
Gu, Yingfei; Lee, Ching Hua; Wen, Xueda; Cho, Gil Young; Ryu, Shinsei; Qi, Xiao-Liang
2016-09-01
In this paper, we study (2 +1 ) -dimensional quantum anomalous Hall states, i.e., band insulators with quantized Hall conductance, using exact holographic mapping. Exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in (3 +1 ) -dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a (3 +1 ) -dimensional topological insulator. The dual description enables a characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.
Duality Theory and Categorical Universal Logic: With Emphasis on Quantum Structures
Directory of Open Access Journals (Sweden)
Yoshihiro Maruyama
2014-12-01
Full Text Available Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras, which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical, intuitionistic, and diverse substructural logics. Here we show there are those dual adjunctions that have inherent hyperdoctrine structures in their predicate functor parts. We systematically investigate into the categorical logics of dual adjunctions by utilising Johnstone-Dimov-Tholen's duality-theoretic framework. Our set-theoretical duality-based hyperdoctrines for quantum logic have both universal and existential quantifiers (and higher-order structures, giving rise to a universe of Takeuti-Ozawa's quantum sets via the tripos-to-topos construction by Hyland-Johnstone-Pitts. The set-theoretical hyperdoctrinal models of quantum logic, as well as all quantum hyperdoctrines with cartesian base categories, turn out to give sound and complete semantics for Faggian-Sambin's first-order quantum sequent calculus over cartesian type theory; in addition, quantum hyperdoctrines with monoidal base categories are sound and complete for the calculus over linear type theory. We finally consider how to reconcile Birkhoff-von Neumann's quantum logic and Abramsky-Coecke's categorical quantum mechanics (which is modernised quantum logic as an antithesis to the traditional one via categorical universal logic.
A generalization of Schur-Weyl duality with applications in quantum estimation
Marvian, Iman
2011-01-01
Schur-Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to develop a general framework for the study of a family of quantum estimation problems wherein one is given n copies of an unknown quantum state according to some prior and the goal is to estimate certain parameters of the given state. In particular, we are interested to know whether collective measurements are useful and if so to find an upper bound on the amount of entanglement which is required to achieve the optimal estimation. In the case of pure states, we show that commutativity of the set of observables that define the estimation problem implies the sufficiency of unentangled measurements.
Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition
Qin, Yan Qi; He, Yuan-Yao; You, Yi-Zhuang; Lu, Zhong-Yi; Sen, Arnab; Sandvik, Anders W.; Xu, Cenke; Meng, Zi Yang
2017-07-01
Recently, significant progress has been made in (2 +1 )-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities; i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly correlated quantum-matter systems: the one relating the easy-plane noncompact CP1 model (NCCP1 ) and noncompact quantum electrodynamics (QED) with two flavors (N =2 ) of massless two-component Dirac fermions. The easy-plane NCCP1 model is the field theory of the putative deconfined quantum-critical point separating a planar (X Y ) antiferromagnet and a dimerized (valence-bond solid) ground state, while N =2 noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work, we present strong numerical support for the proposed duality. We realize the N =2 noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC simulations, we study a planar version of the S =1 /2 J -Q spin Hamiltonian (a quantum X Y model with additional multispin couplings) and show that it hosts a continuous transition between the X Y magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships. In the J -Q model, we find both continuous and first-order transitions, depending on the degree of planar anisotropy, with deconfined quantum criticality surviving only up to moderate strengths of the anisotropy. This explains previous claims of no deconfined quantum
Maxwell and the classical wave particle dualism.
Mendonça, J T
2008-05-28
Maxwell's equations are one of the greatest theoretical achievements in physics of all times. They have survived three successive theoretical revolutions, associated with the advent of relativity, quantum mechanics and modern quantum field theory. In particular, they provide the theoretical framework for the understanding of the classical wave particle dualism.
Kreshchuk, Michael
2016-01-01
The phenomenon of duality reflects a link between the behaviour of a system in different regimes. The goal of this work is to expose the classical origins of such links, and to demonstrate how they come to life in some quasi-exactly solvable problems of quantum mechanics. By studying the global properties of the Riemannian surface of the classical momentum, we reveal that the abbreviated classical action possesses a symmetry which holds also at the quantum level and underlies the energy reflection symmetry of the quantum energy levels.
Tales of the quantum understanding physics' most fundamental theory
Hobson, Art
2016-01-01
This is a book about the quanta that make up our universe--the highly unified bundles of energy of which everything is made. It explains wave-particle duality, randomness, quantum states, non-locality, Schrodinger's cat, quantum jumps, and more, in everyday language for non-scientists and scientists who wish to fathom science's most fundamental theory.
A Portable Double-Slit Quantum Eraser with Individual Photons
Dimitrova, T. L.; Weis, A.
2011-01-01
The double-slit experiment has played an important role in physics, from supporting the wave theory of light, via the discussions of the wave-particle duality of light (and matter) to the foundations of modern quantum optics. Today it keeps playing an active role in the context of quantum optics experiments involving single photons. In this paper,…
Mross, David F; Alicea, Jason; Motrunich, Olexei I
2016-07-01
We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2+1) dimensions (QED_{3}) with N=1 fermion flavors. The duality proceeds via an exact, nonlocal mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED_{3} scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and N=2 QED_{3}.
Distance between Quantum States and Gauge-Gravity Duality
Miyaji, Masamichi; Numasawa, Tokiro; Shiba, Noburo; Takayanagi, Tadashi; Watanabe, Kento
2015-12-01
We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an anti-de Sitter spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.
Position-dependent mass quantum Hamiltonians: general approach and duality
Rego-Monteiro, M. A.; Rodrigues, Ligia M. C. S.; Curado, E. M. F.
2016-03-01
We analyze a general family of position-dependent mass (PDM) quantum Hamiltonians which are not self-adjoint and include, as particular cases, some Hamiltonians obtained in phenomenological approaches to condensed matter physics. We build a general family of self-adjoint Hamiltonians which are quantum mechanically equivalent to the non-self-adjoint proposed ones. Inspired by the probability density of the problem, we construct an ansatz for the solutions of the family of self-adjoint Hamiltonians. We use this ansatz to map the solutions of the time independent Schrödinger equations generated by the non-self-adjoint Hamiltonians into the Hilbert space of the solutions of the respective dual self-adjoint Hamiltonians. This mapping depends on both the PDM and on a function of position satisfying a condition that assures the existence of a consistent continuity equation. We identify the non-self-adjoint Hamiltonians here studied with a very general family of Hamiltonians proposed in a seminal article of Harrison (1961 Phys. Rev. 123 85) to describe varying band structures in different types of metals. Therefore, we have self-adjoint Hamiltonians that correspond to the non-self-adjoint ones found in Harrison’s article.
Singh, T P
2008-01-01
There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the `weakly quantum, strongly gravitational' dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the `strongly quantum, weakly gravitational' dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.
Parables of Physics and a Quantum Romance
Machacek, A. C.
2014-01-01
Teachers regularly use stories to amplify the concepts taught and to encourage student engagement. The literary form of a parable is particularly suitable for classroom use, and examples are given, including a longer one intended to stimulate discussion on the nature of quantum physics (and the wave-particle duality in particular).
Parables of physics and a quantum romance
Machacek, A. C.
2014-01-01
Teachers regularly use stories to amplify the concepts taught and to encourage student engagement. The literary form of a parable is particularly suitable for classroom use, and examples are given, including a longer one intended to stimulate discussion on the nature of quantum physics (and the wave-particle duality in particular).
Parables of Physics and a Quantum Romance
Machacek, A. C.
2014-01-01
Teachers regularly use stories to amplify the concepts taught and to encourage student engagement. The literary form of a parable is particularly suitable for classroom use, and examples are given, including a longer one intended to stimulate discussion on the nature of quantum physics (and the wave-particle duality in particular).
Marshman, Emily; Singh, Chandralekha
2017-01-01
Single photon experiments involving a Mach-Zehnder interferometer can illustrate the fundamental principles of quantum mechanics, e.g., the wave-particle duality of a single photon, single photon interference, and the probabilistic nature of quantum measurement involving single photons. These experiments explicitly make the connection between the…
Quantum Interference: How to Measure the Wavelength of a Particle
Brom, Joseph M.
2017-01-01
The concept of wave-particle duality in quantum theory is difficult to grasp because it attributes particle-like properties to classical waves and wave-like properties to classical particles. There seems to be an inconsistency involved with the notion that particle-like or wave-like attributes depend on how you look at an entity. The concept comes…
Gu, Yingfei; Wen, Xueda; Cho, Gil Young; Ryu, Shinsei; Qi, Xiao-Liang
2016-01-01
In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$-dimensional topological insulator. The dual description enables a new characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.
Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna
2017-01-01
In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman's sum over paths approach in the Italian high school. Our study focuses on students' understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle. In view of recent…
Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna
2017-01-01
In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman's sum over paths approach in the Italian high school. Our study focuses on students' understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle. In view of recent…
Spatio-temporal second-order quantum correlations of surface plasmon polaritons
Berthel, Martin; Drezet, Aurélien
2016-01-01
We present an experimental methodology to observe spatio-temporal second-order quantum coherence of surface plasmon polaritons which are emitted by nitrogen vacancy color centers attached at the apex of an optical tip. The approach relies on leakage radiation microscopy in the Fourier space and we use this approach to test wave-particle duality for surface plasmon polaritons.
Rae, Alastair I M
2007-01-01
PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC
On powercounting in perturbative quantum gravity theories through color-kinematic duality
Boels, Rutger H.; Isermann, Reinke Sven
2013-06-01
The standard argument why gravity is not renormalisable relies on direct powercounting of Feynman graphs to estimate the degree of UV divergence. In several (highly) supersymmetric examples the actual divergences have been shown to be considerably better. In these examples the improvement follows from a conjectured duality between color and kinematics. In this paper we initiate the systematic study of quite general powercounting under the assumption that color-kinematic duality exists. The main technical tool is a reformulation of the duality in terms of linear maps, modulo subtleties at loop level mostly inherent to the duality. This tool may have wider applications in both gauge and gravity theories, up to resolution of the subtleties. Here it is first applied to the large Britto-Cachazo-Feng-Witten (BCFW) shift behavior of gravity integrands constructed through the duality. Assuming color-kinematic duality and reasonable technical requirements hold these shifts are shown to be independent of loop order. This is a new quantitative measure for massive cancellations with respect to the Feynman graph expression. More speculatively, the same approach is then applied to provide estimates of the overall degree of UV divergence in quite general gravity theories, assuming the duality exists. The manifest cancellations obtained in these estimates depends on the exact implementation of the duality at loop level, especially on graph topology. The developed arguments apply to all multiplicity. Finally, some evidence for the duality to all loop orders is provided from an analysis of BCFW shifts of gauge theory integrands through Feynman graphs.
A portable double-slit quantum eraser with individual photons
Energy Technology Data Exchange (ETDEWEB)
Dimitrova, T L [Physics Faculty, University of Plovdiv ' Paissi Hilendarski' , Tzar Assen Str. 24, BG-4000 Plovdiv (Bulgaria); Weis, A, E-mail: doradimitrova@uni-plovdiv.bg [Physics Department, University of Fribourg, Chemin du Musee 3, CH-1700 Fribourg (Switzerland)
2011-11-15
The double-slit experiment has played an important role in physics, from supporting the wave theory of light, via the discussions of the wave-particle duality of light (and matter) to the foundations of modern quantum optics. Today it keeps playing an active role in the context of quantum optics experiments involving single photons. In this paper, we present a truly portable double-slit apparatus which demonstrates both the wave-particle duality of light and the phenomenon of quantum erasing. The device can be operated either with strong laser light and screen projection, or with individual photons, in which case quantum interference and quantum erasing are detected by a photomultiplier whose pulses are rendered acoustically by means of a loudspeaker. Alternatively, the phenomena can be displayed using multimedia projection of oscilloscope traces.
Duality, Quantum Vortices and Anyons in Maxwell-Chern-Simons-Higgs Theories
Marino, E C
1993-01-01
The order-disorder duality structure is exploited in order to obtain a quantum description of anyons and vortices in: a) the Maxwell theory; b) the Abelian Higgs Model; c) the Maxwell-Chern-Simons theory; d) the Maxwell-Chern-Simons-Higgs theory. A careful construction of a charge bearing order operator($\\sigma$) and a magnetic flux bearing disorder operator (vortex operator) ($\\mu$) is performed, paying attention to the necessary requirements for locality. An anyon operator is obtained as the product $\\varphi=\\sigma\\mu$. A detailed and comprehensive study of the euclidean correlation functions of $\\sigma$, $\\mu$ and $\\varphi$ is carried on in the four theories above. The exact correlation functions are obtained in cases $\\underline{a}$ and $\\underline{c}$. The large distance behavior of them is obtained in cases $\\underline{b}$ and $\\underline{d}$. The study of these correlation functions allows one to draw conclusions about the condensation of charge and magnetic flux, establishing thereby an analogy with t...
Higher AGT Correspondences, W-algebras, and Higher Quantum Geometric Langlands Duality from M-Theory
Tan, Meng-Chwan
2016-01-01
We further explore the implications of our framework in [arXiv:1301.1977, arXiv:1309.4775], and physically derive, from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent, (i) a 5d AGT correspondence for any compact Lie group, (ii) a 5d and 6d AGT correspondence on ALE space of type ADE, and (iii) identities between the ordinary, q-deformed and elliptic affine W-algebras associated with the 4d, 5d and 6d AGT correspondence, respectively, which also define a quantum geometric Langlands duality and its higher analogs formulated by Feigin-Frenkel-Reshetikhin in [3,4]. As an offshoot, we are led to the sought-after connection between the gauge-theoretic realization of the geometric Langlands correspondence by Kapustin-Witten [5,6] and its algebraic CFT formulation by Beilinson-Drinfeld [7], where one can also understand Wilson and 't Hooft-Hecke line operators in 4d gauge theory as monodromy loop operators in 2d CFT, for example. In turn, this will allow ...
Modified Wave Particle Duality and Black Hole Physics
Institute of Scientific and Technical Information of China (English)
LI Xiang
2007-01-01
de Broglie relation is revisited, in consideration of a generalization of canonical commuting relation. The possible effects on particle's localization and black hole physics are also discussed, in a heuristic manner.
Gauge/gravity duality. From quantum phase transitions towards out-of-equilibrium physics
Energy Technology Data Exchange (ETDEWEB)
Ngo Thanh, Hai
2011-05-02
In this dissertation we use gauge/gravity duality to investigate various phenomena of strongly coupled field theories. Of special interest are quantum phase transitions, quantum critical points, transport phenomena of charges and the thermalization process of strongly coupled medium. The systems studied in this thesis might be used as models for describing condensed matter physics in a superfluid phase near the quantum critical point and the physics of quark-gluon plasma (QGP), a deconfinement phase of QCD, which has been recently created at the Relativistic Heavy Ion Collider (RHIC). Moreover, we follow the line of considering different gravity setups whose dual field descriptions show interesting phenomena of systems in thermal equilibrium, slightly out-of-equilibrium and far-from-equilibrium. We first focus on systems in equilibrium and construct holographic superfluids at finite baryon and isospin charge densities. For that we use two different approaches, the bottom-up with an U(2) Einstein-Yang-Mills theory with back-reaction and the top-down approach with a D3/D7 brane setup with two coincident D7-brane probes. In both cases we observe phase transitions from a normal to a superfluid phase at finite and also at zero temperature. In our setup, the gravity duals of superfluids are Anti-de Sitter black holes which develop vector-hair. Studying the order of phase transitions at zero temperature, in the D3/D7 brane setup we always find a second order phase transition, while in the Einstein-Yang-Mills theory, depending on the strength of the back-reaction, we obtain a continuous or first order transition. We then move to systems which are slightly out-of-equilibrium. Using the D3/D7 brane setup with N{sub c} coincident D3-branes and N{sub f} coincident D7-brane probes, we compute transport coefficients associated with massive N=2 supersymmetric hypermultiplet fields propagating through an N=4 SU(N{sub c}) super Yang-Mills plasma in the limit of N{sub f}<
Burgess, C P
2001-01-01
We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers satisfying Fermi statistics (or those related to fermions by the action of the group), the resulting group is known to imply many, if not all, of the remarkable features of Quantum Hall systems. For conductors with boson charge carriers (modulo group transformations) a different group is predicted, implying equally striking implications for the conductivities of these systems, including a super-universality of the critical exponents for conductor/insulator and superconductor/insulator transitions in two dimensions and a hierarchical structure, analogous to that of the quantum Hall effect but different in its details. Our derivation shows how this symmetry emerges at low energies, depending only weakly on the details of dynamics of the underlying systems.
Conservation Laws in Quantum-Correlation-Function Dynamics
Directory of Open Access Journals (Sweden)
Wei Wang
2010-01-01
Full Text Available For a complete and lucid discussion of quantum correlation, we introduced two new first-order correlation tensors defined as linear combinations of the general coherence tensors of the quantized fields and derived the associated coherence potentials governing the propagation of quantum correlation. On the basis of these quantum optical coherence tensors, we further introduced new concepts of scalar, vector and tensor densities and presented some related properties, such as conservation laws and the wave-particle duality for quantum correlation, which provide new insights into photon statistics and quantum correlation.
Santos, Emilio
2012-01-01
It is stressed the advantage of a realistic interpretation of quantum mechanics providing a physical model of the quantum world. After some critical comments on the most popular interpretations, the difficulties for a model are pointed out and possible solutions proposed. In particular the existence of discrete states, the quantum jumps, the alleged lack of objective properties, measurement theory, the probabilistic character of quantum physics, the wave-particle duality and the Bell inequalities are commented. It is conjectured that an intuitive picture of the quantum world could be obtained compatible with the quantum predictions for actual experiments, although maybe incompatible with alleged predictions for ideal, unrealizable, experiments.
Holographic duality and applications
Bea, Yago
2016-01-01
In this thesis we review some results on the generalization of the gauge/gravity duality to new cases by using T-duality and by including fundamental matter, finding applications to condensed matter physics. First, we construct new supersymmetric solutions of type IIA/B and eleven-dimensional supergravity by using non-abelian T-duality. Second, we construct a type IIA supergravity solution with D6-brane sources, dual to an unquenched massive flavored version of the ABJM theory. Third, we study a probe D6-brane with worldvolume gauge fields in the ABJM background, obtaining the dual description of a quantum Hall system. Moreover, we consider a system of a probe D6-brane in the ABJM background and study quantum phase transitions of its dual theory.
Loop-tree duality and quantum field theory in four dimensions
Sborlini, German F R
2016-01-01
Loop-tree duality allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct comparison with real radiation terms. In this talk, we review the basis of the method and describe its application to regularize Feynman integrals. Performing an integrand-level combination of real and virtual terms, we obtain finite contributions that can be computed in four-dimensions. Moreover, this method provides a natural physical interpretation of infrared singularities, their origin and the way that they cancel in the complete computation.
Destructive Interference of Dualities
Wotzasek, C
1998-01-01
We show that the fusion of two (diffeomorphism) invariant self-dual scalars described by right and left chiral-WZW actions, produces a Hull non-mover field. After fusion, right and left moving modes disappear from the spectrum, displaying in this way the phenomenon of (destructive) quantum interference of dualities.
Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
Frenkel, Edward
2016-01-01
We prove a system of relations in the Grothendieck ring of the category O of representations of the Borel subalgebra of an untwisted quantum affine algebra U_q(g^) introduced in [HJ]. This system was discovered in [MRV1, MRV2], where it was shown that solutions of this system can be attached to certain affine opers for the Langlands dual affine Kac-Moody algebra of g^, introduced in [FF5]. Together with the results of [BLZ3, BHK], which enable one to associate quantum g^-KdV Hamiltonians to representations from the category O, this provides strong evidence for the conjecture of [FF5] linking the spectra of quantum g^-KdV Hamiltonians and affine opers for the Langlands dual affine algebra. As a bonus, we obtain a direct and uniform proof of the Bethe Ansatz equations for a large class of quantum integrable models associated to arbitrary untwisted quantum affine algebras, under a mild genericity condition.
Horvat, Raul; Trampetic, Josip; You, Jiangyang
2016-01-01
In this article we expound a discovery of the quantum equivalence/duality of U(N) noncommutative quantum field theories (NC QFT) related by the theta-exact Seiberg-Witten (SW) maps and at all orders in the perturbation theory with respect to the coupling constant. We show that this proof holds for Super Yang-Mills (SYM) theories with N=0,1,2,4$ supersymmetry. In short, Seiberg-Witten map does commute with the quantization of the U(N) NCQFT independently, with or without supersymmetry.
Theoretical foundations and applications of the Loop-Tree Duality in Quantum Field Theories
Buchta, Sebastian
2015-01-01
The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level scattering amplitudes. This is achieved by directly applying the Residue Theorem to the loop-energy-integration. The result is a sum over all possible single cuts of the Feynman diagram in consideration integrated over a modified phase space. These single-cut integrals, called Dual contributions, are in fact tree-level objects and thus give rise to the opportunity of bringing loop- and tree-contributions together, treating them simultaneously in a common Monte Carlo event generator. Initially introduced for one-loop scalar integrals, the applicability of the LTD has been expanded ever since. In this thesis, we show how to deal with Feynman graphs beyond simple poles by taking advantage of Integration By Parts (IBP) relations. Furthermore, we investigate the cancellation of singularities among Dual contributions as well as between real and virtual corrections. For the first time, a nu...
Institute of Scientific and Technical Information of China (English)
GUO TieXin; CHEN XinXiang
2009-01-01
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules.First,the complicated stratification structure of a module over the algebra L(μ,K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory,thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules.Then,we give the representation theorem of weakly continuous canonical module homomorphisms,the theorem of existence of random Mackey structure,and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably difierent from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
Kaloyerou, P. N.
2016-02-01
I argue that quantum optical experiments that purport to refute Bohr's principle of complementarity (BPC) fail in their aim. Some of these experiments try to refute complementarity by refuting the so called particle-wave duality relations, which evolved from the Wootters-Zurek reformulation of BPC (WZPC). I therefore consider it important for my forgoing arguments to first recall the essential tenets of BPC, and to clearly separate BPC from WZPC, which I will argue is a direct contradiction of BPC. This leads to a need to consider the meaning of particle-wave duality relations and to question their fundamental status. I further argue (albeit, in opposition to BPC) that particle and wave complementary concepts are on a different footing than other pairs of complementary concepts.
Non-abelian quantum Hall states -- exclusion statistics, K-matrices and duality
Ardonne, E.; Bouwknegt, P.; Schoutens, K.
2001-01-01
We study excitations in edge theories for non-abelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edge-electrons and edge-quasiholes, we
Which quantum theory must be reconciled with gravity? (And what does it mean for black holes?)
Lake, Matthew J
2016-01-01
We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic QFTs, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map between classical Poisson brackets and their associated commutators, such schemes give rise to quantum states obeying canonical dispersion relations, obtained by substituting the de Broglie relations into the relevant (classical) energy-momentum relation. In canonical QM, this yields a dispersion relation involving $\\hbar$ but not $c$, whereas the canonical relativistic dispersion relation involves both. Extending this logic to the canonical quantization of the gravitational field gives rise to loop quantum gravity, and a map between classical variables containing $G$ and $c$, and associated commutators involving $\\hbar$. This naturally defines a "wave-gravity duality", suggesting that a quantum wave packet describing {\\it self-gravitating matter} obeys a dispersion relation...
Quantum duality under the theta-exact Seiberg-Witten map
Martin, Carmelo P; You, Jiangyang
2016-01-01
We show that in the perturbative regime defined by the coupling constant, the theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with or without Supersymmetry-- gives an ordinary gauge theory which is, at the quantum level, dual to the former. We do so by using the on-shell DeWitt effective action and dimensional regularization. We explicitly compute the one-loop two-point function contribution to the on-shell DeWitt effective action of the ordinary U(1) theory furnished by the theta-exact Seiberg-Witten map. We find that the non-local UV divergences found in the propagator in the Feynman gauge all but disappear, so that they are not physically relevant. We also show that the quadratic noncommutative IR divergences are gauge-fixing independent and go away in the Supersymmetric version of the U(1) theory.
Quantum duality under the θ-exact Seiberg-Witten map
Martin, Carmelo P.; Trampetic, Josip; You, Jiangyang
2016-09-01
We show that in the perturbative regime defined by the coupling constant, the θ-exact Seiberg-Witten map applied to the noncommutative U(N) Yang-Mills — with or without Supersymmetry — gives an ordinary gauge theory which is, at the quantum level, dual to the former. We do so by using the on-shell DeWitt effective action and dimensional regularization. We explicitly compute the one-loop two-point function contribution to the on-shell DeWitt effective action of the ordinary U(1) theory furnished by the θ-exact Seiberg-Witten map. We find that the non-local UV divergences found in the propagator in the Feynman gauge all but disappear, so that they are not physically relevant. We also show that the quadratic noncommutative IR divergences are gauge-fixing independent and go away in the Supersymmetric version of the U(1) theory.
Prime Factorization in the Duality Computer
Institute of Scientific and Technical Information of China (English)
WANG Wan-Ying; SHANG Bin; WANG Chuan; LONG Gui-Lu
2007-01-01
We give algorithms to factorize large integers in the duality computer.We provide three duality algorithms for factorization based on a naive factorization method,the Shor algorithm in quantum computing,and the Fermat's method in classical computing.All these algorithms may be polynomial in the input size.
Abelian Duality and Abelian Wilson Loops
Zucchini, R
2003-01-01
We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological selection rules. Finally, we show that, to have manifest duality, one must assume the existence of twisted topological sectors besides the standard untwisted one.
Space-time duality and superduality
Burgess, C P; Kamela, M; Knutt-Wehlau, M E; Page, P; Quevedo, Fernando; Zebarjad, M
1999-01-01
We introduce a new class of duality symmetries amongst quantum field theories. The new class is based upon global space-time symmetries, such as Poincare invariance and supersymmetry, in the same way as the existing duality transformations are based on global internal symmetries. We illustrate these new duality transformations by dualizing several scalar and spin-half field theories in 1 + 1 space-time dimensions, involving non-supersymmetric as well as (1, 1) and (2, 2) supersymmetric models. For (2, 2) models the new duality transformations can interchange chiral and twisted chiral multiplets.
Emergence of Quantum Mechanics from a Sub-Quantum Statistical Mechanics
Grössing, Gerhard
2015-10-01
A research program within the scope of theories on "Emergent Quantum Mechanics" is presented, which has gained some momentum in recent years. Via the modeling of a quantum system as a non-equilibrium steady-state maintained by a permanent throughput of energy from the zero-point vacuum, the quantum is considered as an emergent system. We implement a specific "bouncer-walker" model in the context of an assumed sub-quantum statistical physics, in analogy to the results of experiments by Couder and Fort on a classical wave-particle duality. We can thus give an explanation of various quantum mechanical features and results on the basis of a "21st century classical physics", such as the appearance of Planck's constant, the Schrödinger equation, etc. An essential result is given by the proof that averaged particle trajectories' behaviors correspond to a specific type of anomalous diffusion termed "ballistic" diffusion on a sub-quantum level...
Quantum Fluctuations Of The Stress Tensor
Wu, C
2002-01-01
Quantum fluctuations of the stress tensor are important in many branches of physics, including the study of the validity of semiclassical gravity and the backreaction problem in stochastic semiclassical gravity. The geometry fluctuations induced by stress tensor fluctuations are important to understand quantum gravity and the problem of lightcone fluctuations. Stress tensor fluctuations also hold the key to understand fundamental physical effects like quantum fluctuations of radiation pressure, and that is crucial to the sensitivity of interferometers and the limitations on the detection of gravitational waves. Even the wave-particle duality of light can be better understood by the study of quantum fluctuations of thermal radiation. It is well known in quantum field theory that the expectation value of the energy density, which contains quadratic field operators (e.g. E2 and B2 in the electromagnatic field case), is divergent and can be renormalized simply by normal ordering, which is subtracting out the vac...
Dualities and emergent gravity: Gauge/gravity duality
de Haro, Sebastian
2017-08-01
In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as 'isomorphism', from the physics literature, cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; and I argue that this exhausts the possibilities for combining dualities and emergence (via coarse-graining). I apply this framework to gauge/gravity dualities, considering in detail three examples: AdS/CFT, Verlinde's scheme, and black holes. My main point about gauge/gravity dualities is that the theories involved, qua theories of gravity, must be background-independent. I distinguish two senses of background-independence: (i) minimalistic and (ii) extended. I argue that the former is sufficiently strong to allow for a consistent theory of quantum gravity; and that AdS/CFT is background-independent on this account; while Verlinde's scheme best fits the extended sense of background-independence. I argue that this extended sense should be applied with some caution: on pain of throwing the baby (general relativity) out with the bath-water (extended background-independence). Nevertheless, it is an interesting and potentially fruitful heuristic principle for quantum gravity theory construction. It suggests some directions for possible generalisations of gauge/gravity dualities. The interpretation of dualities is discussed; and the so-called 'internal' vs. 'external' viewpoints are articulated in terms of: (i) epistemic and metaphysical commitments; (ii) parts vs. wholes. I then analyse the emergence of gravity in gauge/gravity dualities in terms of the two available conceptualisations of emergence; and I show how emergence in AdS/CFT and in Verlinde's scenario differ from each other. Finally, I give a novel derivation of the Bekenstein-Hawking black hole entropy formula based on
From classical to quantum physics
Stehle, Philip
2017-01-01
Suitable for lay readers as well as students, this absorbing survey explores the twentieth-century transition from classical to quantum physics. Author Philip Stehle traces the shift in the scientific worldview from the work of Galileo, Newton, and Darwin to the modern-day achievements of Max Planck, Albert Einstein, Ernest Rutherford, Niels Bohr, and others of their generation. His insightful overview examines not only the history of quantum physics but also the ways that progress in the discipline changed our understanding of the physical world and forces of nature. This chronicle of the second revolution in the physical sciences conveys the excitement and suspense that new developments produced in the scientific community. The narrative ranges from the classical physics of the seventeenth-century to the emergence of quantum mechanics with the entrance of the electron, the rise of relativity theory, the development of atomic theory, and the recognition of wave-particle duality. Relevant mathematical details...
Unified relativistic physics from a standing wave particle model
Vera, R A
1995-01-01
An extremely simple and unified base for physics comes out by starting all over from a single postulate on the common nature of matter and stationary forms of radiation quanta. Basic relativistic, gravitational (G) and quantum mechanical properties of a standing wave particle model have been derived. This has been done from just dual properties of radiation's and strictly homogeneous relationships for nonlocal cases in G fields. This way reduces the number of independent variables and puts into relief (and avoid) important inhomogeneity errors of some G theories. It unifies and accounts for basic principles and postulates physics. The results for gravity depend on linear radiation properties but not on arbitrary field relations. They agree with the conventional tests. However they have some fundamental differences with current G theories. The particle model, at a difference of the conventional theories, also fixes well-defined cosmological and astrophysical models that are different from the rather convention...
Energy Technology Data Exchange (ETDEWEB)
Green, Daniel; /SLAC /Stanford U., Phys. Dept.; Lawrence, Albion; /Brandeis U.; McGreevy, John; /MIT, LNS; Morrison, David R.; /Duke U., CGTP /UC, Santa Barbara; Silverstein,; /SLAC /Stanford U., Phys. Dept.
2007-05-18
We show that string theory on a compact negatively curved manifold, preserving a U(1)b1 winding symmetry, grows at least b1 new effective dimensions as the space shrinks. The winding currents yield a ''D-dual'' description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b{sub 1}-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.
Wave-particle Interactions In Rotating Mirrors
Energy Technology Data Exchange (ETDEWEB)
Abraham J. Fetterman and Nathaniel J. Fisch
2011-01-11
Wave-particle interactions in E×B rotating plasmas feature an unusual effect: particles are diffused by waves in both potential energy and kinetic energy. This wave-particle interaction generalizes the alpha channeling effect, in which radio frequency waves are used to remove alpha particles collisionlessly at low energy. In rotating plasmas, the alpha particles may be removed at low energy through the loss cone, and the energy lost may be transferred to the radial electric field. This eliminates the need for electrodes in the mirror throat, which have presented serious technical issues in past rotating plasma devices. A particularly simple way to achieve this effect is to use a high azimuthal mode number perturbation on the magnetic field. Rotation can also be sustained by waves in plasmas without a kinetic energy source. This type of wave has been considered for plasma centrifuges used for isotope separation. Energy may also be transferred from the electric field to particles or waves, which may be useful for ion heating and energy generation.
Duality Symmetry and Soldering in Different Dimensions
Banerjee, R
1997-01-01
We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in four dimensions. In all cases there are two such distinct actions. Furthermore, by soldering these distinct actions in any dimension a master action is obtained which is duality invariant under a much bigger set of symmetries than is usually envisaged. The concept of swapping duality is introduced and its implications are discussed. The effects of coupling to gravity are also elaborated. Finally, the extension of the analysis for arbitrary dimensions is indicated.
Pointlessness and dangerousness of the postulates of quantum mechanics
Moret-Bailly, J
2001-01-01
The formalism of quantum mechanics produces spectacular results, but its rules, its parameters are empirical, either deduced from classical physics, or from experimental results rather than from the postulates. Thus, quantum mechanics is purely phenomenological; for instance, the computation of the eigenvalues of the energy is generally a simple interpolation in the discrete space of the quantum numbers. The attempts to show that quantum electrodynamics is more precise than classical electrodynamics are based on wrong computations. The lack of paradoxes in the classical theory, the appearance of classical, true interpretations of the wave-particle duality justify the criticism of Ehrenfest and Einstein. The obscurity of the quantum concepts leads to wrong conclusions that handicap the development of physics. Just as building a laser was considered absurd before the first maser worked, the concept of photon leads to deny a type of coherent Raman scattering necessary to understand some redshifts of spectra in a...
Phase sorting wave-particle correlator
Kletzing, C. A.; LaBelle, J.; Bounds, S. R.; Dolan, J.; Kaeppler, S. R.; Dombrowski, M.
2017-02-01
Wave-particle correlations, particularly of Langmuir waves and electrons, have been the subject of significant interest extending back to the 1970s. Often, these correlations have been simply observing modulation of the electrons at the plasma frequency with no phase resolution. The first phase-resolving correlators were developed at UC Berkeley in the late 1980s and reported by Ergun in the early 1990s. A design is presented which further improves on phase resolution in correlations of Langmuir waves and electrons with phase resolution of 22.5°. In this technique, a phase-locked loop (PLL) is used to lock onto the wave and subdivide the phase. Electrons are sorted on-the-fly as they arrive into the phase bins. Discussed are details of accurate timing, testing, and calibration of this system as well as results from rocket flights in which statistically significant phase correlations have been observed.
Quantum mechanics: Myths and facts
Nikolic, H
2006-01-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
Quantum Mechanics: Myths and Facts
Nikolić, Hrvoje
2007-11-01
A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
A proposed physical analog for a quantum probability amplitude
Boyd, Jeffrey
What is the physical analog of a probability amplitude? All quantum mathematics, including quantum information, is built on amplitudes. Every other science uses probabilities; QM alone uses their square root. Why? This question has been asked for a century, but no one previously has proposed an answer. We will present cylindrical helices moving toward a particle source, which particles follow backwards. Consider Feynman's book QED. He speaks of amplitudes moving through space like the hand of a spinning clock. His hand is a complex vector. It traces a cylindrical helix in Cartesian space. The Theory of Elementary Waves changes direction so Feynman's clock faces move toward the particle source. Particles follow amplitudes (quantum waves) backwards. This contradicts wave particle duality. We will present empirical evidence that wave particle duality is wrong about the direction of particles versus waves. This involves a paradigm shift; which are always controversial. We believe that our model is the ONLY proposal ever made for the physical foundations of probability amplitudes. We will show that our ``probability amplitudes'' in physical nature form a Hilbert vector space with adjoints, an inner product and support both linear algebra and Dirac notation.
Hewson, S F
1996-01-01
We investigate non-abelian gaugings of WZNW models. When the gauged group is semisimple we are able to present exact formulae for the dual conformal field theory, for all values of the level k. The results are then applied to non-abelian target space duality in string theory, showing that the standard formulae are quantum mechanically well defined in the low energy limit if the gauged group is semisimple.
The quantum divide why Schrödinger's cat is either dead or alive
Gerry, Christopher C
2013-01-01
Using a selection of key experiments performed over the past 30 years or so, we present a discussion of the strikingly counter-intuitive phenomena of the quantum world that defy explanation in terms of everyday "common sense" reasoning, and we provide the corresponding quantum mechanical explanations with a very elementary use of associated formalism. Most, but certainly not all, of the experiments we describe are optical experiments involving a very small number of photons (particles of light). We begin with experiments on the wave-particle duality of electrons, proceed to experiments on the particle nature of light and single photon interference, delayed choice experiments and interaction-free detection, then go on to experiments involving the interference of two photons, quantum entanglement and Bell's Theorem, quantum teleportation, large-scale quantum effects and the divide between the classical and quantum worlds, addressing the question as to whether or not there is such a divide.
Uncertainty relations and approximate quantum error correction
Renes, Joseph M.
2016-09-01
The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the outcome. Two variants are possible: either Alice tells Bob which observable she measured, or he has to furnish guesses for both cases. Here I derive uncertainty relations for both, formulated directly in terms of Bob's guessing probabilities. For the former these relate to the entanglement that can be recovered by action on Bob's system alone. This gives an explicit quantum circuit for approximate quantum error correction using the guessing measurements for "amplitude" and "phase" information, implicitly used in the recent construction of efficient quantum polar codes. I also find a relation on the guessing probabilities for the latter game, which has application to wave-particle duality relations.
Kirchbach, M.; Compean, C. B.
2016-07-01
The real parts of the complex squared energies defined by the resonance poles of the transfer matrix of the Pöschl-Teller barrier, are shown to equal the squared energies of the levels bound within the trigonometric Scarf well potential. By transforming these potentials into parts of the Laplacians describing free quantum motions on the mutually orthogonal open-time-like hyperbolic-, and closed-space-like spherical geodesics on the conformally invariant de Sitter space-time, dS4, the conformal symmetries of these interactions are revealed. On dS4 the potentials under consideration naturally relate to interactions within colorless two-body systems and to cusped Wilson loops. In effect, with the aid of the dS4 space-time as unifying geometry, a conformal symmetry based bijective correspondence (duality) between bound and resonant meson spectra is established at the quantum mechanics level and related to confinement understood as color charge neutrality. The correspondence allows to link the interpretation of mesons as resonance poles of a scattering matrix with their complementary description as states bound by an instantaneous quark interaction and to introduce a conformal symmetry based classification scheme of mesons. As examples representative of such a duality we organize in good agreement with data 71 of the reported light flavor mesons with masses below ˜ 2350 MeV into four conformal families of particles placed on linear f0, π , η , and a0 resonance trajectories, plotted on the ℓ/ M plane. Upon extending the sec2 χ by a properly constructed conformal color dipole potential, shaped after a tangent function, we predict the masses of 12 "missing" mesons. We furthermore notice that the f0 and π trajectories can be viewed as chiral partners, same as the η and a0 trajectories, an indication that chiral symmetry for mesons is likely to be realized in terms of parity doubled conformal multiplets rather than, as usually assumed, only in terms of parity
Energy Technology Data Exchange (ETDEWEB)
Kirchbach, M. [UASLP, Instituto de Fisica, San Luis Potosi (Mexico); Compean, C.B. [Instituto Tecnologico de San Luis Potosi, San Luis Potosi (Mexico)
2016-07-15
The real parts of the complex squared energies defined by the resonance poles of the transfer matrix of the Poeschl-Teller barrier, are shown to equal the squared energies of the levels bound within the trigonometric Scarf well potential. By transforming these potentials into parts of the Laplacians describing free quantum motions on the mutually orthogonal open-time-like hyperbolic-, and closed-space-like spherical geodesics on the conformally invariant de Sitter space-time, dS{sub 4}, the conformal symmetries of these interactions are revealed. On dS{sub 4} the potentials under consideration naturally relate to interactions within colorless two-body systems and to cusped Wilson loops. In effect, with the aid of the dS{sub 4} space-time as unifying geometry, a conformal symmetry based bijective correspondence (duality) between bound and resonant meson spectra is established at the quantum mechanics level and related to confinement understood as color charge neutrality. The correspondence allows to link the interpretation of mesons as resonance poles of a scattering matrix with their complementary description as states bound by an instantaneous quark interaction and to introduce a conformal symmetry based classification scheme of mesons. As examples representative of such a duality we organize in good agreement with data 71 of the reported light flavor mesons with masses below ∝ 2350 MeV into four conformal families of particles placed on linear f{sub 0}, π, η, and a{sub 0} resonance trajectories, plotted on the l/M plane. Upon extending the sec{sup 2} χ by a properly constructed conformal color dipole potential, shaped after a tangent function, we predict the masses of 12 ''missing'' mesons. We furthermore notice that the f{sub 0} and π trajectories can be viewed as chiral partners, same as the η and a{sub 0} trajectories, an indication that chiral symmetry for mesons is likely to be realized in terms of parity doubled conformal
Spectral Duality in Integrable Systems from AGT Conjecture
Mironov, A; Zenkevich, Y; Zotov, A
2012-01-01
We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N) Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrodinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2x2 and NxN representations of the Toda chain and the famous AHH duality.
Generalized complex geometry and T-duality
Cavalcanti, Gil R
2011-01-01
We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically distinct torus bundles, and prescribes a method for transporting geometrical structures between them. We describe how this relation may be understood as a Courant algebroid isomorphism between the spaces in question. This then allows us to transport Dirac structures, generalized Riemannian metrics, generalized complex and generalized Kahler structures, extending the "Buscher rules" well-known to physicists. Finally, we re-interpret T-duality as a Courant reduction, and explain that T-duality between generalized complex manifolds may be viewed as a generalized complex submanifold (D-brane) of the product, in a way that establishes a direct analogy with the Fourier-Mukai transform.
Review of lattice supersymmetry and gauge-gravity duality
Energy Technology Data Exchange (ETDEWEB)
Joseph, Anosh [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cambridge Univ. (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics (DAMTP)
2015-12-15
We review the status of recent investigations on validating the gauge-gravity duality conjecture through numerical simulations of strongly coupled maximally supersymmetric thermal gauge theories. In the simplest setting, the gauge-gravity duality connects systems of D0-branes and black hole geometries at finite temperature to maximally supersymmetric gauged quantum mechanics at the same temperature. Recent simulations show that non-perturbative gauge theory results give excellent agreement with the quantum gravity predictions, thus proving strong evidence for the validity of the duality conjecture and more insight into quantum black holes and gravity.
T-duality trivializes bulk-boundary correspondence
Mathai, Varghese
2015-01-01
Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that T-duality trivializes the bulk-boundary correspondence.
Lab-Tutorials for teaching quantum physics (Lab-Tutorials fuer den Quantenphysik Unterricht)
Wittmann, M C
2006-01-01
English abstract: In the "Intuitive Quantum Physics" course, we use graphical interpretations of mathematical equations and qualitative reasoning to develop and teach a simplified model of quantum physics. Our course contains three units: Wave physics, Development of a conceptual toolbox, and quantum physics. It also contains three key themes: wave-particle duality, the Schroedinger equation, and tunneling of quantum particles. Students learn most new material in lab-tutorials in which students work in small groups (3 to 3 people) on specially designed worksheets. Lecture reinforces the lab-tutorial content and focuses more on issues about the nature of science. Data show that students are able to learn some of the most difficult concepts in the course, and also that students learn to believe that there is a conceptually accessible structure to the physics in the course. German abstract: Im Kurs "Intuitive Quantum Physics" werden graphische Interpretationen mathematischer Gleichungen und qualitatives Denken d...
Aspects of Duality in Cosmology
J., Gabriele Gionti S
2016-01-01
In the first part of this article, given the intent to stay at a popular level, it has been introduced and explained briefly basic concepts of Einstein's General Relativity, Dark Matter, Dark Energy, String Theory, Quantum Gravity and Extended Theories of Gravity. The core of this research is based on selecting a class of f(R) theories of gravity, which exhibits scale factor duality transformations. The starting point of this theory is the effective theory of gravity derived from Bosonic String Theory, which is called tree level effective theory of gravity. It is shown that this theory can be cast in a class of f(R) theories of gravity (modified theories of Einstein's General Relativity). It is imposed that FLRW metric be solution of this class of $f(R)$ theories, and, using the Noether symmetry approach, it is found that the cosmological model has scale factor duality like the Pre-Big Bang cosmology of Gasperini and Veneziano.
Seeing Wave-Particle Superposition with Cavity Input-Output Process
Min, Rui
2016-10-01
We present an experimental protocol to implement quantum delay-choice experiment in the context of cavity input-output process. In our protocol, the single-atom is employed as ancillary qubit to test the wave-particle feature of a single photon. With the cavity input-output process, we show that the controlled phase shift gate between single-atom and single-photon can be naturally used to generate the controlled Hadamard gate, which thus allows us to construct the quantum circuit for realizing the quantum delay-choice experiment. We also demonstrate the photonic wavelike and particlelike states can be simultaneously observed in our platform. Our protocol may open a new prospect using cavity quantum electrodynamics system to study some counterintuitive fundamental phenomenons in quantum mechanics.
Duality in vector optimization
Bot, Radu Ioan
2009-01-01
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the s
Test of mutually unbiased bases for six-dimensional photonic quantum systems.
D'Ambrosio, Vincenzo; Cardano, Filippo; Karimi, Ebrahim; Nagali, Eleonora; Santamato, Enrico; Marrucci, Lorenzo; Sciarrino, Fabio
2013-09-25
In quantum information, complementarity of quantum mechanical observables plays a key role. The eigenstates of two complementary observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low as six, the identification of a maximal set of MUBs remains an open problem, although there is strong numerical evidence that no more than three simultaneous MUBs do exist. Here, by exploiting a newly developed holographic technique, we implement and test different sets of three MUBs for a single photon six-dimensional quantum state (a "qusix"), encoded exploiting polarization and orbital angular momentum of photons. A close agreement is observed between theory and experiments. Our results can find applications in state tomography, quantitative wave-particle duality, quantum key distribution.
ReleQuant – Improving teaching and learning in quantum physics through educational design research
Directory of Open Access Journals (Sweden)
Berit Bungum
2015-05-01
Full Text Available Quantum physics and relativity are demanding for teachers and students, but have the potential for students to experience physics as fascinating and meaningful. Project ReleQuant engaged in educational design research to improve teaching and learning in these topics in Norwegian upper secondary schools. The paper focuses on the first cycle of development of a teaching module on quantum physics and how design principles were developed. We construct the design principles by reviewing relevant research literature and conducting three pilot studies. The process resulted in the following principles for designing the quantum physics teaching module: 1 clarify how quantum physics breaks with classical physics; 2 use simulations of phenomena that cannot be experienced directly; 3 provide students to use written and oral language; 4 address and discuss wave-particle duality and the uncertainty
Electromagnetic duality anomaly in curved spacetimes
Agullo, I; Navarro-Salas, J
2016-01-01
The source-free Maxwell action is invariant under electric-magnetic duality rotations in arbitrary spacetimes. This leads to a conserved classical Noether charge. We show that this conservation law is broken at the quantum level in presence of a background classical gravitational field with a non-trivial Chern-Pontryagin invariant, in a parallel way to the chiral anomaly for massless Dirac fermions. Among the physical consequences, the net polarization of the quantum electromagnetic field is not conserved.
Extending dualities to trialities deepens the foundations of dynamics
Smolin, Lee
2015-01-01
Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, and show how breaking its natural triality symmetry by imposing different compactifications yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born's duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.
Abelian Duality on Globally Hyperbolic Spacetimes
Becker, Christian; Benini, Marco; Schenkel, Alexander; Szabo, Richard J.
2017-01-01
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.
Wave-particle interactions in the outer radiation belts
Agapitov, O V; Artemyev, A V; Mourenas, D; Krasnoselskikh, V V
2015-01-01
Data from the Van Allen Probes have provided the first extensive evidence of non-linear (as opposed to quasi-linear) wave-particle interactions in space with the associated rapid (fraction of a bounce period) electron acceleration to hundreds of keV by Landau resonance in the parallel electric fields of time domain structures (TDS) and very oblique chorus waves. The experimental evidence, simulations, and theories of these processes are discussed. {\\bf Key words:} the radiation belts, wave-particle interaction, plasma waves and instabilities
Directory of Open Access Journals (Sweden)
Reiter E. S.
2014-04-01
Full Text Available A famous beam-split coincidence test of the photon model was performed with -rays instead of visible light. A similar test was performed to split -rays. In both tests, co- incidence rates greatly exceed chance, leading to an unquantum effect. In contradiction to quantum theory and the photon model, these new results are strong evidence of the long abandoned accumulation hypothesis, also known as the loading theory. Attention is drawn to assumptions applied to past key experiments that led to quantum mechan- ics. The history of the loading theory is outlined, and a few key experiment equations are derived, now free of wave-particle duality. Quantum theory usually works because there is a subtle difference between quantized and thresholded absorption.
A quantum delayed choice experiment
Peruzzo, Alberto; Brunner, Nicolas; Popescu, Sandu; O'Brien, Jeremy L
2012-01-01
Quantum systems exhibit particle-like or wave-like behaviour depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics, and is fully captured in Wheeler's famous delayed choice gedanken experiment. In this variant of the double slit experiment, the observer chooses to test either the particle or wave nature of a photon after it has passed through the slits. Here we report on a quantum delayed choice experiment, based on a quantum controlled beam-splitter, in which both particle and wave behaviours can be investigated simultaneously. The genuinely quantum nature of the photon's behaviour is tested via a Bell inequality, which here replaces the delayed choice of the observer. We observe strong Bell inequality violations, thus showing that no model in which the photon knows in advance what type of experiment it will be confronted by, hence behaving either as a particle or as wave, can account for the experimental data.
Was Einstein Wrong on Quantum Physics?
Bhaumik, Mani
2015-01-01
Einstein is considered by many as the father of quantum physics in some sense. Yet there is an unshakable view that he was wrong on quantum physics. Although it may be a subject of considerable debate, the core of his allegedly wrong demurral was the insistence on finding an objective reality underlying the manifestly bizarre behavior of quantum objects. The uncanny wave-particle duality of a quantum particle is a prime example. In view of the latest developments, particularly in quantum field theory, objections of Einstein are substantially corroborated. Careful investigation suggests that a travelling quantum particle is a holistic wave packet consisting of an assemblage of irregular disturbances in quantum fields. It acts as a particle because only the totality of all the disturbances in the wave packet yields the energy momentum with the mass of a particle, along with its other conserved quantities such as charge and spin. Thus the wave function representing a particle is not just a fictitious mathematica...
Holographic duality in condensed matter physics
Zaanen, Jan; Sun, Ya-Wen; Schalm, Koenraad
2015-01-01
A pioneering treatise presenting how the new mathematical techniques of holographic duality unify seemingly unrelated fields of physics. This innovative development morphs quantum field theory, general relativity and the renormalisation group into a single computational framework and this book is the first to bring together a wide range of research in this rapidly developing field. Set within the context of condensed matter physics and using boxes highlighting the specific techniques required, it examines the holographic description of thermal properties of matter, Fermi liquids and superconductors, and hitherto unknown forms of macroscopically entangled quantum matter in terms of general relativity, stars and black holes. Showing that holographic duality can succeed where classic mathematical approaches fail, this text provides a thorough overview of this major breakthrough at the heart of modern physics. The inclusion of extensive introductory material using non-technical language and online Mathematica not...
Maxwell Duality, Lorentz Invariance, and Topological Phase
Dowling, J P; Franson, J D; Dowling, Jonathan P.; Williams, Colin P.
1999-01-01
We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three phenomena. We also elucidate Lorentz transformations that allow these effects to be understood in an intuitive fashion in the rest frame of the moving quantum particle. Finally, we propose a realistic set up for measuring and interpreting the He-McKellar-Wilkens phase directly in an experiment.
From Koszul duality to Poincaré duality
Indian Academy of Sciences (India)
Michel Dubois-Violette
2012-06-01
We discuss the notion of Poincaré duality for graded algebras and its connections with the Koszul duality for quadratic Koszul algebras. The relevance of the Poincaré duality is pointed out for the existence of twisted potentials associated to Koszul algebras as well as for the extraction of a good generalization of Lie algebras among the quadratic-linear algebras.
Duality and 'particle' democracy
Castellani, Elena
2017-08-01
Weak/strong duality is usually accompanied by what seems a puzzling ontological feature: the fact that under this kind of duality what is viewed as 'elementary' in one description gets mapped to what is viewed as 'composite' in the dual description. This paper investigates the meaning of this apparent 'particle democracy', as it has been called, by adopting an historical approach. The aim is to clarify the nature of the correspondence between 'dual particles' in the light of a historical analysis of the developments of the idea of weak/strong duality, starting with Dirac's electric-magnetic duality and its successive generalizations in the context of (Abelian and non-Abelian) field theory, to arrive at its first extension to string theory. This analysis is then used as evidential basis for discussing the 'elementary/composite' divide and, after taking another historical detour by analyzing an instructive analogy case (DHS duality and related nuclear democracy), drawing some conclusions on the particle-democracy issue.
Gravitation and Duality Symmetry
D'Andrade, V C; Pereira, J G
2005-01-01
By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation does not present duality symmetry, there is a particular theory in which this symmetry is present. This theory is a self dual (or anti-self dual) teleparallel gravity in which, owing to the fact that it does not contribute to the gravitational interaction of fermions, the purely tensor part of torsion is assumed to vanish. The corresponding fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory will probably be much more amenable to renormalization than teleparallel gravity or general relativity. Although obtained in the context of teleparallel gravity, these results must also be true for general relativity.
Homomorphisms of quantum groups
Meyer, Ralf; Woronowicz, Stanisław Lech
2010-01-01
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups, respectively.
Kinetic equation for nonlinear resonant wave-particle interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
Energy Technology Data Exchange (ETDEWEB)
Brown, T.W.
2010-11-15
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super- Yang-Mills. It is dual to another complex matrix model where the couplings of the first model are encoded in the Kontsevich-like variables of the second. The duality between the theories is mirrored by the duality of their Feynman diagrams. Analogously to the Hermitian Kontsevich- Penner model, the correlation functions of the second model can be written as sums over discrete points in subspaces of the moduli space of punctured Riemann surfaces. (orig.)
Allowable Generalized Quantum Gates
Institute of Scientific and Technical Information of China (English)
LONG Gui-Lu; LIU Yang; WANG Chuan
2009-01-01
In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form Σ(d-1)(i=0)piUi, and the Pi's are complex numbers with module less or equal to I and constrained by |Σipi|≤1.
Bosonisation and Duality Symmetry in the Soldering Formalism
Banerjee, R
1998-01-01
We develop a technique that solders the dual aspects of some symmetry. Using this technique it is possible to combine two theories with such symmetries to yield a new effective theory. Some applications in two and three dimensional bosonisation are discussed. In particular, it is shown that two apparently independent three dimensional massive Thirring models with same coupling but opposite mass signatures, in the long wavelegth limit, combine by the process of bosonisation and soldering to yield an effective massive Maxwell theory. Similar features also hold for quantum electrodynamics in three dimensions. We also provide a systematic derivation of duality symmetric actions and show that the soldering mechanism leads to a master action which is duality invariant under a bigger set of symmetries than is usually envisaged. The concept of duality swapping is introduced and its implications are analysed. The example of electromagnetic duality is discussed in details.
A "fair sampling" perspective on an apparent violation of duality
Bolduc, Eliot; Miatto, Filippo M; Leuchs, Gerd; Boyd, Robert W
2014-01-01
In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that "the simultaneous observation of wave and particle behavior is prohibited". [M. O. Scully, B.-G. Englert, and H. Walther. Nature, 351:111-116, 1991.] emphasized the importance of additional degrees of freedom in the context of complementarity. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work contributes to the explanation of previous experimental apparent violations of duality [R. Menzel, D. Puhlmann, A. Heuer, and W. P. Schleich. Proc. Natl. Acad. Sci., 109(24):9314-9319, 2012.] and opens up the way for novel experimental tests of duality.
On-chip interaction-free measurements via the quantum Zeno effect
Ma, Xiao-song; Schuck, Carsten; Fong, King Y; Jiang, Liang; Tang, Hong X
2014-01-01
Although interference is a classical-wave phenomenon, the superposition principle, which underlies interference of individual particles, is at the heart of quantum physics. An interaction-free measurements (IFM) harnesses the wave-particle duality of single photons to sense the presence of an object via the modification of the interference pattern, which can be accomplished even if the photon and the object haven't interacted with each other. By using the quantum Zeno effect, the efficiency of an IFM can be made arbitrarily close to unity. Here we report an on-chip realization of the IFM based on silicon photonics. We exploit the inherent advantages of the lithographically written waveguides: excellent interferometric phase stability and mode matching, and obtain multipath interference with visibility above 98%. We achieved a normalized IFM efficiency up to 68.2%, which exceeds the 50% limit of the original IFM proposal.
Duality and conformal twisted boundaries in the Ising model
Grimm, U
2002-01-01
There has been recent interest in conformal twisted boundary conditions and their realisations in solvable lattice models. For the Ising and Potts quantum chains, these amount to boundary terms that are related to duality, which is a proper symmetry of the model at criticality. Thus, at criticality, the duality-twisted Ising model is translationally invariant, similar to the more familiar cases of periodic and antiperiodic boundary conditions. The complete finite-size spectrum of the Ising quantum chain with this peculiar boundary condition is obtained.
Geometric Constraints from Subregion Duality Beyond the Classical Regime
Akers, Chris; Leichenauer, Stefan; Levine, Adam
2016-01-01
Subregion duality in AdS/CFT implies certain constraints on the geometry: entanglement wedges must contain causal wedges, and nested boundary regions must have nested entanglement wedges. We elucidate the logical connections between these statements and the Quantum Focussing Conjecture, Quantum Null Energy Condition, Boundary Causality Condition, and Averaged Null Energy Condition. Our analysis does not rely on the classical limit of bulk physics, but instead works to all orders in \\(G\\hbar \\sim 1/N\\). This constitutes a nontrivial check on the consistency of subregion duality, entanglement wedge reconstruction, and holographic entanglement entropy beyond the classical regime.
Spectral dualities in XXZ spin chains and five dimensional gauge theories
Mironov, A; Runov, B; Zenkevich, Y; Zotov, A
2013-01-01
Motivated by recent progress in the study of supersymmetric gauge theories we propose a very compact formulation of spectral duality between XXZ spin chains. The action of the quantum duality is given by the Fourier transform in the spectral parameter. We investigate the duality in various limits and, in particular, prove it for q-->1, i.e. when it reduces to the XXX/Gaudin duality. We also show that the universal difference operators are given by the normal ordering of the classical spectral curves.
Intrinsic periodicity: the forgotten lesson of quantum mechanics
Dolce, Donatello
2013-01-01
Wave-particle duality, together with the concept of elementary particles, was introduced by de Broglie in terms of intrinsically "periodic phenomena". However, after nearly 90 years, the physical origin of such undulatory mechanics remains unrevealed. We propose a natural realization of the de Broglie "periodic phenomenon" in terms of harmonic vibrational modes associated to space-time periodicities. In this way we find that, similarly to a vibrating string or a particle in a box, the intrinsic recurrence imposed as a constraint to elementary particles represents a fully consistent quantization condition. The resulting classical cyclic dynamics formally match ordinary relativistic Quantum Mechanics in both the canonical and Feynman formulations. Interactions are introduced in a geometrodynamical way, similarly to general relativity, by simply considering that variations of kinematical state can be equivalently described in terms of modulations of space-time recurrences, as known from undulatory mechanics. We ...
Dislocations in the Spacetime Continuum: Framework for Quantum Physics
Directory of Open Access Journals (Sweden)
Millette P. A.
2015-10-01
Full Text Available This paper provides a framework for the physical description of physical processes at the quantum level based on dislocations in the spacetime continuum within STCED (Spacetime Continuum Elastodynamics. In this framework, photon and particle self- energies and interactions are mediated by the strain energy density of the dislocations, replacing the role played by virtual particles in QED. We postulate that the spacetime continuum has a granularity characterized by a length b 0 corresponding to the smallest STC elementary Burgers dislocation-displacement vector. Screw dislocations corre- sponding to transverse displacements are identified with photons, and edge dislocations corresponding to longitudinal displacements are identified with particles. Mixed dislo- cations give rise to wave-particle duality. The strain energy density of the dislocations are calculated and proposed to explain the QED problem of mass renormalization.
Duality group actions on fermions
Pantev, Tony; Sharpe, Eric
2016-11-01
In this short paper we look at the action of T-duality and string duality groups on fermions, in maximally-supersymmetric theories and related theories. Briefly, we argue that typical duality groups such as SL(2 , ℤ) have sign ambiguities in their actions on fermions, and propose that pertinent duality groups be extended by ℤ2, to groups such as the metaplectic group. Specifically, we look at duality groups arising from mapping class groups of tori in M theory compactifications, T-duality, ten-dimensional type IIB S-duality, and (briefly) four-dimensional N = 4 super Yang-Mills, and in each case, propose that the full duality group is a nontrivial ℤ2 extension of the duality group acting on bosonic degrees of freedom, to more accurately describe possible actions on fermions. We also walk through U-duality groups for toroidal compactifications to nine, eight, and seven dimensions, which enables us to perform cross-consistency tests of these proposals.
Duality group actions on fermions
Pantev, T
2016-01-01
In this short paper we look at the action of T-duality and string duality groups on fermions, in maximally-supersymmetric theories and related theories. Briefly, we argue that typical duality groups such as SL(2,Z) have sign ambiguities in their actions on fermions, and propose that pertinent duality groups be extended by Z_2, to groups such as the metaplectic group. Specifically, we look at duality groups arising from mapping class groups of tori in M theory compactifications, T-duality, ten-dimensional type IIB S-duality, and (briefly) four-dimensional N=4 super Yang-Mills, and in each case, propose that the full duality group is a nontrivial Z_2 extension of the duality group acting on bosonic degrees of freedom, to more accurately describe possible actions on fermions. We also walk through U-duality groups for toroidal compactifications to nine, eight, and seven dimensions, which enables us to perform cross-consistency tests of these proposals.
Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna
2017-06-01
In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman's sum over paths approach in the Italian high school. Our study focuses on students' understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle. In view of recent research reporting the fragmentation of students' mental models of quantum concepts after initial instruction, we collected and analyzed data using the assessment tools provided by knowledge integration theory. Our results on the group of n =14 students who performed the final test indicate that the functional explanation of wave particle duality provided by the sum over paths approach may be effective in leading students to build consistent mental models of quantum objects, and in providing them with a unified perspective on both the photon and the electron. Results on the uncertainty principle are less clear cut, as the improvements over traditional instruction appear less significant. Given the low number of students in the sample, this work should be interpreted as a case study, and we do not attempt to draw definitive conclusions. However, our study suggests that (i) the sum over paths approach may deserve more attention from researchers and educators as a possible route to introduce basic concepts of quantum physics in high school, and (ii) more research should be focused not only on the correctness of students' mental models on individual concepts, but also on the ability of students to connect different ideas and experiments related to quantum theory in an organized whole.
Subdifferentials with respect to dualities
Energy Technology Data Exchange (ETDEWEB)
Martinez-Legaz, J.E.; Singer, I.
1994-12-31
Let X and W be two sets. We introduce and study the subdifferential of an extended real valued function defined on X at a point, with respect to a duality from the set of functions on X into the set of functions on W (by a duality we mean a mapping transforming infima into suprema). We also consider some particular cases as, e.g., when the duality is a (Fenchel-Moreau) conjugation.
Finite Temperature Maps in Vector/Higher Spin Duality
Jevicki, Antal; Suzuki, Kenta; Yoon, Junggi
We discuss the question of reconstructing higher spin bulk fields from finite temperature N-component vector models. This is done in the framework of thermofield quantum theory at Large N. A bi-local construction of connected dual space-times is accomplished, and issues related to the implementation of domain duality are discussed.
On domain-wall/QFT dualities in various dimensions
Behrndt, Klaus; Bergshoeff, Eric; Halbersma, Rein; Schaar, Jan Pieter van der
1999-01-01
We investigate domain-wall/quantum field-theory correspondences in various dimensions. Our general analysis covers not only the well studied cases in 10 and 11 dimensions, but also enables us to discuss new cases like a type I/heterotic 6-brane in 10 dimensions and domain-wall dualities in lower
Comparing dualities and gauge symmetries
De Haro, Sebastian; Teh, Nicholas; Butterfield, Jeremy N.
2017-08-01
We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the 'flavour' that two dual theories are 'closer in content' than you might think. For both points, we adopt a simple conception of a duality as an 'isomorphism' between theories: more precisely, as appropriate bijections between the two theories' sets of states and sets of quantities. The first point (Section 3) is that this conception of duality meshes with two dual theories being 'gauge related' in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be 'gauge'. The second point (Sections 4-6) is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries (in the physical sense of symmetry transformations that are spacetime-dependent) to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory.
Group dualities, T-dualities, and twisted K-theory
Mathai, Varghese
2016-01-01
This paper explores further the connection between Langlands duality and T-duality for compact simple Lie groups, which appeared in work of Daenzer-Van Erp and Bunke-Nikolaus. We show that Langlands duality gives rise to isomorphisms of twisted K-groups, but that these K-groups are trivial except in the simplest case of SU(2) and SO(3). Along the way we compute explicitly the map on $H^3$ induced by a covering of compact simple Lie groups, which is either 1 or 2 depending in a complicated way on the type of the groups involved. We also give a new method for computing twisted K-theory using the Segal spectral sequence, giving simpler computations of certain twisted K-theory groups of compact Lie groups relevant for D-brane charges in WZW theories and rank-level dualities. Finally we study a duality for orientifolds based on complex Lie groups with an involution.
Grimm, U; Grimm, Uwe; Schuetz, Gunter M.
1993-01-01
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c<1 including the unitary and non-unitary minimal series. Taking into account the half-integer angular momentum sectors - which correspond to chains with an odd number of sites - in many cases leads to new spinor operators appearing in the projected systems. These new sectors in the XXZ chain correspond to a new type of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however diffe...
Comparing Dualities and Gauge Symmetries
De Haro, Sebastian; Butterfield, Jeremy N
2016-01-01
We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the 'flavour' that two dual theories are 'closer in content' than you might think. For both points, we adopt a simple conception of a duality as an 'isomorphism' between theories: more precisely, as appropriate bijections between the two theories' sets of states and sets of quantities. The first point (Section 3) is that this conception of duality meshes with two dual theories being 'gauge related' in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be 'gauge'. The second point (Sections 4, 5 and 6) is much more specific. We give a result about gauge/gravity duality that shows its rela...
Hewson, S F
1997-01-01
We discuss the application of T-duality to massive supersymmetric sigma models. In particular (1,1) supersymmetric models with off-shell central charges reveal an interesting structure. The T-duality transformations of the BPS states of these theories are also discussed and an explicit example of Q-kinks is given.
Characteristics of Wave-Particle Interaction in a Hydrogen Plasma
Institute of Scientific and Technical Information of China (English)
HE Hui-Yong; CHEN Liang-Xu; LI Jiang-Fan
2008-01-01
We study the characteristics of cyclotron wave-particle interaction in a typical hydrogen plasma. The numerical calculations of minimum resonant energy Emin, resonant wave frequency w, and pitch angle diffusion coefficient Dαα for interactions between R-mode/L-mode and electrons/protons are presented. It is found that Emin decreases with ω for R-mode/electron, L-mode/proton and L-mode/electron interactions, but increase with w for R-mode/proton interaction. It is shown that both R-mode and L-mode waves can efficiently scatter energetic (10 keV～100 keV) electrons and protons and cause precipitation loss at L=4, indicating that perhaps waveparticle interaction is a serious candidate for the ring current decay.
Probabilistic approach to nonlinear wave-particle resonant interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2017-02-01
In this paper we provide a theoretical model describing the evolution of the charged-particle distribution function in a system with nonlinear wave-particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the particle distribution. In this equation, effects of charged-particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test-particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed.
Duality and Dimensional Reduction of 5D BF Theory
Amoretti, Andrea; Caruso, Giacomo; Maggiore, Nicola; Magnoli, Nicodemo
2013-01-01
A planar boundary introduced \\`a la Symanzik in the 5D topological BF theory, with the only requirement of locality and power counting, allows to uniquely determine a gauge invariant, non topological 4D Lagrangian. The boundary condition on the bulk fields is interpreted as a duality relation for the boundary fields, in analogy with the fermionization duality which holds in the 3D case. This suggests that the 4D degrees of freedom might be fermionic, although starting from a bosonic bulk theory. The method we propose to dimensionally reduce a Quantum Field Theory and to identify the resulting degrees of freedom can be applied to a generic spacetime dimension.
Tinkertoys for Gaiotto Duality
Chacaltana, Oscar
2010-01-01
We describe a procedure for classifying N=2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A_{N-1} SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N=5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian N=2 SCFTs.
Electromagnetic Duality and Entanglement Anomalies
Donnelly, William; Wall, Aron
2016-01-01
Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of freedom rearranged in a nonlocal fashion. We study this phenomenon in the context of the electromagnetic duality of abelian $p$-forms. A careful calculation of the duality anomaly on an arbitrary $D$-dimensional manifold shows that the effective actions agree exactly in odd $D$, while in even $D$ they differ by a term proportional to the Euler number. Despite this anomaly, the trace of the stress tensor agrees between the dual theories. We also compute the change in the vacuum entanglement entropy under duality, relating this entanglement anomaly to the duality of an "edge mode" theory in two fewer dimensions. Previous work on this subject has led to conflicting results; we explain and resolve these discrepancies.
Langham, Jacob; Barkley, Dwight
2013-03-01
Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries. Here, numerical simulations are used to study reflections from two types of boundaries. The first is a no-flux boundary which waves cannot cross, while the second is a step change in the medium excitability which waves do cross. Both small-core and large-core spirals are investigated. The predominant feature in all cases is that the reflected angle varies very little with incident angle for large ranges of incident angles. Comparisons are made to the theory of Biktashev and Holden. Large-core spirals exhibit other phenomena such as binding to boundaries. The dynamics of multiple reflections is briefly considered.
Directory of Open Access Journals (Sweden)
Kurt L. Polzin
2017-06-01
Full Text Available There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.
van Dongen, Jeroen
2007-01-01
In 1926 Emil Rupp published a number of papers on the interference properties of light emitted by canal ray sources. These articles, particularly one paper that came into being in collaboration with Albert Einstein, drew quite some attention as they probed the wave versus particle nature of light. They also significantly propelled Rupp's career, even though that from the outset they were highly controversial. This article will review this episode, and in particular Rupp's collaboration with Einstein. Evidence that Rupp forged his results is presented and their critical reception in the socially and politically divided German physics community is discussed. These divisions fail to explain the full dynamic; the latter is attempted by turning to the role that theoretical bias on occasion has in assessing experiment. Einstein's responses in particular are analyzed in this context.
The quantum physics bible the definitive guide to 200 years of subatomic science
Clegg, Brian
2017-01-01
An easy-to-understand guide to the complex subject of quantum physics. Quantum physics is how scientists describe the world of the very small. For other people, however, the rules of quantum physics seem to violate all logic: How can a particle be in more than one place at the same time? How can it tunnel through an impenetrable barrier? How can a cat in a box be both alive and dead? This book explains the complexities of quantum physics in bite-sized "lessons" that make it clear and accessible to all readers. The sections and chapters are: 1. Atoms -- quantum; quantum physics in everyday life; the periodic table; atoms and nuclei; isotopes; hydrogen atom (energy levels and spectra) 2. Photons -- photoelectric effect; thermal emission and the Planck distribution; wave particle duality (Young's slit experiment) 3. Quantum devices -- superconductors; transistor, diode; light-emitting diode; laser 4. Spin -- spin; fermions; exclusion principle; Fermi Dirac distribution; Bose-Einstein statistics 5. Wave Mechan...
Quantum mechanical reality according to Copenhagen 2.0
Din, Allan M.
2016-05-01
The long-standing conceptual controversies concerning the interpretation of nonrelativistic quantum mechanics are argued, on one hand, to be due to its incompleteness, as affirmed by Einstein. But on the other hand, it appears to be possible to complete it at least partially, as Bohr might have appreciated it, in the framework of its standard mathematical formalism with observables as appropriately defined self-adjoint operators. This completion of quantum mechanics is based on the requirement on laboratory physics to be effectively confined to a bounded space region and on the application of the von Neumann deficiency theorem to properly define a set of self-adjoint extensions of standard observables, e.g. the momenta and the Hamiltonian, in terms of certain isometries on the region boundary. This is formalized mathematically in the setting of a boundary ontology for the so-called Qbox in which the wave function acquires a supplementary dependence on a set of Additional Boundary Variables (ABV). It is argued that a certain geometric subset of the ABV parametrizing Quasi-Periodic Translational Isometries (QPTI) has a particular physical importance by allowing for the definition of an ontic wave function, which has the property of epitomizing the spatial wave function “collapse.” Concomitantly the standard wave function in an unbounded geometry is interpreted as an epistemic wave function, which together with the ontic QPTI wave function gives rise to the notion of two-wave duality, replacing the standard concept of wave-particle duality. More generally, this approach to quantum physics in a bounded geometry provides a novel analytical basis for a better understanding of several conceptual notions of quantum mechanics, including reality, nonlocality, entanglement and Heisenberg’s uncertainty relation. The scope of this analysis may be seen as a foundational update of the multiple versions 1.x of the Copenhagen interpretation of quantum mechanics, which is
Extending Dualities to Trialities Deepens the Foundations of Dynamics
Smolin, Lee
2016-11-01
Dualities are often supposed to be foundational, but they may come into conflict with a strong form of background independence, which is the principle that the dynamical equations of a theory not depend on arbitrary, fixed, non-dynamical structures. This is because a hidden fixed structures is needed to define the duality transformation. Examples include a fixed, absolute notion of time, a fixed non-dynamical background geometry, or the metric of Hilbert space. We show that this conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, which have a natural triality symmetry. We show how breaking this triality symmetry by imposing different compactifications, which are expansions around fixed classical solutions, yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born's duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.
Lee, Taejin
2016-09-01
We study the dissipative Hofstadter model on a triangular lattice, making use of the O(2, 2; R) T-dual transformation of string theory. The O(2, 2; R) dual transformation transcribes the model in a commutative basis into the model in a noncommutative basis. In the zero-temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two-dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence relation, which identifies the points on the two-dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.
New dualities of supersymmetric gauge theories
2016-01-01
This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures. The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have ...
Brane actions and string dualities
Eyras, E; Lozano, Y; Ceresole, A; Kounnas, C; Lust, D; Theisen, S
1999-01-01
An effective action for the M9-brane is proposed. We study its relation with other branes via dualities. Among these, we find actions for branes which are not suggested by the central charges of the Type II superalgebras.
Meana, M L; Meana, Marco Laucelli; Peñalba, Jesús Puente
2000-01-01
We use the AdS/SYM correspondence to study the relevant effects ofcompactified dimensions on the D-brane dynamics. We present a detailed pictureof the T-duality transition between branes in type IIA and type IIBsupergravity. An analysis of the renormalization scheme coming from theexpectation values of background fields and the role of Wilson lines in it isgiven. We finally explore finite size effects and T-duality maps on thedescription of Wilson loops by supergravity.
From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
Wu, Hong-Tu; Guo, Han-Ying
2008-01-01
By means of Dirac procedure, we re-examine Yang's quantized space-time model, its relation to Snyder's model, the de Sitter special relativity and their UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a complete Yang model at both classical and quantum level can be presented and there really exist Snyder's model, the dS special relativity and the duality.
Duality and confinement in D=3 models driven by condensation of topological defects
Wotzasek, P G C; Wotzasek, Patricio and Gaete Clovis
2005-01-01
We study the interplay of duality and confinement in certain three-dimensional models induced by the condensation of topological defects. To this end we check for the confinement phenomenon, in both sides of the duality, using the static quantum potential within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy contains a linear term leading to the confinement of static probe charges.
From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
Institute of Scientific and Technical Information of China (English)
WU Hong-Tu; HUANG Chao-Guang; GUO Han-Ying
2008-01-01
@@ By means of the Dirac procedure, we re-examine Yang's quantized space-time model, its relation to Snyder's model, the dS special relativity and their UV-IR duality. Starting from a dimensionless dS5-space in a (5+1)-dimensional Mink-space a complete Yang model at both classical and quantum level can be presented and there really exists Snyder's model, the dS special relativity and the duality.
Kirchbach, M
2016-01-01
We seek for a pair of a well and barrier potentials such that the real parts of the complex energies of the resonances transmitted through the barrier equal the energies of the states bound within the well and find the hyperbolic Poeschl-Teller barrier, ~sech^2\\rho, and the trigonometric Scarf well, ~ \\sec^2\\chi. The potentials are shown to be conformally symmetric by the aid of the de Sitter space time, dS4, related to flat conformal space time by a conformal map. Namely, we transform the quantum mechanical wave equations with the above potentials to free quantum motions on the respective open time like hyperbolic and the closed space like hyper spherical, S3, geodesics of dS4, the former by itself is related to Minkowski space time by a conformal map.We formulate a conformal symmetry respecting classification scheme for mesons seen either as resonances in scattering, or as states bound within a potential, according to trajectories in which the total spin of the meson, l-depends linearly on the first power o...
The braneology of 3D dualities
Amariti, Antonio; Klare, Claudius; Orlando, Domenico; Reffert, Susanne
2015-01-01
In this paper we study the reduction of four-dimensional Seiberg duality to three dimensions from a brane perspective. We reproduce the non-perturbative dynamics of the three-dimensional field theory via a T-duality at finite radius and the action of Euclidean D-strings. In this way we also overcome certain issues regarding the brane description of Aharony duality. Moreover we apply our strategy to more general dualities, such as toric duality for M2-branes and dualities with adjoint matter fields.
Anisotropic phenomena in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Zeller, Hansjoerg
2014-05-26
In this thesis we use gauge/gravity duality to model anisotropic effects realised in nature. Firstly we analyse transport properties in holographic systems with a broken rotational invariance. Secondly we discuss geometries dual to IR fixed points with anisotropic scaling behaviour, which are related to quantum critical points in condensed matter systems. Gauge/gravity duality relates a gravity theory in Anti-de Sitter space to a lower dimensional strongly coupled quantum field theory in Minkowski space. Over the past decade this duality provided many insights into systems at strong coupling, e.g. quark-gluon plasma and condensed matter close to quantum critical points. One very important result computed in this framework is the value of the shear viscosity divided by the entropy density in strongly coupled theories. The quantitative result agrees very well with measurements of the ratio in quark-gluon plasma. However, for isotropic two derivative Einstein gravity it is temperature independent. We show that by breaking the rotational symmetry of a system we obtain a temperature dependent shear viscosity over entropy density. This is important to make contact with real world systems, since substances in nature display such dependence. In addition, we derive various transport properties in strongly coupled anisotropic systems using the gauge/gravity dictionary. The most notable results include an electrical conductivity with Drude behaviour in the low frequency region. This resembles conductors with broken translational invariance. However, we did not implement the breaking explicitly. Furthermore, our analysis shows that this setup models effects, resembling the piezoelectric and exoelectric effects, known from liquid crystals. In a second project we discuss a geometry with non-trivial scaling behaviour in order to model an IR fixed point of condensed matter theories. We construct the UV completion of this geometry and analyse its properties by computing the
Szyld, Martín
2011-01-01
The purpose of this work is twofold: to expose the existing similarities between the generalizations of the Tannaka and Galois theories, and on the other hand, to develop in detail our own treatment of part of the content of Joyal and Street [1] paper, generalizing from vector spaces to an abstract tensor category. We also develop in detail the proof of the Tannaka equivalence of categories in the case of vector spaces. Saavedra Rivano [2], Deligne and Milne [3] generalize classical Tannaka theory to the context of K-linear tensor (or monoidal) categories. They obtain a lifting-equivalence into a category of \\group representations" for a ?nite-dimensional vector space valued monoidal functor. This lifting theorem is similar to the one of Grothendieck Galois theory [4] for a ?nite sets valued functor. On the other hand, Joyal and Street [1] work on the algebraic side of the duality between algebra and geometry, and also obtain a lifting-equivalence, but now to the category of ?nite-dimensional comodules over a...
String dualities and superpotential
Energy Technology Data Exchange (ETDEWEB)
Ha, Tae-Won
2010-09-15
The main objective of this thesis is the computation of the superpotential induced by D5- branes in the type IIB string theory and by five-branes in the heterotic string theory. Both superpotentials have the same functional form which is the chain integral of the holomorphic three-form. Using relative (co)homology we can unify the flux and brane superpotential. The chain integral can be seen as an example of the Abel-Jacobi map. We discuss many structures such as mixed Hodge structure which allows for the computation of Picard-Fuchs differential equations crucial for explicit computations. We blow up the Calabi-Yau threefold along the submanifold wrapped by the brane to obtain geometrically more appropriate configuration. The resulting geometry is non-Calabi-Yau and we have a canonically given divisor. This blown-up geometry makes it possible to restrict our attention to complex structure deformations. However, the direct computation is yet very difficult, thus the main tool for computation will be the lift of the brane configuration to a F-theory compactification. In F-theory, since complex structure, brane and, if present, bundlemoduli are all contained in the complex structure moduli space of the elliptic Calabi-Yau fourfold, the computation can be dramatically simplified. The heterotic/F-theory duality is extended to include the blow-up geometry and thereby used to give the blow-up geometry amore physical meaning. (orig.)
Supersymmetry, Duality And Holonomy
Wen, W
2005-01-01
In this thesis, I study various aspects of solutions to eleven-dimensional supergravity and its descendents. The former is at one corner of the moduli space of M-theory. While it is not clear how to formulate M-theory; it is equally interesting to see how far we can proceed from this low energy window. First of all, various techniques are applied to construct supergravity solutions preserving partial supersymmetry. A seven-dimensional membrane solution in the gauged supergravity is constructed by lifting a self-dual string in six dimensions, and its supersymmetric property is explored in certain detail. Then fractional BPS solutions from Sn × Sn reduction of six and ten-dimensional supergravities are constructed via the method of G-structures. The form of the solutions is totally determined by Laplace equations with specified boundary conditions. Secondly, the concept of duality is realized in two aspects. A certain type of *-theory, obtained from time-like T-dualization of the usual string and M-t...
Quantum Phase from the Twin Paradox
Ord, G. N.
2012-05-01
The modern concept of spacetime usually emerges from the consideration of moving clocks on the assumption that world-lines are continuous. In this paper we start with the assumption that natural clocks are digital and that events are discrete. By taking different continuum limits we show that the phase of non-relativistic quantum mechanics and the odd metric of spacetime both emerge from the consideration of discrete clocks in relative motion. From this perspective, the continuum limit that manifests itself in 'spacetime' is an infinite mass limit. The continuum limit that gives rise to the Schrödinger equation retains a finite mass as a beat frequency superimposed on the 'Zitterbewegung' at the Compton frequency. We illustrate this in a simple model in which a Poisson process drives a relativistic clock that gives rise to a Feynman path integral, where the phase is a manifestation of the twin paradox. The example shows that the non-Euclidean character of spacetime and the wave-particle duality of quantum mechanics share a common origin. They both emerge from the necessity that clocks age at rates that are path dependent.
One-dimensional contact process: duality and renormalization.
Hooyberghs, J; Vanderzande, C
2001-04-01
We study the one-dimensional contact process in its quantum version using a recently proposed real-space renormalization technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates that are comparable in accuracy with the best known in the literature.
Projective duality and homogeneous spaces
Tevelev, E A
2006-01-01
Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.
The Duality on Vector Optimization Problems
Institute of Scientific and Technical Information of China (English)
HUANG Long-guang
2012-01-01
Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.
Duality for cochain DG algebras
Jorgensen, Peter
2010-01-01
This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-commutative aspects. One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology. As an application, it is proved that if the canonical module $A / A^{\\geq 1}$ has a semi-free resolution where the cohomological degree of the generators is bounded above, then the same is t...
Brane Tilings and Specular Duality
Hanany, Amihay
2012-01-01
We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which have the same combined mesonic and baryonic moduli space, otherwise called the master space. We obtain the associated Hilbert series which encodes both the generators and defining relations of the moduli space. We illustrate our findings with a set of brane tilings that have reflexive toric diagrams.
Energy Technology Data Exchange (ETDEWEB)
Kimura, I.; Hashimoto, K.; Matsumoto, H.; Mukai, T.; Bell, T.F.; Inan, U.S.; Helliwell, R.A.; Katsufrakis, J.P.
1983-01-01
In situ measurements of both energetic particles and VLF waves have been carried out in a joint program involving the Japanese satellite EXOS-B and the Siple Station VLF transmitter. A general description of the experiment is given as well as some results concerning wave-particle correlations. Detailed analysis of the observed wave characteristics is given in a companion paper. Correlations of electron flux and pitch angle anisotropy in the energy range from 85 eV to 6.9 keV with waves in a range from 300 Hz to 9 kHz are examined. These electrons sometimes have a pitch angle distributions with a peak flux at 90/sup 0/ pitch angle (so-called pancake distribution). On five passes out of a total of 50 during the summer campaign in 1979, the energy of the electrons that showed a high pitch angle anisotropy shifted upward as the satellite moved into the plasmasphere, crossing the plasmapause in the equatorial region. In two cases out of five, strong Siple signals were observed in the geomagnetic equatorial region just outside the plasmapause, in association with such a pancake pitch angle distribution of electrons. The Siple signals are most likely amplified by the cyclotron instability due to the high pitch angle anisotropy (HPAA), although the flux of resonant electrons was relatively small. For three other cases of HPAA, the satellite location was so far away from the Siple meridian that the signal level, even if amplified, was too weak to be detected by the satellite. Emissions associated with Siple signals were detected on five (two equatorial and three high latitude) passes, which were all confined on 6 days after a large magnetic storm. On the days when the Siple triggered emissions were observed, the pitch angle anisotropy was low, but the electron flux at resonant energies in the equatorial region was four or five times larger than that on other non-triggering days in all energy channels from 85 eV to 6.9 keV.
Einstein's Revolutionary Light-Quantum Hypothesis
Stuewer, Roger H.
2005-05-01
The paper in which Albert Einstein proposed his light-quantum hypothesis was the only one of his great papers of 1905 that he himself termed ``revolutionary.'' Contrary to widespread belief, Einstein did not propose his light-quantum hypothesis ``to explain the photoelectric effect.'' Instead, he based his argument for light quanta on the statistical interpretation of the second law of thermodynamics, with the photoelectric effect being only one of three phenomena that he offered as possible experimental support for it. I will discuss Einstein's light-quantum hypothesis of 1905 and his introduction of the wave-particle duality in 1909 and then turn to the reception of his work on light quanta by his contemporaries. We will examine the reasons that prominent physicists advanced to reject Einstein's light-quantum hypothesis in succeeding years. Those physicists included Robert A. Millikan, even though he provided convincing experimental proof of the validity of Einstein's equation of the photoelectric effect in 1915. The turning point came after Arthur Holly Compton discovered the Compton effect in late 1922, but even then Compton's discovery was contested both on experimental and on theoretical grounds. Niels Bohr, in particular, had never accepted the reality of light quanta and now, in 1924, proposed a theory, the Bohr-Kramers-Slater theory, which assumed that energy and momentum were conserved only statistically in microscopic interactions. Only after that theory was disproved experimentally in 1925 was Einstein's revolutionary light-quantum hypothesis generally accepted by physicists---a full two decades after Einstein had proposed it.
Duality in Dynamic Fuzzy Systems
Yoshida, Yuji
1995-01-01
This paper shows the resolvent equation, the maximum principle and the co-balayage theorem for a dynamic fuzzy system. We define a dual system for the dynamic fuzzy system, and gives a duality for Snell's optimal stopping problem by the dual system.
Pursuing Gravitational S-Duality
García-Compéan, H; Ramírez, C
1998-01-01
Recently a strong-weak coupling duality in non-abelian non-supersymmetric theories in four dimensions has been found. An analogous procedure is reviewed, which allows to find the `dual action' to the gauge theory of dynamical gravity constructed by the MacDowell-Mansouri model plus the superposition of a
Dualities in Covering Rough Operations
Institute of Scientific and Technical Information of China (English)
William Zhu
2006-01-01
Rough set theory is a technique of granular computing. In this paper, we study a type of generalized rough sets based on covering. There are several literatures[ 1,40-43 ] exploring covering-based rough sets. Our focus of this paper is on the dualities in rough operations.
Splitting Spacetime and Cloning Qubits: Linking No-Go Theorems across the ER=EPR Duality
Bao, Ning; Remmen, Grant N
2015-01-01
We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement.
Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality
Energy Technology Data Exchange (ETDEWEB)
Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States); Pollack, Jason; Remmen, Grant N. [Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States)
2015-11-15
We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Trigonometric version of quantum–classical duality in integrable systems
Energy Technology Data Exchange (ETDEWEB)
Beketov, M., E-mail: beketov@phystech.edu [MIPT, Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Liashyk, A., E-mail: a.liashyk@gmail.com [National Research University Higher School of Economics, Myasnitskaya str. 20, 101000, Moscow (Russian Federation); BITP, Metrolohichna str. 14-b, 03680, Kiev (Ukraine); Zabrodin, A., E-mail: zabrodin@itep.ru [National Research University Higher School of Economics, Myasnitskaya str. 20, 101000, Moscow (Russian Federation); Institute of Biochemical Physics, Kosygina str. 4, 119991, Moscow (Russian Federation); ITEP, Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); Zotov, A., E-mail: zotov@mi.ras.ru [Steklov Mathematical Institute, RAS, Gubkina str. 8, 119991, Moscow (Russian Federation); ITEP, Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT, Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation)
2016-02-15
We extend the quantum–classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars–Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix). In the rational version of the duality, the action variables of the Ruijsenaars–Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation) numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix). The limit corresponding to the classical Calogero–Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.
Trigonometric version of quantum–classical duality in integrable systems
Directory of Open Access Journals (Sweden)
M. Beketov
2016-02-01
Full Text Available We extend the quantum–classical duality to the trigonometric (hyperbolic case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars–Schneider model and the inhomogeneous twisted XXZ spin chain on N sites. Similarly to the rational version, the spin chain data fixes a certain Lagrangian submanifold in the phase space of the classical integrable system. The inhomogeneity parameters are equal to the coordinates of particles while the velocities of classical particles are proportional to the eigenvalues of the spin chain Hamiltonians (residues of the properly normalized transfer matrix. In the rational version of the duality, the action variables of the Ruijsenaars–Schneider model are equal to the twist parameters with some multiplicities defined by quantum (occupation numbers. In contrast to the rational version, in the trigonometric case there is a splitting of the spectrum of action variables (eigenvalues of the classical Lax matrix. The limit corresponding to the classical Calogero–Sutherland system and quantum trigonometric Gaudin model is also described as well as the XX limit to free fermions.
Systematic classical continuum limits of integrable spin chains and emerging novel dualities
Avan, Jean; Sfetsos, Konstadinos
2010-01-01
We examine certain classical continuum long wave-length limits of prototype integrable quantum spin chains. We define the corresponding construction of classical continuum Lax operators. Our discussion starts with the XXX chain, the anisotropic Heisenberg model and their generalizations and extends to the generic isotropic and anisotropic gl_n magnets. Certain classical and quantum integrable models emerging from special "dualities" of quantum spin chains, parametrized by c-number matrices, are also presented.
Lectures on Cohomology, T-Duality, and Generalized Geometry
Bouwknegt, P.
These are notes for lectures, originally entitled "Selected Mathematical Aspects of Modern Quantum Field Theory", presented at the Summer School "New Paths Towards Quantum Gravity", Holbæ k, Denmark, 10-16 May 2008. My aim for these lectures was to introduce a mixture of physics and mathematics postgraduate students into a selection of exciting new developments on the interface of mathematics and quantum field theory. This write-up covers three topics: (1) cohomology and differential characters, (2) T-duality, and (3) generalized geometry. The three chapters can be read, more or less, independent of each other, but there is a common central theme, namely the occurrence of a (local) 2-form gauge field in certain quantum fields theories, the so-called B-field, which plays a role analogous to the electromagnetic gauge field.
Challenges to the Bohr Wave Particle Complementarity Principle
Rabinowitz, Mario
2012-01-01
Contrary to the Bohr complementarity principle, in 1995 Rabinowitz proposed that by using entangled particles from the source it would be possible to determine which slit a particle goes through while still preserving the interference pattern in the Young two slit experiment. In 2000, Kim et al used spontaneous parametric down conversion to prepare entangled photons as their source, and almost achieved this. In 2012, Menzel et al. experimentally succeeded in doing this. When the source emits entangled particle pairs, the traversed slit is inferred from measurement of the entangled particle location by using triangulation. The violation of complementarity breaches the prevailing probabilistic interpretation of quantum mechanics, and benefits the Bohm pilot wave theory.
Computational and theoretical study of the wave-particle interaction of protons and waves
Energy Technology Data Exchange (ETDEWEB)
Moya, P.S.; Munoz, V. [Chile Univ., Santiago (Chile). Dept. de Fisica; Vinas, A.F. [NASA Goddard Space Flight Center, Greenbelt, MD (United States). Heliophysics Science Div.; Valdivia, J.A. [Chile Univ., Santiago (Chile). Dept. de Fisica; Centro para el Desarrollo de la Nanociencia y Nanotecnologia, CEDENNA (Chile); CEIBA complejidad, Bogota (Colombia)
2012-11-01
We study the wave-particle interaction and the evolution of electromagnetic waves propagating through a plasma composed of electrons and protons, using two approaches. First, a quasilinear kinetic theory has been developed to study the energy transfer between waves and particles, with the subsequent acceleration and heating of protons. Second, a one-dimensional hybrid numerical simulation has been performed, with and without including an expanding-box model that emulates the spherical expansion of the solar wind, to investigate the fully nonlinear evolution of this wave-particle interaction. Numerical results of both approaches show that there is an anisotropic evolution of proton temperature. (orig.)
Kleshchev, Alexander
2017-01-01
The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules-one for each real positive root for the corresponding affine root system {\\tt X}_l^{(1)}, as well as irreducible imaginary modules-one for each l-multiplication. The authors study imaginary modules by means of "imaginary Schur-Weyl duality" and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.
Gauge Theory and Langlands Duality
Frenkel, Edward
2009-01-01
The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves on moduli spaces of (flat) bundles on algebraic curves. Three years ago, in a groundbreaking advance, Kapustin and Witten have linked the geometric Langlands correspondence to the S-duality of 4D supersymmetric gauge theories. This and subsequent works have already led to striking new insights into the geometric Langlands Program, which in particular involve the Homological Mirror Symmetry of the Hitchin moduli spaces of Higgs bundles on algebraic curves associated to two Langlands dual Lie groups.
Awodey, Steve
2010-01-01
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this case $2$. In the present work, we generalize the entire arrangement from propositional to first-order logic. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed first in the form of a contravariant adjunction, is established by homming into a common dualizing object, now $\\Sets$, regarded once as a boolean category, and...
Classical Geometry and Target Space Duality
1995-01-01
This is the written version of lectures presented at Cargese 95. A new formulation for a ``restricted'' type of target space duality in classical two dimensional nonlinear sigma models is presented. The main idea is summarized by the analogy: euclidean geometry is to riemannian geometry as toroidal target space duality is to ``restricted'' target space duality. The target space is not required to possess symmetry. These lectures only discuss the local theory. The restricted target space duali...
Duality Theorems on Multi-objective Programming of Generalized Functions
Institute of Scientific and Technical Information of China (English)
Li-ping Pang; Wei Wang; Zun-quan Xia
2006-01-01
The form of a dual problem of Mond-Weir type for multi-objective programming problems of generalized functions is defined and theorems of the weak duality, direct duality and inverse duality are proven.
T-Duality in $\\sigma$ Models with Kaluza-Klein Metric as Electric-Magnetic Duality
Jafarizadeh, M A
1999-01-01
It is shown that the T-duality in \\sigma-model with Kaluza-Klein metric, without or with a torsion term, can be interpreted as electric-magnetic duality for some of their solitonic solutions. Actually Buscher's duality transformation interchanges the topological and Noether charges.
The Electromagnetic Duality Formulation of Geometric Phases
Zhang, Yuchao; Li, Kang
2015-06-01
This paper focuses on the electromagnetic(EM) duality formulation of geometric phases of Aharonov-Bohm(A-B) effect and Aharonov-Casher(A-C) effect. Through the two four-vector potential formulation of electromagnetic theory, we construct a EM duality formulation for both A-B effect and A-C effect. The He-McKellar-Wilkens(HMW) effect is included as a EM duality counterpart of the A-C effect, and also the EM duality counterpart of the A-B effect is also predicted.
T-Duality in Type II String Theory via Noncommutative Geometry and Beyond
Mathai, V.
This brief survey on how nocommutative and nonassociative geometry appears naturally in the study of T-duality in type II string theory, is essentially a transcript of my talks given at the 21st Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics: Noncommutative Geometry and Quantum Spacetime in Physics, Japan, 11--15 November 2006.
U-duality transformation of membrane on Tn revisited
Hu, Shan; Li, Tianjun
2016-08-01
The problem with the U-duality transformation of membrane on T n is recently addressed in [arXiv:1509.02915]. We will consider the U-duality transformation rule of membrane on T n × R. It turns out that winding modes on T n should be taken into account, since the duality transformation may bring the membrane configuration without winding modes into the one with winding modes. With the winding modes added, the membrane worldvolume theory in lightcone gauge is equivalent to the n + 1 dimensional super-Yang-Mills (SYM) theory in {tilde{T}}^n , which has SL(2 , Z) × SL(3 , Z) and SL(5 , Z) symmetries for n = 3 and n = 4, respectively. The SL(2 , Z) × SL(3 , Z) transformation can be realized classically, making the on-shell field configurations transformed into each other. However, the SL(5 , Z) symmetry may only be realized at the quantum level, since the classical 5 d SYM field configurations cannot form the representation of SL(5 , Z).
Fair sampling perspective on an apparent violation of duality
Bolduc, Eliot; Leach, Jonathan; Miatto, Filippo M.; Leuchs, Gerd; Boyd, Robert W.
2014-01-01
In the event in which a quantum mechanical particle can pass from an initial state to a final state along two possible paths, the duality principle states that “the simultaneous observation of wave and particle behavior is prohibited” [Scully MO, Englert B-G, Walther H (1991) Nature 351:111–116]. Whereas wave behavior is associated with the observation of interference fringes, particle behavior generally corresponds to the acquisition of which-path information by means of coupling the paths to a measuring device or part of their environment. In this paper, we show how the consequences of duality change when allowing for biased sampling, that is, postselected measurements on specific degrees of freedom of the environment of the two-path state. Our work gives insight into a possible mechanism for obtaining simultaneous high which-path information and high-visibility fringes in a single experiment. Further, our results introduce previously unidentified avenues for experimental tests of duality. PMID:25114237
Introduction to the Quantum Theory of Elementary Cycles
Dolce, Donatello
Elementary Cycles Theory (ECT) is a novel exact formulation of quantum-relativistic mechanics. Here, we present an introduction to its basic quantum aspects. On the one hand, Newton's law of inertia states that every isolated particle has persistent motion, i.e. constant energy and momentum. On the other hand, undulatory mechanics associates, by means of the Planck constant, a recurrence in time and space to the energy and the momentum of an elementary particle, respectively. Paraphrasing these two fundamental principles of modern physics, ECT postulates that every elementary constituent of nature (every elementary particle) is characterized by persistent intrinsic periodicity (as long it does not interact) whose space-time duration determines its kinematical state (energy and momentum). In other words, undulatory mechanics is imposed as constraint "overdetermining" relativistic mechanics, with fundamental motivations on Einstein's proposal of unification of quantum and relativistic theories. Every free particle is a (de Broglie) "periodic phenomenon" which can also be regarded as a reference clock and every system is decomposable in modulated elementary cycles. Indeed, ECT introduces a cyclic nature to the ordinary relativistic space-time coordinates. The resulting classical-relativistic mechanics turns out to be fully consistent with relativity and, at the same time, reproduces exactly all the fundamental aspects of ordinary quantum-relativistic mechanics (without any explicit quantisation). Relativity only fixes the differential structure of space-time without giving any prescription about the boundary of space-time, and the constraint of covariant periodicity (or similar relativistic boundary conditions) is allowed by the variational principle for relativistic theories. The constraint of intrinsic periodicity enforces the local nature of relativistic space-time and the wave-particle duality. Besides such unified description of relativistic and quantum dynamics
The Hall module of an exact category with duality
Young, Matthew B.
2012-01-01
We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the representation theory of a quiver with involution. In this case we show that the Hall module is naturally a module over the specialized reduced sigma-analogue of the quantum Kac-Moody algebra attached to the quiver. For finite type quivers, we explicitly determin...
Holographic duality and the resistivity of strange metals
Davison, Richard A; Zaanen, Jan
2013-01-01
We present a strange metal, described by a holographic duality, which reproduces the famous linear resistivity of the normal state of the copper oxides, in addition to the linear specific heat. This holographic metal reveals a simple and general mechanism for producing such a resistivity, which requires only quenched disorder and a strongly interacting quantum critical state. The key is the minimal viscosity of the latter: unlike in a Fermi-liquid, the viscosity is very small and therefore is important for the electrical transport. This mechanism produces a resistivity proportional to the electronic entropy.
Modular Schrödinger equation and dynamical duality.
Garbaczewski, Piotr
2008-09-01
We discuss quite surprising properties of the one-parameter family of modular nonlinear Schrödinger equations [G. Auberson and P. G. Sabatier, J. Math. Phys. 35, 4028 (1994)]. We develop a unified theoretical framework for this family. Special attention is paid to the emergent dual time evolution scenarios which, albeit running in the real time parameter of the pertinent nonlinear equation, in each considered case may be mapped among each other by means of a suitable analytic continuation-in-time procedure. This dynamical duality is characteristic for nondissipative quantum motions and their dissipative (diffusion-type processes) partners, and naturally extends to classical motions in confining and scattering potentials.
Morita duality for monoids / Peeter Normak
Normak, Peeter
1990-01-01
In this paper Morita duality for monoids is introduced. Necessary and sufficient conditions for two monoids S and T to be Morita dual are given. Moreover, it is shown that if S and T are Morita dual monoids, then S and U are Moriaddition, every finite monoid having Morita duality is selfdual and even reflexive.
Mirror Symmetry and Polar Duality of Polytopes
Directory of Open Access Journals (Sweden)
David A. Cox
2015-09-01
Full Text Available This expository article explores the connection between the polar duality from polyhedral geometry and mirror symmetry from mathematical physics and algebraic geometry. Topics discussed include duality of polytopes and cones as well as the famous quintic threefold and the toric variety of a reflexive polytope.
Managing Dualities in Planned Change Initiatives
Barge, J. Kevin; Lee, Michael; Maddux, Kristy; Nabring, Richard; Townsend, Bryan
2008-01-01
Dualities play an important role in creating the conditions for change and managing planned change initiatives. Building on Seo, Putnam, and Bartunek's (2003) work, this study focuses on the dualities associated with managing change processes. A case study of a planned change process called the Circle of Prosperity Initiative, a multi-stakeholder…
A Vademecum on Quark-Hadron Duality
Bigi, Ikaros I; Bigi, Ikaros; Uraltsev, Nikolai
2001-01-01
We present an elementary introduction to the problem of quark-hadron duality and its practical limitations, in particular as it concerns local duality violation in inclusive B meson decays. We show that the accurate definition of duality violation elaborated over the recent years allows one to derive informative constraints on violations of local duality. The magnitude of duality violation is particularly restricted in the total semileptonic widths. This explains its strong suppression in concrete dynamical estimates. We analyze the origin of the suppression factors in a model-independent setting, including a fresh perspective on the Small Velocity expansion. A new potentially significant mechanism for violation of local duality in \\Gamma_sl(B) is analyzed. Yet we conclude that the amount of duality violation in \\Gamma_sl(B) must be safely below the half percent level, with realistic estimates being actually much smaller. Violation of local duality in \\Gamma_sl(B) is thus far below the level relevant to pheno...
Morita duality for monoids / Peeter Normak
Normak, Peeter
1990-01-01
In this paper Morita duality for monoids is introduced. Necessary and sufficient conditions for two monoids S and T to be Morita dual are given. Moreover, it is shown that if S and T are Morita dual monoids, then S and U are Moriaddition, every finite monoid having Morita duality is selfdual and even reflexive.
Which Quantum Theory Must be Reconciled with Gravity? (And What Does it Mean for Black Holes?
Directory of Open Access Journals (Sweden)
Matthew J. Lake
2016-10-01
Full Text Available We consider the nature of quantum properties in non-relativistic quantum mechanics (QM and relativistic quantum field theories, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map between classical Poisson brackets and their associated commutators, such schemes give rise to quantum states obeying canonical dispersion relations, obtained by substituting the de Broglie relations into the relevant (classical energy-momentum relation. In canonical QM, this yields a dispersion relation involving ℏ but not c, whereas the canonical relativistic dispersion relation involves both. Extending this logic to the canonical quantization of the gravitational field gives rise to loop quantum gravity, and a map between classical variables containing G and c, and associated commutators involving ℏ. This naturally defines a “wave-gravity duality”, suggesting that a quantum wave packet describing self-gravitating matter obeys a dispersion relation involving G, c and ℏ. We propose an Ansatz for this relation, which is valid in the semi-Newtonian regime of both QM and general relativity. In this limit, space and time are absolute, but imposing v max = c allows us to recover the standard expressions for the Compton wavelength λ C and the Schwarzschild radius r S within the same ontological framework. The new dispersion relation is based on “extended” de Broglie relations, which remain valid for slow-moving bodies of any mass m. These reduce to canonical form for m ≪ m P , yielding λ C from the standard uncertainty principle, whereas, for m ≫ m P , we obtain r S as the natural radius of a self-gravitating quantum object. Thus, the extended de Broglie theory naturally gives rise to a unified description of black holes and fundamental particles in the semi-Newtonian regime.
A Vademecum on Quark-Hadron Duality
Bigi, Ikaros; Uraltsev, Nikolai
We present an elementary introduction to the problem of quark-hadron duality and its practical limitations, in particular as it concerns local duality violation in inclusive B meson decays. We show that the accurate definition of duality violation elaborated over the recent years allows one to derive informative constraints on violations of local duality. The magnitude of duality violation is particularly restricted in the total semileptonic widths. This explains its strong suppression in concrete dynamical estimates. We analyze the origin of the suppression factors in a model-independent setting, including a fresh perspective on the small velocity expansion. A new potentially significant mechanism for the violation of local duality in Γsl(B) is analyzed. Yet we conclude that the amount of duality violation in Γsl(B) must be safely below the half percent level, with realistic estimates being actually much smaller. The violation of local duality in Γsl(B) is thus far below the level relevant to phenomenology. We also present a cautionary note on the B-->D* decay amplitude at zero recoil and show that it is much more vulnerable to violations of quark-hadron duality than Γsl(B). A critical review of some recent literature is given. We point out that the presently limiting factor in genuinely model-independent extraction of Vcb is the precise value of the short-distance charm quark mass. We suggest a direct and precise experimental check of local quark-hadron duality in semileptonic B--> Xclν decays.
Ring wormholes via duality rotations
Directory of Open Access Journals (Sweden)
Gary W. Gibbons
2016-09-01
Full Text Available We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy–Voorhees–Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than −c4/4G. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a hole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes, for example by vacuum fluctuations.
Local duality in Loewner equations
Contreras, Manuel D; Gumenyuk, Pavel
2012-01-01
Among diversity of frameworks and constructions introduced in Loewner Theory by different authors, one can distinguish two closely related but still different ways of reasoning, which colloquially may be described as "increasing" and "decreasing". In this paper we review in short the main types of (deterministic) Loewner evolution discussed in the literature and describe in detail the local duality between "increasing" and "decreasing" cases within the general unifying approach in Loewner Theory proposed recently in [Bracci et al. to appear in J Reine Angew Math; arXiv:0807.1594v1], [Bracci et al. in Math Ann 344:947-962, 2009; arXiv:0807.1715v1], [Contreras et al. in Revista Matem\\'atica Iberoamericana 26:975-1012, 2010; arXiv:0902.3116v1]. In particular, we extend several results of R.O.Bauer [in J Math Anal Appl 302:484-501, 2005; arXiv:math/0306130v1], which deal with the chordal Loewner evolution, to this general setting. Although the duality is given by a simple change of the parameter, not all the resu...
Ring wormholes via duality rotations
Gibbons, Gary W
2016-01-01
We apply duality rotations and complex transformations to the Schwarzschild metric to obtain wormhole geometries with two asymptotically flat regions connected by a throat. In the simplest case these are the well-known wormholes supported by phantom scalar field. Further duality rotations remove the scalar field to yield less well known vacuum metrics of the oblate Zipoy-Voorhees-Weyl class, which describe ring wormholes. The ring encircles the wormhole throat and can have any radius, whereas its tension is always negative and should be less than $-c^4/4G$. If the tension reaches the maximal value, the geometry becomes exactly flat, but the topology remains non-trivial and corresponds to two copies of Minkowski space glued together along the disk encircled by the ring. The geodesics are straight lines, and those which traverse the ring get to the other universe. The ring therefore literally produces a whole in space. Such wormholes could perhaps be created by negative energies concentrated in toroidal volumes...
Generalized dualities in one-time physics as holographic predictions from two-time physics
Araya, Ignacio J.; Bars, Itzhak
2014-03-01
In the conventional formalism of physics, with one time, systems with different Hamiltonians or Lagrangians have different physical interpretations and are considered to be independent systems unrelated to each other. However, in this paper we construct explicitly canonical maps in one-time (1T) phase space (including timelike components, specifically the Hamiltonian) to show that it is appropriate to regard various 1T physics systems, with different Lagrangians or Hamiltonians, as being duals of each other. This concept is similar in spirit to dualities discovered in more complicated examples in field theory or string theory. Our approach makes it evident that such generalized dualities are widespread. This suggests that, as a general phenomenon, there are hidden relations and hidden symmetries that conventional 1T physics does not capture, implying the existence of a more unified formulation of physics that naturally supplies the hidden information. In fact, we show that two-time (2T) physics in (d +2) dimensions is the generator of these dualities in 1T physics in d dimensions by providing a holographic perspective that unifies all the dual 1T systems into one. The unifying ingredient is a gauge symmetry in phase space. Via such dualities it is then possible to gain new insights toward new physical predictions not suspected before, and suggest new methods of computation that yield results not obtained before. As an illustration, we will provide concrete examples of 1T systems in classical mechanics that are solved analytically for the first time via our dualities. These dualities in classical mechanics have counterparts in quantum mechanics and field theory, and in some simpler cases they have already been constructed in field theory. We comment on the impact of our approach on the meaning of space-time and on the development of new computational methods based on dualities.
Exact Duality of The Dissipative Hofstadter Model on a Triangular Lattice
Lee, Taejin
2016-01-01
We study the dissipative Hofstadter model on a triangular lattice, making use of the $O(2,2;R)$ T-dual transformation of string theory. The $O(2,2;R)$ dual transformation transcribes the model in a commutative basis into the model in a non-commutative basis. In the zero temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence condition, which identifies the points on the two dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.
Contact terms and duality symmetry in the critical dissipative Hofstadter model
Freed, D E
1993-01-01
The dissipative Hofstadter model describes the quantum mechanics of a charged particle in two dimensions subject to a periodic potential, uniform magnetic field, and dissipative force. Its phase diagram exhibits an SL(2,Z) duality symmetry and has an infinite number of critical circles in the dissipation/magnetic field plane. In addition, multi-critical points on a particular critical circle correspond to non-trivial solutions of open string theory. The duality symmetry is expected to provide relations between correlation functions at different multi-critical points. Many of these correlators are contact terms. However we expect them to have physical significance because under duality they transform into functions that are non-zero for large separations of the operators. Motivated by the search for exact, regulator independent solutions for these contact terms, in this paper we derive many properties and symmetries of the coordinate correlation functions at the special multi-critical points. In particular, we...
Wave-particle interactions induced by SEPAC on Spacelab 1 Wave observations
Taylor, W. W. L.; Obayashi, T.; Kawashima, N.; Sasaki, S.; Yanagisawa, M.; Burch, J. L.; Reasoner, D. L.; Roberts, W. T.
1985-01-01
Space experiments with particle accelerators (SEPAC) flew on Spacelab 1 in November and December 1983. SEPAC included an accelerator which emitted electrons into the ionospheric plasma with energies up to 5 keV and currents up to 300 mA. The SEPAC equipment also included an energetic plasma generator, a neutral gas generator, and an extensive array of diagnostics. The diagnostics included plasma wave detectors, and energetic electron analyzer, a photometer, a high sensitivity television camera, a Langmuir probe and a pressure gage. Twenty-eight experiments were performed during the mission to investigate beam-plasma interactions, electron beam dynamics, plasma beam propagation, and vehicle charging. The wave-particle interactions were monitored by the plasma wave instrumentation, by the energetic electron detector and by the optical detectors. All show evidence of wave-particle interactions, which are described in this paper.
Measurements of wave-particle interaction in a single-ended Q machine
DEFF Research Database (Denmark)
Andersen, S.A.; Christoffersen, G.B.; Jensen, Vagn Orla
1971-01-01
A Green-function technique is used to solve the linearized Vlasov equation for the perturbed ion velocity distribution function, f( x,v,t), in a case where a short density pulse is released into a plasma. Some characteristic features in the calculated curves are caused by wave-particle interaction....... Experimentally, short density pulses are generated in the plasma in a single-ended Q machine by application of electrical square pulses to a grid immersed in the plasma column. The perturbed ion velocity distribution function in the density pulse is measured by means of an electrostatic energy analyzer....... The features showing the wave-particle interaction appear in the experimental results...
Magnetic vortices in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Strydom, Migael
2014-07-18
We study strongly-coupled phenomena using gauge/gravity duality, with a particular focus on vortex solutions produced by magnetic field and time-dependent problems in holographic models. The main result is the discovery of a counter-intuitive effect where a strong non-abelian magnetic field induces the formation of a triangular vortex lattice ground state in a simple holographic model. Gauge/gravity duality is a powerful theoretical tool that has been used to study strongly-coupled systems ranging from the quark-gluon plasma produced at particle colliders to condensed matter theories. The most important idea is that of duality: a strongly coupled quantum field theory can be studied by investigating the properties of a particular gravity background described by Einstein's equations. One gravity background we study in this dissertation is AdS-Schwarzschild with an SU(2) gauge field. We switch on the gauge field component that gives the field theory an external magnetic field. When the magnetic field is above a critical value, we find that the system is unstable, indicating a superconducting phase transition. We find the instability in two ways. Firstly, we do a quasinormal mode analysis, studying fluctuations about the background. Secondly, we rewrite the equations in Schroedinger form and numerically find that, as the magnetic field is increased, the potential deepens until it is capable of supporting a bound state. Next we show that the resulting superconducting ground state is a triangular vortex lattice. This is done by performing a perturbative expansion in a small parameter proportional to the condensate size. After solving the equations to third order, we use the holographic dictionary to calculate the total energy of different lattice solutions and identify the minimum energy state. In addition, we show that the result holds in an AdS-hard wall model as well, which is dual to a confining theory. Next we extend the simple gravity model to include a
The Foundations of Quantum Mechanics: Historical Analysis and Open Questions -- Cesena, 2004
Garola, Claudio; Rossi, Arcangelo; Sozzo, Sandro
Introduction / C. Garola, A. Rossi and S. Sozzo -- If Bertlmann had three feet / A. Afriat -- Macroscopic interpretability of quantum component systems / R. Ascoli -- Premeasurement versus measurement: a basic form of complementarity / G. Auletta and G. Tarozzi -- Remarks on conditioning / E. G. Beltrametti -- Entangled state preparation in experiments on quantum non-locality / V. Berardi and A. Garuccio -- The first steps of quantum electrodynamics: what is it that's being quantized? / S. Bergia -- On the meaning of element in the science of italic tradition, the question of physical objectivity (and/or physical meaning) and quantum mechanics / G. Boscarino -- Mathematics and epistemology in Planck's theoretical work (1898-1915) / P. Campogalliani -- On the free motion with noise / B. Carazza and R. Tedeschi -- Field quantization and wave/particle duality / M. Cini -- Parastatistics in econophysics? / D. Costantini and U. Garibaldi -- Theory-laden instruments and quantum mechanics / S. D'Agostino -- Quantum non-locality and the mathematical representation of experience / V. Fano -- On the notion of proposition in classical and quantum mechanics / C. Garola and S. Sozzo -- The electromagnetic conception of nature and the origins of quantum physics / E. A. Giannetto -- What we talk about when we talk about universe computability / S. Guccione -- Bohm and Bohmian mechanics / G. Introzzi and M. Rossetti -- An objective background for quantum theory relying on thermodynamic concepts / L. Lanz and B. Vacchini -- The entrance of quantum mechanics in Italy: from Garbasso to Fermi / M. Leone and N. Robotti -- The measure of momentum in quantum mechanics / F. Logiurato and C. Tarsitani -- On the two-slit interference experiment: a statistical discussion / M. Minozzo -- Why the reactivity of the elements is a relational property, and why it matters / V. Mosini -- Detecting non compatible properties in double-slit experiment without erasure / G. Nisticò -- If you can
The duality principle in the presence of postselection
Leach, Jonathan; Bolduc, Eliot; Miatto, Filippo M.; Piché, Kevin; Leuchs, Gerd; Boyd, Robert W.
2016-01-01
The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility of interference fringes and predictability of paths within a two-alternative system, which are bound by the inequality . However, if such a system is coupled to its environment, it becomes possible to obtain conditional measures of visibility and predictability, i.e. measures that are conditioned on the state of the environment. We show that in this case, the predictability and visibility values can lead to an apparent violation of the duality principle. We experimentally realize this apparent violation in a controlled manner by enforcing a fair-sampling-like loophole via postselection. This work highlights some of the subtleties that one can encounter while interpreting familiar quantities such as which-alternative information and visibility. While we concentrated on an extreme example, it is of utmost importance to realise that such subtleties might also be present in cases where the results are not obviously violating an algebraic bound, making them harder (but not any less crucial) to detect.
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
African Journals Online (AJOL)
agreements on the Nile waters: the 1929 Nile Water Agreement and the 1959 Nile ...... Nile Basin Regional Power Trade; Efficient Water Use for Agricultural Production .... respect to existing bilateral and multilateral agreements on international.
Quark Hadron Duality - Recent Jefferson Lab Results
Energy Technology Data Exchange (ETDEWEB)
Niculescu, Maria Ioana [James Madison Univ., Harrisonburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-08-01
The duality between the partonic and hadronic descriptions of electron--nucleon scattering is a remarkable feature of nuclear interactions. When averaged over appropriate energy intervals the cross section at low energy which is dominated by nucleon resonances resembles the smooth behavior expected from perturbative QCD. Recent Jefferson Lab results indicate that quark-hadron duality is present in a variety of observables, not just the proton F2 structure function. An overview of recent results, especially local quark-hadron duality on the neutron, are presented here.
Wilson Loop Form Factors: A New Duality
Chicherin, Dmitry; Heslop, Paul; Korchemsky, Gregory P.; Sokatchev, Emery
2016-01-01
We find a new duality for form factors of lightlike Wilson loops in planar $\\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality....
Quark Hadron Duality - Recent Jefferson Lab Results
Niculescu, Ioana
2015-01-01
The duality between the partonic and hadronic descriptions of electron--nucleon scattering is a remarkable feature of nuclear interactions. When averaged over appropriate energy intervals the cross section at low energy which is dominated by nucleon resonances resembles the smooth behavior expected from perturbative QCD. Recent Jefferson Lab results indicate that quark-hadron duality is present in a variety of observables, not just the proton F2 structure function. An overview of recent results, especially local quark-hadron duality on the neutron, are presented here.
A physics perspective on geometric Langlands duality
Schlesinger, Karl-Georg
2009-01-01
We review the approach to the geometric Langlands program for algebraic curves via S-duality of an N=4 supersymmetric four dimensional gauge theory, initiated by Kapustin and Witten in 2006. We sketch some of the central further developments. Placing this four dimensional gauge theory into a six dimensional framework, as advocated by Witten, holds the promise to lead to a formulation which makes geometric Langlands duality a manifest symmetry (like coavariance in differential geometry). Furthermore, it leads to an approach toward geometric Langlands duality for algebraic surfaces, reproducing and extending the recent results of Braverman and Finkelberg.
Understanding strongly coupling magnetism from holographic duality
Cai, Rong-Gen
2016-01-01
The unusual magnetic materials are significant in both science and technology. However, because of the strongly correlated effects, it is difficult to understand their novel properties from theoretical aspects. Holographic duality offers a new approach to understanding such systems from gravity side. This paper will give a brief review of our recent works on the applications of holographic duality in understanding unusual magnetic materials. Some quantitative compare between holographic results and experimental data will be shown and some predictions from holographic duality models will be discussed.
Duality in Landau-Zener-Stueckelberg potential curve crossing
Fujikawa, K; Fujikawa, Kazuo; Suzuki, Hiroshi
1997-01-01
It is pointed out that there exists an interesting strong and weak duality in the Landau-Zener-Stueckelberg potential curve crossing. A reliable perturbation theory can thus be formulated in the both limits of weak and strong interactions. It is shown that main characteristics of the potential crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-described by simple (time-independent) perturbation theory without referring to Stokes phenomena. A kink-like topological object appears in the ``magnetic'' picture, which is responsible for the absence of the coupling constant in the prefactor of the Landau-Zener formula. It is also shown that quantum coherence in a double well potential is generally suppressed by the effect of potential curve crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.
Coupling a QFT to a TQFT and duality
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [California Institute of Technology,Pasadena, CA 91125 (United States); Seiberg, Nathan [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States)
2014-04-01
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On ℝ{sup d} the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when we compactify ℝ{sup d}, and they are crucial in the context of electric-magnetic duality. We explore several examples including Dijkgraaf-Witten theories and their generalizations both in the continuum and on the lattice. When we couple them to ordinary quantum field theories the topological degrees of freedom allow us to express certain characteristic classes of gauge fields as integrals of local densities, thus simplifying the analysis of their physical consequences.
Bulk Locality from Entanglement in Gauge/Gravity Duality
Lin, Jennifer
2015-01-01
Gauge/gravity duality posits an equivalence between certain strongly coupled quantum field theories and theories of gravity with negative cosmological constant in a higher number of spacetime dimensions. The map between the degrees of freedom on the two sides is non-local and incompletely understood. I describe recent work towards characterizing this map using entanglement in the QFT, where near the dual AdS boundary, the classical energy density at a point in the bulk is stored in the relative entropies of boundary subregions whose homologous minimal surfaces pass through the bulk point. I also derive bulk classical energy conditions near the AdS boundary from entanglement inequalities in the CFT. This is based on the paper [1] with Matilde Marcolli, Hirosi Ooguri and Bogdan Stoica. More generally, in recent years, there has appeared some evidence that quantum entanglement is responsible for the emergence of spacetime. I review and comment on the state of these developments.
Particle-Hole Duality in the Lowest Landau Level
Nguyen, Dung Xuan; Can, Tankut; Gromov, Andrey
2017-05-01
We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several nontrivial checks of the relations, including for the Jain states and their PH conjugates.
On the quantum mechanics of consciousness, with application to anomalous phenomena
Jahn, Robert G.; Dunne, Brenda J.
1986-08-01
Theoretical explication of a growing body of empirical data on consciousness-related anomalous phenomena is unlikely to be achieved in terms of known physical processes. Rather, it will first be necessary to formulate the basic role of consciousness in the definition of reality before such anomalous experience can adequately be represented. This paper takes the position that reality is constituted only in the interaction of consciousness with its environment, and therefore that any scheme of conceptual organization developed to represent that reality must reflect the processes of consciousness as well as those of its environment. In this spirit, the concepts and formalisms of elementary quantum mechanics, as originally proposed to explain anomalous atomic-scale physical phenomena, are appropriated via metaphor to represent the general characteristics of consciousness interacting with any environment. More specifically, if consciousness is represented by a quantum mechanical wave function, and its environment by an appropriate potential profile, Schrödinger wave mechanics defines eigenfunctions and eigenvalues that can be associated with the cognitive and emotional experiences of that consciousness in that environment. To articulate this metaphor it is necessary to associate certain aspects of the formalism, such as the coordinate system, the quantum numbers, and even the metric itself, with various impressionistic descriptors of consciousness, such as its intensity, perspective, approach/avoidance attitude, balance between cognitive and emotional activity, and receptive/assertive disposition. With these established, a number of the generic features of quantum mechanics, such as the wave/particle duality, and the uncertainty, indistinguishability, and exclusion principles, display metaphoric relevance to familiar individual and collective experiences. Similarly, such traditional quantum theoretic exercises as the central force field and atomic structure, covalent
Open-quantum-systems approach to complementarity in neutral-kaon interferometry
de Souza, Gustavo; de Oliveira, J. G. G.; Varizi, Adalberto D.; Nogueira, Edson C.; Sampaio, Marcos D.
2016-12-01
In bipartite quantum systems, entanglement correlations between the parties exerts direct influence in the phenomenon of wave-particle duality. This effect has been quantitatively analyzed in the context of two qubits by Jakob and Bergou [Opt. Commun. 283, 827 (2010), 10.1016/j.optcom.2009.10.044]. Employing a description of the K -meson propagation in free space where its weak decay states are included as a second party, we study here this effect in the kaon-antikaon oscillations. We show that a new quantitative "triality" relation holds, similar to the one considered by Jakob and Bergou. In our case, it relates the distinguishability between the decay-product states corresponding to the distinct kaon propagation modes KS, KL, the amount of wave-like path interference between these states, and the amount of entanglement given by the reduced von Neumann entropy. The inequality can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature, therefore allowing one to see how it is affected by entanglement correlations. As we will discuss, it allows one to visualize clearly through the K0-K ¯0 oscillations the fundamental role of entanglement in quantum complementarity.
Fermionic T-duality: A snapshot review
Colgáin, Eoin Ó
2012-01-01
Through a self-dual mapping of the geometry AdS5 x S5, fermionic T-duality provides a beautiful geometric interpretation of hidden symmetries for scattering amplitudes in N=4 super-Yang-Mills. Starting with Green-Schwarz sigma-models, we consolidate developments in this area into this small review. In particular, we discuss the translation of fermionic T-duality into the supergravity fields via pure spinor formalism and show that a general class of fermionic transformations can be identified directly in the supergravity. In addition to discussing fermionic T-duality for the geometry AdS4 x CP3, dual to N=6 ABJM theory, we review work on other self-dual geometries. Finally, we present a short round-up of studies with a formal interest in fermionic T-duality.
Quark-Hadron Duality in Electron Scattering
Energy Technology Data Exchange (ETDEWEB)
Wally Melnitchouk; Rolf Ent; Cynthia Keppel
2004-08-01
The duality between partonic and hadronic descriptions of physical phenomena is one of the most remarkable features of strong interaction physics. A classic example of this is in electron-nucleon scattering, in which low-energy cross sections, when averaged over appropriate energy intervals, are found to exhibit the scaling behavior expected from perturbative QCD. We present a comprehensive review of data on structure functions in the resonance region, from which the global and local aspects of duality are quantified, including its flavor, spin and nuclear medium dependence. To interpret the experimental findings, we discuss various theoretical approaches which have been developed to understand the microscopic origins of quark-hadron duality in QCD. Examples from other reactions are used to place duality in a broader context, and future experimental and theoretical challenges are identified.
Introduction to dualities in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Kneipp, Marco A.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: kneipp@cbpf.br
2000-12-01
These notes present a pedagogical introduction to magnetic monopoles, supersymmetry and dualities in gauge theories. They are based on lectures given at the X Jorge Andre Swieca Summer School on Particles and Fields. (author)
Color-kinematic duality for form factors
Energy Technology Data Exchange (ETDEWEB)
Boels, Rutger H.; Kniehl, Bernd A.; Tarasov, Oleg V.; Yang, Gang [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2012-12-15
Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory observables formed by form factors. After a discussion of the general setup the existence of the duality is verified in two and three loop examples in four dimensional maximally supersymmetric Yang-Mills theory which involve the stress energy tensor multiplet. In these cases the duality reproduces known results in a particularly transparent and uniform way. As a non-trivial application we obtain a very simple form of the integrand of the four-loop two-point (Sudakov) form factor which passes a large set of unitarity cut checks.
SLE local martingales, reversibility and duality
Energy Technology Data Exchange (ETDEWEB)
Kytoelae, Kalle; Kemppainen, Antti [Department of Mathematics and Statistics, PO Box 68, FIN-00014 University of Helsinki (Finland)
2006-11-17
We study Schramm-Loewner evolutions (SLEs) reversibility and duality using the Virasoro structure of the space of local martingales. For both problems we formulate a setup where the questions boil down to comparing two processes at a stopping time. We state algebraic results showing that local martingales for the processes have enough in common. When one has in addition integrability, the method gives reversibility and duality for any polynomial expected value. (letter to the editor)
Duality, Entropy and ADM Mass in Supergravity
Energy Technology Data Exchange (ETDEWEB)
Cerchiai, Bianca L.; Ferrara, Sergio; Marrani, Alessio; Zumino, Bruno
2009-02-23
We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both"large" and"small" extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.
Searching for S-duality in Gravitation
García-Compéan, H; Ramírez, C
2000-01-01
We overview some attempts to find S-duality analogues of non-supersymmetric Yang-Mills theory, in the context of gravity theories. The case of MacDowell-Mansouri gauge theory of gravity is discussed. Three-dimensional dimensional reductions from the topological gravitational sector in four dimensions, enable to recuperate the 2+1 Chern-Simons gravity and the corresponding S-dual theory, from the notion of self-duality in the four-dimensional theory.
Seiberg Duality is an Exceptional Mutation
Herzog, C P
2004-01-01
The low energy gauge theory living on D-branes probing a del Pezzo singularity of a non-compact Calabi-Yau manifold is not unique. In fact there is a large equivalence class of such gauge theories related by Seiberg duality. As a step toward characterizing this class, we show that Seiberg duality can be defined consistently as an admissible mutation of a strongly exceptional collection of coherent sheaves.
A nonabelian particle–vortex duality
Directory of Open Access Journals (Sweden)
Jeff Murugan
2016-02-01
Full Text Available We define a nonabelian particle–vortex duality as a 3-dimensional analogue of the usual 2-dimensional worldsheet nonabelian T-duality. The transformation is defined in the presence of a global SU(2 symmetry and, although derived from a string theoretic setting, we formulate it generally. We then apply it to so-called “semilocal strings” in an SU(2G×U(1L gauge theory, originally discovered in the context of cosmic string physics.
Gaugino condensation, duality and supersymmetry breaking
Quevedo, Fernando
1995-01-01
The status of gaugino condensation in low-energy string theory is reviewed. Emphasis is given to the determination of the efective action below condensation scale in terms of the 2PI and Wilson actions. We illustrate how the different perturbative duality symmetries survive this simple nonperturbative phenomenon, providing evidence for the believe that these are exact nonperturbative symmetries of string theory. Consistency with T duality lifts the moduli degeneracy. The B_{\\mu\
Duality and helicity: A symplectic viewpoint
Elbistan, M.; Duval, C.; Horváthy, P. A.; Zhang, P.-M.
2016-10-01
The theorem which says that helicity is the conserved quantity associated with the duality symmetry of the vacuum Maxwell equations is proved by viewing electromagnetism as an infinite dimensional symplectic system. In fact, it is shown that helicity is the moment map of duality acting as an SO (2) group of canonical transformations on the symplectic space of all solutions of the vacuum Maxwell equations.
T-Duality and Topological Insulators
Mathai, Varghese
2015-01-01
It is well known that topological insulators are classified by a family of groups, which coincidentally also classifies D-brane charges on orientifolds in string theory. In this letter, we extend this correlation via a geometric analog of the real Fourier transform to obtain a novel duality of topological insulators that can be viewed as a condensed matter analog of T-duality in string theory.
On local duality invariance in electromagnetism
Tiwari, S C
2011-01-01
Duality is one of the oldest known symmetries of Maxwell equations. In recent years the significance of duality symmetry has been recognized in superstrings and high energy physics and there has been a renewed interest on the question of local duality rotation invariance. In the present paper we re-visit global duality symmetry in the Maxwell action and delineate the ambiguous role of gauge invariance and time locality. We have recently demonstrated that local duality invariance in a Lorentz covariant form can be carried out in the Maxwell equations. In this paper it is shown that in the four-pseudo vector Lagrangian theory of Sudbery a local duality generalization can be naturally and unambiguously implemented and the Euler-Lagrange equations of motion are consistent with the generalized Maxwell field equations. It is pointed out that the extension of Noether theorem in full genrality for a vector action is an important open problem in mathematical physics. Physical consequences of this theory for polarized ...
Quantum Simulation of Phylogenetic Trees
Ellinas, Demosthenes
2011-01-01
Quantum simulations constructing probability tensors of biological multi-taxa in phylogenetic trees are proposed, in terms of positive trace preserving maps, describing evolving systems of quantum walks with multiple walkers. Basic phylogenetic models applying on trees of various topologies are simulated following appropriate decoherent quantum circuits. Quantum simulations of statistical inference for aligned sequences of biological characters are provided in terms of a quantum pruning map operating on likelihood operator observables, utilizing state-observable duality and measurement theory.
Features and states of microscopic particles in nonlinear quantum-mechanics systems
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we present the elementary principles of nonlinear quantum mechanics(NLQM),which is based on some problems in quantum mechanics.We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles.Concretely speaking,we study in this paper the wave-particle duality of the solution of the nonlinear Schr6dinger equation,the stability of microscopic particles described by NLQM,invariances and conservation laws of motion of particles,the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations,the classical rule of microscopic particle motion,the mechanism and rules of particle collision,the features of reflection and the transmission of particles at interfaces,and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles,and so on.We obtained the invariance and conservation laws of mass,energy and momentum and angular momenturn for the microscopic particles,which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions.We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics(LQM).They have a lot of new properties;for example,the particles possess the real wave-corpuscle duality,obey the classical rule of motion and conservation laws of energy,momentum and mass,satisfy minimum uncertainty relation,can be localized due to the nonlinear interaction,and its position and momentum can also be determined,etc.From these studies,we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM.Therefore,the NLQM is a new physical theory,and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems,which can
Energy Technology Data Exchange (ETDEWEB)
Khots, Boris, E-mail: bkhots@cccglobal.com [Compressor Controls Corp., Des Moines, Iowa (United States); Khots, Dmitriy, E-mail: dkhots@imathconsulting.com [iMath Consulting LLC Omaha, Nebraska (United States)
2014-12-10
Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.
A Two-loop Test of Buscher's T-duality, 1
Horváth, Z; Palla, L; Horvath, Zalan; Karp, Robert L.; Palla, Laszlo
2000-01-01
We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.
Conformal Aspects of Spinor-Vector Duality
Faraggi, Alon E; Mohaupt, Thomas; Tsulaia, Mirian
2011-01-01
We present a detailed study of various aspects of Spinor-Vector duality in Heterotic string compactifications and expose its origin in terms of the internal conformal field theory. In particular, we illustrate the main features of the duality map by using simple toroidal orbifolds preserving N_4 = 1 and N_4 = 2 spacetime supersymmetries in four dimensions. We explain how the duality map arises in this context by turning on special values of the Wilson lines around the compact cycles of the manifold. We argue that in models with N_4 = 2 spacetime supersymmetry, the interpolation between the Spinor-Vector dual vacua can be continuously realized. We trace the origin of the Spinor-Vector duality map to the presence of underlying N = (2, 2) and N = (4, 4) SCFTs, and explicitly show that the induced spectral-flow in the twisted sectors is responsible for the observed duality. The isomorphism between current algebra representations gives rise to a number of chiral character identities, reminiscent of the recently-di...
Bergshoeff, Eric A
2011-01-01
We construct for arbitrary dimensions a universal T-duality covariant expression for the Wess-Zumino terms of supersymmetric String Solitons in toroidally compactified string theories with 32 supercharges. The worldvolume fields occurring in the effective action of these String Solitons form either a vector or a tensor multiplet with 16 supercharges. We determine the dimensions of the conjugacy classes under T-duality to which these String Solitons belong. We do this in two steps. First, we determine the T-duality representations of the $p$-forms of maximal supergravities that contain the potentials that couple to these String Solitons. We find that these are p-forms, with D-4\\le p\\le 6 if D \\ge 6 and with D-4\\le p\\le D if D < 6, transforming in the antisymmetric representation of rank m=p+4-D\\le 4 of the T-duality symmetry SO(10-D,10-D). All branes support vector multiplets except when m=10-D. In that case the T-duality representation splits, for D<10, into a selfdual and anti-selfdual part, correspond...
Large N Dualities In Topological String Theory
Okuda, T
2005-01-01
We investigate the phenomenon of large N duality in topological string theory from three different perspectives: worldsheets, matrix models, and melting crystals. In the first part, we utilize the technique of mirror symmetry to generalize the worldsheet derivation of the duality, originally given by Ooguri and Vafa for the A- model on the conifold, to the A-model on more general geometries. We also explain how the Landau-Ginzburg models can be used to perform the worldsheet derivation of the B-model large N dualities. In the second part, we consider a class of A-model large N dualities where the open string theory reduces through the Chern-Simons theory on a lens space to a matrix model. We compute and compare the matrix model spectral curve and the Calabi-Yau geometry mirror to the closed string geometry, confirming the predictions of the duality. Finally in the third part, we propose a crystal model that describes the A-model on the resolved conifold. This is a generalization of the crystal for C3. We also...
Issues on 3D Noncommutative Electromagnetic Duality
Rodrigues, D C; Rodrigues, Davi C.; Wotzasek, Clovis
2006-01-01
We extend the ordinary 3D electromagnetic duality to the noncommutative (NC) space-time through a Seiberg-Witten map to second order in the noncommutativity parameter $\\theta$, defining a new scalar field model. There are similarities with the 4D NC duality, these are exploited to clarify properties of both cases. Up to second order in $\\theta$, we find duality interchanges the 2-form $\\theta$ with its 1-form Hodge dual ${^\\star} \\theta $ times the gauge coupling constant, i.e., $ \\theta \\to {^\\star} \\theta g^2$ (similar to the 4D NC electromagnetic duality). We prove that this property is false in the third order expansion in both 3D and 4D space-times. Starting from the third order expansion, $\\theta$ cannot be rescaled to attain an S-duality; on the other hand, to any order in $\\theta$, it is possible to rescale the fields to obtain the same coupling constants in both dual descriptions. In addition to possible applications on effective models, the 3D space-time is useful for studying general properties of ...
Gravitational duality in General Relativity and Supergravity theories
Energy Technology Data Exchange (ETDEWEB)
Dehouck, F. [Service de physique mathematique et interactions fondamentales. Universite Libre de Bruxelles, Campus Plaine CP-231, 1050 Bruxelles (Belgium)
2011-07-15
We quickly review the current status of gravitational duality in General Relativity. We summarize and comment some recent work on constructing dual (topological) charges and understanding how this duality acts in supergravity theories.
Kucharek, Harald; Galvin, Antoinette; Farrugia, Charles; Klecker, Berndt; Pogorelov, Nikolai
2016-04-01
Wave-particle interactions, ion acceleration, and magnetic turbulence are closely interlinked and the physical processes may occur on different scales. These scales range from the kinetic scale to the macro-scale (MHD-scale). These processes are likely universal and the same basic processes occur at the Earth's environment, at the Earth's bow shock, the solar wind, and around the heliosphere. Undoubtedly, the Earth's environment as well as the close interplanetary space are the best plasma environments to study these processes using satellite measurements. Recently, ACE, STEREO, IBEX and Voyager observations clearly showed that turbulence and wave-particle interactions and turbulence are extremely important in interplanetary space and in the heliosphere. Using data from STEREO, Wind, we have investigated the spectral properties of suprathermal ion distributions. The results show that spectral slopes are very variable and depend on the plasma properties. We have also performed 3D hybrid simulations and studied particle dynamics. These simulations show that the particle dynamics in the turbulent magnetic wave field is Levy-Flight like which leads to a kappa distribution, which is often found in various space environments. This result is very significant of future mission such as THOR and IMAP and current operating missions such as STEREO, IBEX, and MMS.
The Roles of Transport and Wave-Particle Interactions on Radiation Belt Dynamics
Fok, Mei-Ching; Glocer, Alex; Zheng, Qiuhua
2011-01-01
Particle fluxes in the radiation belts can vary dramatically during geomagnetic active periods. Transport and wave-particle interactions are believed to be the two main types of mechanisms that control the radiation belt dynamics. Major transport processes include substorm dipolarization and injection, radial diffusion, convection, adiabatic acceleration and deceleration, and magnetopause shadowing. Energetic electrons and ions are also subjected to pitch-angle and energy diffusion when interact with plasma waves in the radiation belts. Important wave modes include whistler mode chorus waves, plasmaspheric hiss, electromagnetic ion cyclotron waves, and magnetosonic waves. We investigate the relative roles of transport and wave associated processes in radiation belt variations. Energetic electron fluxes during several storms are simulated using our Radiation Belt Environment (RBE) model. The model includes important transport and wave processes such as substorm dipolarization in global MHD fields, chorus waves, and plasmaspheric hiss. We discuss the effects of these competing processes at different phases of the storms and validate the results by comparison with satellite and ground-based observations. Keywords: Radiation Belts, Space Weather, Wave-Particle Interaction, Storm and Substorm
Teaching Quantum Physics without Paradoxes
Hobson, Art
2007-01-01
Although the resolution to the wave-particle paradox has been known for 80 years, it is seldom presented. Briefly, the resolution is that material particles and photons are the quanta of extended spatially continuous but energetically quantized fields. But because the resolution resides in quantum field theory and is not usually spelled out in…
Teaching Quantum Physics without Paradoxes
Hobson, Art
2007-01-01
Although the resolution to the wave-particle paradox has been known for 80 years, it is seldom presented. Briefly, the resolution is that material particles and photons are the quanta of extended spatially continuous but energetically quantized fields. But because the resolution resides in quantum field theory and is not usually spelled out in…
M5-branes, orientifolds, and S-duality
Hwang, Yoonseok; Kim, Seok
2016-01-01
We study the instanton partition functions of 5d maximal super Yang-Mills theories with all classical gauge groups. They are computed from the ADHM quantum mechanics of the D0-D4-O4 systems. Our partition functions respect S-dualities of the circle compactified Yang-Mills theories and various orientifold backgrounds. We also compute and study the $S^5$ partition functions that correspond to the 6d (2,0) superconformal indices. Our SO(2N) index takes the form of the vacuum character of $\\mathcal{W}_D$ algebra in a special limit, supporting the $\\mathcal{W}$ algebra conjecture. We propose new indices for (2,0) theories with outer automorphism twists along the temporal circle, obtained from non-simply-laced SYMs on $S^5$.
Duality and hidden symmetries in interacting particle systems
Giardina, Cristian; Redig, Frank; Vafayi, Kiamars
2008-01-01
In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the "hidden" symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.
Integrable Structure in SUSY Gauge Theories, and String Duality
Nam, S
1996-01-01
There is a close relation between duality in $N=2$ SUSY gauge theories and integrable models. In particular, the quantum moduli space of vacua of $N=2$ SUSY $SU(3)$ gauge theories coupled to two flavors of massless quarks in the fundamental representation can be related to the spectral curve of the Goryachev-Chaplygin top. Generalizing this to the cases with {\\it massive} quarks, and $N_f = 0,1,2$, we find a corresponding integrable system in seven dimensional phase space where a hyperelliptic curve appears in the Painlevé test. To understand the stringy origin of the integrability of these theories we obtain exact nonperturbative point particle limit of type II string compactified on a Calabi-Yau manifold, which gives the hyperelliptic curve of $SU(2)$ QCD with $N_f =1$ hypermultiplet.
M5-branes, orientifolds, and S-duality
Hwang, Yoonseok; Kim, Joonho; Kim, Seok
2016-12-01
We study the instanton partition functions of 5d maximal super Yang-Mills theories with all classical gauge groups. They are computed from the ADHM quantum mechanics of the D0-D4-O4 systems. Our partition functions respect S-dualities of the circle compactified Yang-Mills theories and various orientifold backgrounds. We also compute and study the S 5 partition functions that correspond to the 6d (2 , 0) superconformal indices. Our SO(2 N ) index takes the form of the vacuum character of W_D algebra in a special limit, supporting the W algebra conjecture. We propose new indices for (2 , 0) theories with outer automorphism twists along the temporal circle, obtained from non-simply-laced SYMs on S 5.
Duality between noise and spatial resolution in linear systems.
Gureyev, Timur E; Nesterets, Yakov I; de Hoog, Frank; Schmalz, Gerd; Mayo, Sheridan C; Mohammadi, Sara; Tromba, Giuliana
2014-04-21
It is shown that in a broad class of linear systems, including general linear shift-invariant systems, the spatial resolution and the noise satisfy a duality relationship, resembling the uncertainty principle in quantum mechanics. The product of the spatial resolution and the standard deviation of output noise in such systems represents a type of phase-space volume that is invariant with respect to linear scaling of the point-spread function, and it cannot be made smaller than a certain positive absolute lower limit. A corresponding intrinsic "quality" characteristic is introduced and then evaluated for the cases of some popular imaging systems, including computed tomography, generic image convolution and phase-contrast imaging. It is shown that in the latter case the spatial resolution and the noise can sometimes be decoupled, potentially leading to a substantial increase in the imaging quality.
The FZZ-Duality Conjecture - A Proof
Hikida, Yasuaki
2009-01-01
We prove that the cigar conformal field theory is dual to the Sine-Liouville model, as conjectured originally by Fateev, Zamolodchikov and Zamolodchikov. Since both models possess the same chiral algebra, our task is to show that correlations of all tachyon vertex operators agree. We accomplish this goal through an off-critical version of the geometric Langlands duality for sl(2). More explicitly, we combine the well-known self-duality of Liouville theory with an intriguing correspondence between the cigar and Liouville field theory. The latter is derived through a path integral treatment. After a very detailed discussion of genus zero amplitudes, we extend the duality to arbitrary closed surfaces.
Duality theories for Boolean algebras with operators
Givant, Steven
2014-01-01
In this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.
Electromagnetic-Magnetoelectric Duality for Waveguides
Sang-Nourpour, Nafiseh; Kheradmand, R; Rezaei, M; Sanders, Barry C
2015-01-01
We develop a theory for waveguides that respects the duality of electromagnetism, namely the symmetry of the equations arising through inclusion of magnetic monopoles in addition to including electrons (electric monopoles). The term magnetoelectric potential is sometimes used to signify the magnetic-monopole induced dual to the usual electromagnetic potential. To this end, we introduce a general theory for describing modes and characteristics of waveguides based on mixed-monopole materials, with both electric and magnetic responses. Our theory accommodates exotic media such as double-negative, near-zero and zero-index materials, and we demonstrate that our general theory exhibits the electromagnetic duality that would arise if we were to incorporate magnetic monopoles into the media. We consider linear, homogeneous, isotropic waveguide materials with slab and cylindrical geometries. To ensure manifest electromagnetic duality, we construct generic electromagnetic susceptibilities that are dual in both electric...
The FZZ-duality conjecture. A proof
Energy Technology Data Exchange (ETDEWEB)
Hikida, Y. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan); Schomerus, V. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2008-05-15
We prove that the cigar conformal field theory is dual to the Sine-Liouville model, as conjectured originally by Fateev, Zamolodchikov and Zamolodchikov. Since both models possess the same chiral algebra, our task is to show that correlations of all tachyon vertex operators agree. We accomplish this goal through an off-critical version of the geometric Langlands duality for sl(2). More explicitly, we combine the well-known self-duality of Liouville theory with an intriguing correspondence between the cigar and Liouville field theory. The latter is derived through a path integral treatment. After a very detailed discussion of genus zero amplitudes, we extend the duality to arbitrary closed surfaces. (orig.)
Projective Fourier duality and Weyl quantization
Energy Technology Data Exchange (ETDEWEB)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs.
Particle-Vortex Duality from 3d Bosonization
Karch, Andreas
2016-01-01
We provide a simple derivation of particle-vortex duality in d=2+1 dimensions. Our starting point is a relativistic form of flux attachment, designed to transmute the statistics of particles. From this seed, we derive a web of new dualities. These include particle-vortex duality for bosons as well as the recently discovered counterpart for fermions.
A Horizontal Categorification of Gelfand Duality
Bertozzini, Paolo; Lewkeeratiyutkul, Wicharn
2008-01-01
In the setting of C*-categories, we provide a definition of "spectrum" of a commutative full C*-category as a one-dimensional unital saturated Fell bundle over a suitable groupoid (equivalence relation) and prove a categorical Gelfand duality theorem generalizing the usual Gelfand duality between the categories of commutative unital C*-algebras and compact Hausdorff spaces. Although many of the individual ingredients that appear along the way are well-known, the somehow unconventional way we "glue" them together seems to shed some new light on the subject.
Duality of boiling systems and uncertainty phenomena
Institute of Scientific and Technical Information of China (English)
柴立合; 彭晓峰; 王补宣
2000-01-01
Interactions among dry patches at high heat flux are theoretically analyzed. The high heat flux boiling experiments on metal plate wall with different materials and thickness are correspondingly conducted. The duality of boiling system, i.e. hydrodynamic performance and self-organized performance is identified. A unified explanation of hydrodynamic models and dry patches models is given. The scatter and uncertainty in boiling data can be mainly attributed to the intrinsic duality, but not the sole surface effects. The present experimental results explain why the deviation point at high flux boiling is seen only on occasion and why the self-organization of dry patches is often ignored in available literature.
U-Duality and the Leech Lattice
Rios, Michael
2013-01-01
It has recently been shown that the full automorphism group of the Leech lattice, Conway's group Co_0, can be generated by 3 x 3 matrices over the octonions. We show such matrices are of type F_4 in E_{6(-26)}, the U-duality group for N=2, D=5 exceptional magic supergravity. By mapping points of the Leech lattice to black hole charge vectors, it is seen Conway's group Co_0 is generated by U-duality transformations acting as rotations in the charge space for BPS black holes.
Duality between random trap and barrier models
Energy Technology Data Exchange (ETDEWEB)
Jack, Robert L [Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720 (United States); Sollich, Peter [Department of Mathematics, King' s College London, London WC2R 2LS (United Kingdom)
2008-08-15
We discuss the physical consequences of a duality between two models with quenched disorder, in which particles propagate in one dimension among random traps or across random barriers. We derive an exact relation between their diffusion fronts at fixed disorder and deduce from this that their disorder-averaged diffusion fronts are exactly equal. We use effective dynamics schemes to isolate the different physical processes by which particles propagate in the models and discuss how the duality arises from a correspondence between the rates for these different processes.
Noether symmetries and duality transformations in cosmology
Paliathanasis, Andronikos
2016-01-01
We discuss the relation between local transformations generated by Noether (point) symmetries and discrete transformations for a class of minisuperspace cosmological models. Moreover as far as concerns the scale-factor duality of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations. In particular, the same point symmetry exists for the Brans-Dicke- scalar field with linear potential for $\\omega_{BD}=1$ . Furthermore, in the context of the O'Hanlon theory for $f\\left( R\\right) $-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Classical signal model reproducing quantum probabilities for single and coincidence detections
Khrennikov, Andrei; Nilsson, Börje; Nordebo, Sven
2012-05-01
We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wave model. QM predicts that the relative probability of coincidence detection, the coefficient g(2) (0), is zero (for one photon states), but in (semi-)classical models g(2)(0) >= 1. In TSD the coefficient g(2)(0) decreases as 1/ɛ2d, where ɛd > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g(2) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g(2)(0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.
Classical signal model reproducing quantum probabilities for single and coincidence detections
Khrennikov, Andrei; Nordebo, Sven
2011-01-01
We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 \\cite{Grangier} played a crucial role in rejection of (semi-)classical field models in favor of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favor of a purely wave model. QM predicts that the relative probability of coincidence detection, the coefficient $g^{(2)}(0),$ is zero (for one photon states), but in (semi-)classical models $g^{(2)}(0)\\geq 1.$ In TSD the coefficient $g^{(2)}(0)$ decreases as $1/{\\cal E}_d^2,$ where ${\\cal E}_d>0$ is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient $g^{(2)}...
An open quantum system approach to complementarity in neutral kaon interferometry
de Souza, Gustavo; Varizi, Adalberto D; Nogueira, Edson C; Sampaio, Marcos D
2016-01-01
In bipartite quantum systems, entanglement correlations between the parties exerts direct influence in the phenomenon of wave-particle duality. This effect has been quantitatively analyzed in the context of two qubits by M. Jakob and J. Bergou [Optics Communications 283(5) (2010) 827]. Employing a description of the K-meson propagation in free space where its weak decay states are included as a second party, we study here this effect in the kaon-antikaon oscillations. We show that a new quantitative "triality" relation similar to the one considered by Jakob and Bergou holds. In our case, it relates the distinguishability between the decay products states corresponding to the distinct kaon propagation modes $K_S $, $K_L $, the amount of wave-like path interference between these states, and the amount of entanglement given by the reduced von Neumann entropy. The inequality can account for the complementarity between strangeness oscillations and lifetime information previously considered in the literature, there...
On the role of wave-particle interactions in the macroscopic dynamics of collisionless plasmas
Wilson, Lynn B; Osmane, Adnane; Malaspina, David M
2015-01-01
What is the relative importance of small-scale (i.e., electron to sub-electron scales), microphysical plasma processes to the acceleration of particles from thermal to suprathermal or even to cosmic-ray energies? Additionally, can these microphysical plasma processes influence or even dominate macroscopic (i.e., greater than ion scales) processes, thus affecting global dynamics? These are fundamental and unresolved questions in plasma and astrophysical research. Recent observations of large amplitude electromagnetic waves in the terrestrial radiation belts [i.e., Cattell et al., 2008; Kellogg et al., 2010; Wilson III et al., 2011] and in collisionless shock waves [i.e., Wilson III et al., 2014a,b] have raised questions regarding the macrophysical effect of these microscopic waves. The processes thought to dominate particle acceleration and the macroscopic dynamics in both regions have been brought into question with these recent observations. The relative importance of wave-particle interactions has recently ...
Electron Fluid Description of Wave-Particle Interactions in Strong Buneman Turbulence
Che, H
2014-01-01
To understand the nature of anomalous resistivity in magnetic reconnection, we investigate turbulence-induced momentum transport and energy dissipation during Buneman instability in force-free current sheets. Using 3D particle-in-cell simulations, we find that the macroscopic effects generated by wave-particle interactions in Buneman instability can be approximately described by a set of electron fluid equations. These equations show that the energy dissipation and momentum transports along current sheets are locally quasi-static but globally non-static and irreversible. Turbulence drag dissipates both the streaming energy of current sheets and the associated magnetic energy. The decrease of magnetic field maintains an inductive electric field that re-accelerates electrons. The net loss of streaming energy is converted into the heat of electrons moving along the magnetic field and increases the electron Boltzmann entropy. The growth of self-sustained Buneman waves satisfies a Bernoulli-like equation that rela...
Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction
de Buyl, Pierre; Bachelard, Romain; De Ninno, Giovanni
2009-01-01
The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g., electrostatic instabilities in plasma physics, particle acceleration and free-electron lasers. The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent relaxation theory. In this context, the transition is explained as a dynamical switch between two metastable regimes, and related to the change of nature of a stationary point of an entropic functional.
Level/rank Duality and Chern-Simons-Matter Theories
Hsin, Po-Shen
2016-01-01
We discuss in detail level/rank duality in three-dimensional Chern-Simons theories and various related dualities in three-dimensional Chern-Simons-matter theories. We couple the dual Lagrangians to appropriate background fields (including gauge fields, spin$_c$ connections and the metric). The non-trivial maps between the currents and the line operators in the dual theories is accounted for by mixing of these fields. In order for the duality to be valid we must add finite counterterms depending on these background fields. This analysis allows us to resolve a number of puzzles with these dualities, to provide derivations of some of them, and to find new consistency conditions and relations between them. In addition, we find new level/rank dualities of topological Chern-Simons theories and new dualities of Chern-Simons-matter theories, including new boson/boson and fermion/fermion dualities.
On the dimensional dependence of the electromagnetic duality groups
Wotzasek, C
1998-01-01
We study the two-fold dimensional dependence of the electromagnetic duality groups. We introduce the dual projection operation that systematically discloses the presence of an internal space of potentials where the group operation is defined. A two-fold property of the kernel in the projection is shown to define the dimensional dependence of the duality groups. The dual projection is then generalized to reveal another hidden two-dimensional structure. The new unifying concept of the external duality space remove the dimensional dependence of the kernel, allowing the presence of both $Z_2$ and SO(2) duality groups in all even dimensions. This result, ultimately unifies the notion of selfduality to all D=2k+2 dimensions. Finally, we show the presence of an unexpected duality between the internal and external spaces leading to a duality of the duality groups.
Local Duality for 2-Dimensional Local Ring
Indian Academy of Sciences (India)
Belgacem Draouil
2008-11-01
We prove a local duality for some schemes associated to a 2-dimensional complete local ring whose residue field is an -dimensional local field in the sense of Kato–Parshin. Our results generalize the Saito works in the case =0 and are applied to study the Bloch–Ogus complex for such rings in various cases.
Refined large N duality for torus knots
DEFF Research Database (Denmark)
Nawata, Satoshi; Kameyama, Masaya
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate...
New duality Transformations in Orbifold Theory
J. de Boer; J. Evslin; M. Halpern; J.E. Wang
2000-01-01
We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold $A(H)/H$, where $A(H)$ is the set of all current-algebraic conformal field theories with a finite symmetry group $H \\subset Aut(g)$. The permutation orbifolds with $H = Z_\\la
Noether symmetries and duality transformations in cosmology
Paliathanasis, Andronikos; Capozziello, Salvatore
2016-09-01
We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Two Point Pade Approximants and Duality
Banks, Tom
2013-01-01
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a strong/weak duality, when the symmetries do not determine exact expressions for some quantity.
Duality properties of Gorringe Leach equations
Grandati, Yves; Bérard, Alain; Mohrbach, Hervé
2009-02-01
In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold Vassiliev type. The specific associated conserved quantities (Laplace Runge Lenz vector and Fradkin Jauch Hill tensor) are then dual reflections of each other.
Two-component Duality and Strings
Freund, Peter G O
2007-01-01
A phenomenologically successful two-component hadronic duality picture led to Veneziano's amplitude, the fundamental first step to string theory. This picture is briefly recalled and its two components are identified as the open strings (mesons and baryons) and closed strings (Pomeron).
Dualities for Logics of Transition Systems
Bonsangue, M.M.; Kurz, A.
2005-01-01
We present a general framework for logics of transition systems based on Stone duality. Transition systems are modelled as coalgebras for a functor T on a category X. The propositional logic used to reason about state spaces from X is modelled by the Stone dual A of X (e.g. if X is Stone spaces then
The Higher Spin/Vector Model Duality
Giombi, Simone; Yin, Xi
2012-01-01
This paper is mainly a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.
Refined large N duality for torus knots
DEFF Research Database (Denmark)
Nawata, Satoshi; Kameyama, Masaya
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate...
Intergenerational equity and dynamic duality principles
Directory of Open Access Journals (Sweden)
Hirofumi Uzawa
2002-01-01
Full Text Available The concept of intergenerational equity concerning intertemporal paths of consumption and capital accumulation is introduced and the analysis of the dynamic processes of capital accumulation and changes in environmental quality that are intergenerationally equitable is developed. The analysis is based upon the dynamic duality principles, as originally developed by Koopmans and Uzawa, and later extended to the case involving environmental quality.
An alternative formulation of classical electromagnetic duality
Li, K; Li, Kang; Naón, Carlos M.
2001-01-01
By introducing a doublet of electromagnetic four dimensional vector potentials, we set up a manifestly Lorentz covariant and SO(2) duality invariant classical field theory of electric and magnetic charges. In our formulation one does not need to introduce the concept of Dirac string.
On the universe's cybernetics duality behavior
Feria, Erlan H.
2015-05-01
Universal cybernetics is the study of control and communications in living and non-living systems. In this paper the universal cybernetics duality principle (UCDP), first identified in control theory in 1978 and expressing a cybernetic duality behavior for our universe, is reviewed. The review is given on the heels of major prizes given to physicists for their use of mathematical dualities in solving intractable problems in physics such as those of cosmology's `dark energy', an area that according to a recent New York Times article has become "a cottage industry in physics today". These dualities are not unlike those of our UCDP that are further enhanced with physical dualities. For instance, in 2008 the UCDP guided us to the derivation of the laws of retention in physics as the space-penalty dual of the laws of motion in physics, including the dark energy thought responsible for the observed increase of the volume of our Universe as it ages. The UCDP has also guided us to the discovery of significant results in other fields such as: 1) in matched processors for quantized control with applications in the modeling of central nervous system (CNS) control mechanisms; 2) in radar designs where the discovery of latency theory, the time-penalty dual of information-theory, has led us to high-performance radar solutions that evade the use of `big data' in the form of SAR imagery of the earth; and 3) in unveiling biological lifespan bounds where the life-expectancy of an organism is sensibly predicted through lingerdynamics, the identified time-penalty dual of thermodynamics, which relates its adult lifespan to either: a. the ratio of its body size to its nutritional consumption rate; or b. its specific heat-capacity; or c. the ratio of its nutritional consumption rate energy to its entropic volume energy, a type of dark energy that is consistent with the observed decrease in the mass density of the organism as it ages.
Indian Academy of Sciences (India)
Taksu Cheon
2002-08-01
The existence of several exotic phenomena, such as duality and spectral anholonomy is pointed out in one-dimensional quantum wire with a single defect. The topological structure in the spectral space which is behind these phenomena is identiﬁed.
Of gluons and gravitons. Exploring color-kinematics duality
Energy Technology Data Exchange (ETDEWEB)
Isermann, Reinke Sven
2013-06-15
In this thesis color-kinematics duality will be investigated. This duality is a statement about the kinematical dependence of a scattering amplitude in Yang-Mills gauge theories obeying group theoretical relations similar to that of the color gauge group. The major consequence of this duality is that gravity amplitudes can be related to a certain double copy of gauge theory amplitudes. The main focus of this thesis is on exploring the foundations of color-kinematics duality and its consequences. It is shown how color-kinematics duality can be made manifest at the one-loop level for rational amplitudes. A Lagrangian-based argument will be given for the validity of the double copy construction for these amplitudes including explicit examples at four points. Secondly, it is studied how color-kinematics duality can be used to improve powercounting in gravity theories. To this end the duality is reformulated in terms of linear maps. It is shown as an example how this can be used to derive the large BCFW shift behavior of a gravity integrand constructed through the duality to any loop order up to subtleties inherent to the duality that is addressed. As it becomes clear the duality implies massive cancellations with respect to the usual powercounting of Feynman graphs indicating that gravity theories are much better behaved than naively expected. As another example the linear map approach will be used to investigate the question of UV-finiteness of N=8 supergravity, and it is seen that the amount of cancellations depends on the exact implementation of the duality at loop level. Lastly, color-kinematics duality is considered from a Feynman-graph perspective reproducing some of the results of the earlier chapters thus giving non-trivial evidence for the duality at the loop level from a different perspective.
de Lima Bernardo, Bertúlio; Canabarro, Askery; Azevedo, Sérgio
2017-01-01
The concept of wave-particle duality, which is a key element of quantum theory, has been remarkably found to manifest itself in several experimental realizations as in the famous double-slit experiment. In this specific case, a single particle seems to travel through two separated slits simultaneously. Nevertheless, it is never possible to measure it in both slits, which naturally appears as a manifestation of the collapse postulate. In this respect, one could as well ask if it is possible to “perceive” the presence of the particle at the two slits simultaneously, once its collapse could be avoided. In this article, we use the recently proposed entanglement mediation protocol to provide a positive answer to this question. It is shown that a photon which behaves like a wave, i.e., which seems to be present in two distant locations at the same time, can modify two existing physical realities in these locations. Calculations of the “weak trace” left by such photon also enforce the validity of the present argumentation.
Duality based optical flow algorithms with applications
DEFF Research Database (Denmark)
Rakêt, Lars Lau
We consider the popular TV-L1 optical flow formulation, and the so-called duality based algorithm for minimizing the TV-L1 energy. The original formulation is extended to allow for vector valued images, and minimization results are given. In addition we consider different definitions of total...... variation regularization, and related formulations of the optical flow problem that may be used with a duality based algorithm. We present a highly optimized algorithmic setup to estimate optical flows, and give five novel applications. The first application is registration of medical images, where X......-ray images of different hands, taken using different imaging devices are registered using a TV-L1 optical flow algorithm. We propose to regularize the input images, using sparsity enhancing regularization of the image gradient to improve registration results. The second application is registration of 2D...
A duality web of linear quivers
Brünner, Frederic
2016-01-01
We show that applying the Bailey lemma to elliptic hypergeometric integrals on the $A_n$ root system leads to a large web of dualities for $\\mathcal{N} = 1$ supersymmetric linear quiver theories. The superconformal index of Seiberg's SQCD with $SU(N_c)$ gauge group and $SU(N_f)\\times SU(N_f)\\times U(1)$ global symmetry is equal to that of $N_f-N_c-1$ distinct linear quivers. Seiberg duality further enlarges this web by adding new quivers. In particular, both interacting electric and magnetic theories with arbitrary $N_c$ and $N_f$ can be constructed by quivering an $s$-confining theory with $N_f=N_c+1$.
Off-shell Color-Kinematics Duality
Mastrolia, Pierpaolo; Schubert, Ulrich; Bobadilla, William J Torres
2015-01-01
We elaborate on the color-kinematics duality for off-shell diagrams in gauge theories coupled to matter, by investigating the scattering process $gg\\to ss, q\\bar q, gg$, and show that the Jacobi relations for the kinematic numerators of off-shell diagrams, built with Feynman rules in axial gauge, reduces to a color-kinematics violating term due to the contributions of sub-graphs only. Such anomaly vanishes when the four particles connected by the Jacobi relation are on their mass shell with vanishing squared momenta, being either external or cut particles, where the validity of the color-kinematics duality is recovered. We discuss the role of this off-shell decomposition in the direct construction of higher-multiplicity numerators satisfying color-kinematics identity, providing an explicit example for the QCD process $gg\\to q\\bar{q}g$.
Mordell integrals and Giveon-Kutasov duality
Energy Technology Data Exchange (ETDEWEB)
Giasemidis, Georgios [CountingLab LTD & Centre for the Mathematics of Human Behaviour (CMoHB),Department of Mathematics and Statistics, University of Reading, Reading, RG6 6AX (United Kingdom); Tierz, Miguel [Departamento de Matemática, Grupo de Física Matemática, Faculdade de Ciências,Universidade de Lisboa, Campo Grande, Edifício C6, Lisboa, 1749-016 (Portugal); Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas,Universidad Complutense de Madrid, Madrid, 28040 (Spain)
2016-01-12
We solve, for finite N, the matrix model of supersymmetric U(N) Chern-Simons theory coupled to N{sub f} massive hypermultiplets of R-charge (1/2), together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix, whose entries are parametric derivatives (of order N{sub f}−1) of Mordell integrals. We obtain finite Gauss sums expressions for the partition functions. We also apply these results to obtain an exhaustive test of Giveon-Kutasov (GK) duality in the N=3 setting, by systematic computation of the matrix models involved. The phase factor that arises in the duality is then obtained explicitly. We give an expression characterized by modular arithmetic (mod 4) behavior that holds for all tested values of the parameters (checked up to N{sub f}=12 flavours).
Conference on Strings, Duality, and Geometry
Phong, Duong; Yau, Shing-Tung; Mirror Symmetry IV
2002-01-01
This book presents contributions of participants of a workshop held at the Centre de Recherches Mathématiques (CRM), University of Montréal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapi...
Duality Covariant Solutions in Extended Field Theories
Rudolph, Felix J
2016-01-01
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to winding modes of the fundamental objects. This geometrically unifies the spacetime metric and the gauge fields (and their local symmetries) in a generalized geometry. Solutions to these extended field theories take the simple form of waves and monopoles in the extended space. From a supergravity point of view they appear as 1/2 BPS objects such as the string, the membrane and the fivebrane in ordinary spacetime. In this thesis double field theory and exceptional field theory are introduced, solutions to their equations of motion are constructed and their properties are analyzed. Further it is established how isometries in the extended space give rise to duality relations between the supergravity solutions. Extensions to these core ideas include studying Goldstone modes, probing s...
Duality orbits of non-geometric fluxes
Energy Technology Data Exchange (ETDEWEB)
Dibitetto, G.; Roest, D. [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Fernandez-Melgarejo, J.J. [Grupo de Fisica Teorica y Cosmologia, Dept. de Fisica, University of Murcia, Campus de Espinardo, 30100-Murcia (Spain); Marques, D. [Institut de Physique Theorique, CEA/ Saclay, 91191 Gif-sur-Yvette Cedex (France)
2012-11-15
Compactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non-geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T- and U-duality orbits of gaugings of (half-)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non-geometric orbits in the half-maximal case. We show how the latter are obtained from compactifications of double field theory. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Natsuume, Makoto
2014-01-01
This is the draft version of a textbook on "real-world" applications of the AdS/CFT duality for beginning graduate students in particle physics and for researchers in the other fields. The aim of this book is to provide background materials such as string theory, general relativity, nuclear physics, nonequilibrium physics, and condensed-matter physics as well as some key applications of the AdS/CFT duality in a single textbook. Contents: (1) Introduction, (2) General relativity and black holes, (3) Black holes and thermodynamics, (4) Strong interaction and gauge theories, (5) The road to AdS/CFT, (6) The AdS spacetime, (7) AdS/CFT - equilibrium, (8) AdS/CFT - adding probes, (9) Basics of nonequilibrium physics, (10) AdS/CFT - nonequilibrium, (11) Other AdS spacetimes, (12) Applications to quark-gluon plasma, (13) Basics of phase transition, (14) AdS/CFT - phase transition.
Duality based optical flow algorithms with applications
DEFF Research Database (Denmark)
Rakêt, Lars Lau
We consider the popular TV-L1 optical flow formulation, and the so-called duality based algorithm for minimizing the TV-L1 energy. The original formulation is extended to allow for vector valued images, and minimization results are given. In addition we consider different definitions of total...... variation regularization, and related formulations of the optical flow problem that may be used with a duality based algorithm. We present a highly optimized algorithmic setup to estimate optical flows, and give five novel applications. The first application is registration of medical images, where X......-ray images of different hands, taken using different imaging devices are registered using a TV-L1 optical flow algorithm. We propose to regularize the input images, using sparsity enhancing regularization of the image gradient to improve registration results. The second application is registration of 2D...
Grassmann Duality and the Particle Spectrum
Delbourgo, Robert
2016-01-01
Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing sensible Lagrangians anyhow. We apply duality to all of the subgroups within the {\\em classification} group SU(3)$\\times$SU(2)$_L\\times$SU(2)$_R$, which encompasses the standard model gauge group, and thereby determine the full state inventory; this includes the definite prediction of quarks with charge -4/3 and other exotic states. Assuming universal gravitational coupling to the gauge fields and parity even property curvature, we also obtain $4\\sin^2\\theta_w = 1 - 2\\alpha/3\\alpha_s$ which is not far from the experimental value around the $M_Z$ mass.
A CMB/Dark Energy Cosmic Duality
DEFF Research Database (Denmark)
Enqvist, Kari; Sloth, Martin Snoager
2004-01-01
We investigate a possible connection between the suppression of the power at low multipoles in the CMB spectrum and the late time acceleration. We show that, assuming a cosmic IR/UV duality between the UV cutoff and a global infrared cutoff given by the size of the future event horizon, the equat......We investigate a possible connection between the suppression of the power at low multipoles in the CMB spectrum and the late time acceleration. We show that, assuming a cosmic IR/UV duality between the UV cutoff and a global infrared cutoff given by the size of the future event horizon......, the equation of state of the dark energy can be related to the apparent cutoff in the CMB spectrum. The present limits on the equation of state of dark energy are shown to imply an IR cutoff in the CMB multipole interval of 9>l>8.5....
Conceptual Aspects of Gauge/Gravity Duality
de Haro, Sebastian; Butterfield, Jeremy
2015-01-01
We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening Sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string theory, that we need for presenting, in Section 5, the central and original example: Maldacena's AdS/CFT correspondence. Sections 6 and 7 develop the ideas of this example, also in applications to condensed matter systems, QCD, and hydrodynamics. Sections 8 and 9 discuss the possible extensions of holographic ideas to de Sitter spacetime and to black holes. Section 10 discusses the bearing of gauge/gravity duality on two philosophical topics: the equivalence of physical theories, and the idea that spacetime, or some features of it, are emergent.
Conceptual Aspects of Gauge/Gravity Duality
De Haro, Sebastian; Mayerson, Daniel R.; Butterfield, Jeremy N.
2016-11-01
We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string theory, that we need for presenting, in Sect. 5, the central and original example: Maldacena's AdS/CFT correspondence. Sections 6 and 7 develop the ideas of this example, also in applications to condensed matter systems, QCD, and hydrodynamics. Sections 8 and 9 discuss the possible extensions of holographic ideas to de Sitter spacetime and to black holes. Section 10 discusses the bearing of gauge/gravity duality on two philosophical topics: the equivalence of physical theories, and the idea that spacetime, or some features of it, are emergent.
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
Distributive lattice orderings and Priestley duality
Krebs, Michel
2007-01-01
The ordering relation of a bounded distributive lattice L is a (distributive) (0, 1)-sublattice of L \\times L. This construction gives rise to a functor \\Phi from the category of bounded distributive lattices to itself. We examine the interaction of \\Phi with Priestley duality and characterise those bounded distributive lattices L such that there is a bounded distributive lattice K such that \\Phi(K) is (isomorphic to) L.
Nash equilibria via duality and homological selection
Indian Academy of Sciences (India)
Arnab Basu; Samik Basu; Mahan MJ
2014-11-01
Given a multifunction from to the -fold symmetric product Sym$_{k}(X)$, we use the Dold–Thom theorem to establish a homological selection theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré duality in addition to the Dold–Thom theorem.
Capturing consumer engagement: duality, dimensionality and measurement
Dessart, Laurence; Veloutsou, Cleopatra; Morgan-Thomas, Anna
2016-01-01
This study advances the conceptualisation and operationalisation of consumer engagement in the context of online brand communities (OBCs). Past scholarship has only partially addressed the dimensionality of engagement and the different engagement foci, and these oversights have important theoretical and empirical consequences. This study contributes to the nascent stream of research that aims to theoretically refine and operationalise engagement by espousing the duality of engagement with two...
Duality without constraint qualification in nonsmooth optimization
S. Nobakhtian
2006-01-01
We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualification. Then we formulate the dual problem corresponding to the primal problem, and some duality res...
Duality properties between spectra and tilings
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Spectra and tilings play an important role in analysis and geometry respectively.The relations between spectra and tilings have bafied the mathematicians for a long time.Many conjectures,such as the Fuglede conjecture,are placed on the establishment of relations between spectra and tilings,although there are no desired results.In the present paper we derive some characteristic properties of spectra and tilings which highlight certain duality properties between them.
Duality properties of Gorringe-Leach equations
Grandati, Yves; Berard, Alain; Mohrbach, Herve
2004-01-01
International audience; In the category of motions preserving the angular momentum's direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold-Vassiliev type. The specific associated conserved quantities (Laplace-Runge-Lenz vector and Fradkin-Jauch-Hill tensor) are then dual reflections one of the other
Duality properties of Gorringe-Leach equations
Grandati, Yves; Mohrbach, Herve
2007-01-01
In the category of motions preserving the angular momentum's direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they're related by a duality correspondence of the Arnold-Vassiliev type. The specific associated conserved quantities (Laplace-Runge-Lenz vector and Fradkin-Jauch-Hill tensor) are then dual reflections one of the other.
Higher-Spin Gauge Fields and Duality
Francia, D
2006-01-01
We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We also discuss duality transformations that give different field theory representations of the same physical degrees of freedom, and discuss the example of gravity in $D$ dimensions and its dual realisations in detail.
Real weights, bound states and duality orbits
Marrani, Alessio; Romano, Luca
2015-01-01
We show that the duality orbits of extremal black holes in supergravity theories with symmetric scalar manifolds can be derived by studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the duality symmetry group. The weight vectors always correspond to weights that are real, where the reality properties are derived from the Tits-Satake diagram that identifies the real form of the Lie algebra of the duality symmetry group. Both N=2 magic Maxwell-Einstein supergravities and the semisimple infinite sequences of N=2 and N=4 theories in D=4 and 5 are considered, and various results, obtained over the years in the literature using different methods, are retrieved. In particular, we show that the stratification of the orbits of these theories occurs because of very specific properties of the representations: in the case of the theory based on the real numbers, whose symmetry group is maximally non-compact and there...
Aspects of duality in gravitational theories
Troessaert, Cedric
2013-01-01
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an action manifestly invariant under duality rotations in presence of both electric and magnetic external sources. It is also shown how, in the reduced phase-space, all higher spin gauge fields can be written as bi-hamiltonian systems. The role of the second hamiltonian is played by the electromagnetic duality generator. The second part is devoted to the study of asymptotic symmetries and their applications to holography. After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In particular, it is argued that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semi-direct sum of su...
Proton Spin Structure Functions and Quark-Hadron Duality
Institute of Scientific and Technical Information of China (English)
DONG Yu-Bing
2006-01-01
@@ Quark-hadron duality of three proton spin structure functions g1, g2 and gT are discussed simultaneously. It is found that the onsets of the quark-hadron dualities of g1p, g2p and g3p are similar and they are expected to be at about Q2 ～ 2 GeV2. In addition, our results show that the elastic peak remarkably breaks local quark-hadron duality.
Measurement in quantum physics
Energy Technology Data Exchange (ETDEWEB)
Danos, M. [Illinois Univ., Chicago, IL (United States); Kieu, T.D. [Melbourne Univ., Parkville, VIC (Australia). School of Physics]|[Columbia Univ., New York, NY (United States). Dept. of Physics
1997-06-01
The conceptual problems in quantum mechanics - including the collapse of the wave functions, the particle-wave duality, the meaning of measurement-arise from the need to ascribe particle character to the wave function, which describes only the wave aspects. It is demonstrated that all these problems can be resolved when working instead with quantum fields, which have both wave and particle character. The predictions of quantum physics, including Bell`s inequalities, remain unchanged from the standard treatments of quantum mechanics. 16 refs.
Topological duality twist and brane instantons in F-theory
Energy Technology Data Exchange (ETDEWEB)
Martucci, Luca [Dipartimento di Fisica ed Astronomia “Galileo Galilei”, Università di Padova andINFN - Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy)
2014-06-30
A variant of the topological twist, involving SL(2,ℤ) dualities and hence named topological duality twist, is introduced and explicitly applied to describe a U(1) N=4 super Yang-Mills theory on a Kähler space with holomorphically space-dependent coupling. Three-dimensional duality walls and two-dimensional chiral theories naturally enter the formulation of the duality twisted theory. Appropriately generalized, this theory is relevant for the study of Euclidean D3-brane instantons in F-theory compactifications. Some of its properties and implications are discussed.
Particle-vortex duality in topological insulators and superconductors
Murugan, Jeff
2016-01-01
We investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path integral in the standard way, while in three dimensions, it takes the form of "self-duality in odd dimensions". In this sense, it is closely related to the particle-vortex duality of planar systems. In particular, we use this to elaborate on Son's conjecture that a three dimensional Dirac fermion that can be thought of as the surface mode of a four dimensional topological insulator is dual to a composite fermion.
Exact results in gauge-string dualities (Stockholm, Sweden, 23 January-17 February 2012)
Zarembo, Konstantin
2012-08-01
Exactly solvable models play a distinguished role in physics, as they help us understand the behavior of strongly correlated, strongly coupled systems in the regimes where other methods fail. For a long time, the exact solvability was associated with (1+1)-dimensional systems, where powerful methods of integrability allow one to find the exact spectrum, to study thermodynamics and to compute correlation functions for a number of strongly interacting field theories. The AdS/CFT duality established a rigorous relationship between gauge fields and strings, and paved the way for applying the methods of integrability in four-dimensional gauge theories. The two-dimensional dynamics on the string worldsheet (dual to the fluctuating electric flux tube in a gauge theory) is in many cases integrable, which opens the avenue for applications of non-perturbative, integrability-based methods to four-dimensional gauge theories. The progress in understanding non-perturbative phenomena in gauge theories has been rapid in recent years, and required synergy of methods from exactly solvable models, gauge theories, strings and integrable systems. The program 'Exact Results in Gauge-String Dualities' took place at Nordita, Stockholm from 23 January to 17 February 2012 and brought together specialists with common interests in string theory, quantum field theory and exactly solvable models. Topics discussed during the program included: (i) exact results in the AdS/CFT correspondence, (ii) scattering amplitudes, (iii) supersymmetric gauge theories, and (iv) Bethe ansatz and exact solvability in quantum field theory and statistical systems. The articles by D Sorokin [1] and M de Leeuw et al [2] give an overview of the string-theory origins of integrability in gauge theories, and of the algebraic structures omnipresent in quantum integrable systems. The topics covered in these articles underpin the integrability approach to gauge--string dualities and lie at the heart of the integrability
An Inequality Concerning Quantitative Duality in an Asymmetry Two-Way Interferometer
Institute of Scientific and Technical Information of China (English)
HAN Yang; WU Chun-Wang; WU Wei; CHEN Ping-Xing; LI Cheng-Zu
2009-01-01
@@ We reinvestigate the measures concerning the notion of duality of a quantum system (the "quanton") in an asymmetry two-way interferometer. A new measure of the which-way information is introduced, which is based on the fidelity F instead of the trace distance Q of the final states of the which-way detector. An improved inequality is derived to be V2 ≤ (R20-P2)(1-F)2, which is more stringent than the previous one of V2 ≤ (1-P2)(1-Q2).
T-duality simplifies bulk-boundary correspondence: the general case
Hannabuss, Keith C; Thiang, Guo Chuan
2016-01-01
We state and prove a general result establishing that T-duality simplifies the bulk-boundary correspondence, in the sense of converting it to a simple geometric restriction map. This settles in the affirmative several earlier conjectures of the authors, and provides a clear geometric picture of the correspondence. In particular, our result holds in arbitrary spatial dimension, in both the real and complex cases, and also in the presence of disorder, magnetic fields, and H-flux. These special cases are relevant both to String Theory and to the study of the quantum Hall effect and topological insulators with defects in Condensed Matter Physics.
Type Ii/heterotic Duality And Mirror Symmetry (bundle Deformation, String Duality)
Perevalov, E V
1998-01-01
Toric geometry is used to systematically construct Type II compactifications dual to Heterotic models in six dimensions involving singular K3 surfaces as well as vector bundles. Reflexive polyhedra are shown to encode the spectra of the resulting low-energy theories. Finally, the connection between mirror symmetry and deformation of bundles on K3 surfaces is exhibited via string duality.
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
Casalderrey-Solana, Jorge; Liu, Hong; Mateos, David; Rajagopal, Krishna; Wiedemann, Urs Achim
2014-06-01
1. Opening remarks; 2. A heavy ion phenomenology primer; 3. Results from lattice QCD at nonzero temperature; 4. Introducing the gauge/string duality; 5. A duality toolbox; 6. Bulk properties of strongly coupled plasma; 7. From hydrodynamics for far-from-equilibrium dynamics; 8. Probing strongly coupled plasma; 9. Quarkonium mesons in strongly coupled plasma; 10. Concluding remarks and outlook; Appendixes; References; Index.
Dualities in M-theory and Born-Infeld Theory
Energy Technology Data Exchange (ETDEWEB)
Brace, Daniel M. [Univ. of California, Berkeley, CA (United States)
2001-01-01
We discuss two examples of duality. The first arises in the context of toroidal compactification of the discrete light cone quantization of M-theory. In the presence of nontrivial moduli coming from the M-theory three form, it has been conjectured that the system is described by supersymmetric Yang-Mills gauge theory on a noncommutative torus. We are able to provide evidence for this conjecture, by showing that the dualities of this M-theory compactification, which correspond to T-duality in Type IIA string theory, are also dualities of the noncommutative supersymmetric Yang-Mills description. One can also consider this as evidence for the accuracy of the Matrix Theory description of M-theory in this background. The second type of duality is the self-duality of theories with U(1) gauge fields. After discussing the general theory of duality invariance for theories with complex gauge fields, we are able to find a generalization of the well known U(1) Born-Infeld theory that contains any number of gauge fields and which is invariant under the maximal duality group. We then find a supersymmetric extension of our results, and also show that our results can be extended to find Born-Infeld type actions in any even dimensional spacetime.
Duality symmetries and the type II string effective action
Bergshoeff, E.
1996-01-01
We discuss the duality symmetries of Type II string effective actions in nine, ten and eleven dimensions. As a by-product we give a covariant action underlying the ten-dimensional Type IIB supergravity theory. We apply duality symmetries to construct dyonic Type II string solutions in six dimensions
S-duality in N=4 Yang-Mills theories
Girardello, L; Porrati, Massimo; Zaffaroni, A
1995-01-01
Evidence in favor of SL(2,Z) S-duality in N=4 supersymmetric Yang-Mills theories in four dimensions and with general compact, simple gauge groups is presented. (Contribution to the Proceedings of the Strings '95 conference, March 13-18, 1995, USC, and the Proceedings of the Trieste Conference on S-Duality and Mirror Symmetry June 5-9, 1995.)
Dualities in M-theory and Born-Infeld Theory
Energy Technology Data Exchange (ETDEWEB)
Brace, Daniel, M
2001-08-01
We discuss two examples of duality. The first arises in the context of toroidal compactification of the discrete light cone quantization of M-theory. In the presence of nontrivial moduli coming from the M-theory three form, it has been conjectured that the system is described by supersymmetric Yang-Mills gauge theory on a noncommutative torus. We are able to provide evidence for this conjecture, by showing that the dualities of this M-theory compactification, which correspond to T-duality in Type IIA string theory, are also dualities of the noncommutative supersymmetric Yang-Mills description. One can also consider this as evidence for the accuracy of the Matrix Theory description of M-theory in this background. The second type of duality is the self-duality of theories with U(1) gauge fields. After discussing the general theory of duality invariance for theories with complex gauge fields, we are able to find a generalization of the well known U(1) Born-Infeld theory that contains any number of gauge fields and which is invariant under the maximal duality group. We then find a supersymmetric extension of our results, and also show that our results can be extended to find Born-Infeld type actions in any even dimensional spacetime.
Duality results for co-compact Gabor systems
DEFF Research Database (Denmark)
Jakobsen, Mads Sielemann; Lemvig, Jakob
2015-01-01
In this paper we give an account of recent developments in the duality theory of Gabor frames. We prove the Wexler-Raz biorthogonality relations and the duality principle for co-compact Gabor systems on second countable, locally compact abelian groups G. Our presentation does not rely...
Puletti, Valentina Giangreco M
2010-01-01
One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensional sigma-models and in the AdS/CFT context. The first part is focused on the AdS_5/CFT_4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS_5 x S^5 are discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to the AdS_4/CFT_3 duality with particular attention to the type IIA superstring on AdS_4 x CP^3 and its integrability. This review is based on a shortened and revised version of the author's PhD thesis, discussed at Uppsala University in September 2...
Duality symmetric string and M-theory
Berman, David S.; Thompson, Daniel C.
2015-03-01
We review recent developments in duality symmetric string theory. We begin with the world-sheet doubled formalism which describes strings in an extended spacetime with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk-Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an En(n) U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extended space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk-Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.
Duality in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
A CMB/Dark Energy Cosmic Duality
Enqvist, K; Enqvist, Kari; Sloth, Martin S.
2004-01-01
We investigate a possible connection between the suppression of the power at low multipoles in the CMB spectrum and the late time acceleration. We show that, assuming a cosmic IR/UV duality between the UV cutoff and a global infrared cutoff given by the size of the future event horizon, the equation of state of the dark energy can be related to the apparent cutoff in the CMB spectrum. The present limits on the equation of state of dark energy are shown to imply an IR cutoff in the CMB multipole interval of 9>l>8.5.
Exact Chern-Simons / Topological String duality
Krefl, Daniel
2015-01-01
We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold found elsewhere in the literature, thereby providing strong evidence that the Chern-Simons / topological string duality is exact, and in particular holds at arbitrary N as well. In the refined case, the non-perturbative corrections we find are novel and appear to be non-trivial. We show that non-perturbatively special treatment is needed for rational valued deformation parameter. Above results are also extend to refined Chern-Simons with orthogonal groups.
Poincare duality angles for Riemannian manifolds with boundary
Shonkwiler, Clayton
2009-01-01
On a compact Riemannian manifold with boundary, the absolute and relative cohomology groups appear as certain subspaces of harmonic forms. DeTurck and Gluck showed that these concrete realizations of the cohomology groups decompose into orthogonal subspaces corresponding to cohomology coming from the interior and boundary of the manifold. The principal angles between these interior subspaces are all acute and are called Poincare duality angles. This paper determines the Poincare duality angles of a collection of interesting manifolds with boundary derived from complex projective spaces and from Grassmannians, providing evidence that the Poincare duality angles measure, in some sense, how "close" a manifold is to being closed. This paper also elucidates a connection between the Poincare duality angles and the Dirichlet-to-Neumann operator for differential forms, which generalizes the classical Dirichlet-to-Neumann map arising in the problem of Electrical Impedance Tomography. Specifically, the Poincare duality...
Duality picture of Superconductor-insulator transitions on Superconducting nanowire
Makise, Kazumasa; Terai, Hirotaka; Tominari, Yukihiro; Tanaka, Shukichi; Shinozaki, Bunju
2016-06-01
In this study, we investigated the electrical transport properties of niobium titanium nitride (NbTiN) nanowire with four-terminal geometries to clarify the superconducting phase slip phenomena and superconducting-insulator transitions (SIT) for one-dimensional superconductors. We fabricated various nanowires with different widths and lengths from epitaxial NbTiN films using the electron beam lithography method. The temperature dependence of resistance R(T) below the superconducting transition temperature Tc was analyzed using thermal activation phase slip (TAPS) and quantum phase slip (QPS) theories. Although the accuracy of experimental data at low temperatures can deviate when using the TAPS model, the QPS model thoroughly represents the R(T) characteristic with resistive tail at low temperatures. From the analyses of data on Tc, we found that NbTiN nanowires exhibit SIT because of the change in the ratio of kinetic inductance energy and QPS amplitude energy with respect to the flux-charge duality theory.
Duality picture of Superconductor-insulator transitions on Superconducting nanowire
Makise, Kazumasa; Terai, Hirotaka; Tominari, Yukihiro; Tanaka, Shukichi; Shinozaki, Bunju
2016-01-01
In this study, we investigated the electrical transport properties of niobium titanium nitride (NbTiN) nanowire with four-terminal geometries to clarify the superconducting phase slip phenomena and superconducting-insulator transitions (SIT) for one-dimensional superconductors. We fabricated various nanowires with different widths and lengths from epitaxial NbTiN films using the electron beam lithography method. The temperature dependence of resistance R(T) below the superconducting transition temperature Tc was analyzed using thermal activation phase slip (TAPS) and quantum phase slip (QPS) theories. Although the accuracy of experimental data at low temperatures can deviate when using the TAPS model, the QPS model thoroughly represents the R(T) characteristic with resistive tail at low temperatures. From the analyses of data on Tc, we found that NbTiN nanowires exhibit SIT because of the change in the ratio of kinetic inductance energy and QPS amplitude energy with respect to the flux-charge duality theory. PMID:27311595
Duality picture of Superconductor-insulator transitions on Superconducting nanowire.
Makise, Kazumasa; Terai, Hirotaka; Tominari, Yukihiro; Tanaka, Shukichi; Shinozaki, Bunju
2016-01-01
In this study, we investigated the electrical transport properties of niobium titanium nitride (NbTiN) nanowire with four-terminal geometries to clarify the superconducting phase slip phenomena and superconducting-insulator transitions (SIT) for one-dimensional superconductors. We fabricated various nanowires with different widths and lengths from epitaxial NbTiN films using the electron beam lithography method. The temperature dependence of resistance R(T) below the superconducting transition temperature Tc was analyzed using thermal activation phase slip (TAPS) and quantum phase slip (QPS) theories. Although the accuracy of experimental data at low temperatures can deviate when using the TAPS model, the QPS model thoroughly represents the R(T) characteristic with resistive tail at low temperatures. From the analyses of data on Tc, we found that NbTiN nanowires exhibit SIT because of the change in the ratio of kinetic inductance energy and QPS amplitude energy with respect to the flux-charge duality theory.
Baryons, monopoles and dualities in Chern-Simons-matter theories
Energy Technology Data Exchange (ETDEWEB)
Aharony, Ofer [Department of Particle Physics and Astrophysics, Weizmann Institute of Science,Rehovot, 7610001 (Israel)
2016-02-15
There is significant evidence for a duality between (non-supersymmetric) U(N) Chern-Simons theories at level k coupled to fermions, and U(k) Chern-Simons theories at level N coupled to scalars. Most of the evidence comes from the large N ’t Hooft limit, where many details of the duality (such as whether the gauge group is U(N) or SU(N), the precise level of the U(1) factor, and order one shifts in the level) are not important. The main evidence for the validity of the duality at finite N comes from adding masses and flowing to pure Chern-Simons theories related by level-rank duality, and from flowing to the non-supersymmetric duality from supersymmetric dualities, whose finite N validity is well-established. In this note we clarify the implications of these flows for the precise form of the duality; in particular we argue that in its simplest form the duality maps SU(N) theories to U(k) theories, though there is also another version relating U(N) to U(k). This precise form strongly affects the mapping under the duality of baryon and monopole operators, and we show, following arguments by Radičević, that their mapping is consistent with our claims. We also discuss the implications of our results for the additional duality between these Chern-Simons matter theories and (the UV completion of) high-spin gravity theories on AdS{sub 4}. The latter theories should contain heavy particles carrying electric and/or magnetic charges under their U(1) gauge symmetry.
Directory of Open Access Journals (Sweden)
T. Hada
proton event edge, where dispersion effects (beaming are the greatest, and at the point of peak proton flux, where the particle energy flux is the greatest.Key words. Interplanetary physics (energetic particles; MHD waves and turbulence – Space plasma physics (charged particle motion and acceleration; wave-particle interactions
Liouville mode in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Moskalets, Tatiana [Karazin Kharkov National University, Department of Physics and Technology, Kharkov (Ukraine); Nurmagambetov, Alexei [Karazin Kharkov National University, Department of Physics and Technology, Kharkov (Ukraine); Akhiezer Institute for Theoretical Physics of NSC KIPT, Kharkov (Ukraine)
2015-11-15
We establish solutions corresponding to AdS{sub 4} static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of the 2D constant curvature space, the metric potential of the internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of gauge/gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in the presence of an inhomogeneity on black hole horizons with planar, spherical, and hyperbolic geometry. We discuss the subtleties of the approach developed for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling within the experimentally relevant range. The solutions obtained are also extended to higher-dimensional AdS space. We observe two different DC conductivities in 4D and higher-dimensional effective strongly coupled dual media and formulate conditions under which the appropriate ratio of different conductivities is qualitatively the same as that observed in an anisotropic strongly coupled fluid. We briefly discuss ways of how the Liouville field could appear in condensed matter physics and outline prospects of further employing the gauge/gravity duality in CMP problems. (orig.)
Liouville mode in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Moskalets, Tatiana, E-mail: tatyana.moskalets@gmail.com [Department of Physics and Technology, Karazin Kharkov National University, 4 Svobody Sq., 61022, Kharkov, UA (Ukraine); Nurmagambetov, Alexei, E-mail: ajn@kipt.kharkov.ua [Department of Physics and Technology, Karazin Kharkov National University, 4 Svobody Sq., 61022, Kharkov, UA (Ukraine); Akhiezer Institute for Theoretical Physics of NSC KIPT, 1 Akademicheskaya St., 61108, Kharkov, UA (Ukraine)
2015-11-25
We establish solutions corresponding to AdS{sub 4} static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of the 2D constant curvature space, the metric potential of the internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of gauge/gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in the presence of an inhomogeneity on black hole horizons with planar, spherical, and hyperbolic geometry. We discuss the subtleties of the approach developed for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling within the experimentally relevant range. The solutions obtained are also extended to higher-dimensional AdS space. We observe two different DC conductivities in 4D and higher-dimensional effective strongly coupled dual media and formulate conditions under which the appropriate ratio of different conductivities is qualitatively the same as that observed in an anisotropic strongly coupled fluid. We briefly discuss ways of how the Liouville field could appear in condensed matter physics and outline prospects of further employing the gauge/gravity duality in CMP problems.
Scale Factor Duality for Conformal Cyclic Cosmologies
dS, U Camara; Sotkov, G M
2016-01-01
The scale factor duality is a symmetry of dilaton gravity which is known to lead to pre-big-bang cosmologies. A conformal time version of the scale factor duality (SFD) was recently implemented as a UV/IR symmetry between decelerated and accelerated phases of the post-big-bang evolution within Einstein gravity coupled to a scalar field. The problem investigated in the present paper concerns the employment of the conformal time SFD methods to the construction of pre-big-bang and cyclic extensions of these models. We demonstrate that each big-bang model gives rise to two qualitatively different pre-big-bang evolutions: a contraction/expansion SFD model and Penrose's Conformal Cyclic Cosmology (CCC). A few examples of SFD symmetric cyclic universes involving certain gauged K\\"ahler sigma models minimally coupled to Einstein gravity are studied. We also describe the specific SFD features of the thermodynamics and the conditions for validity of the generalized second law in the case of Gauss-Bonnet (GB) extension ...
Scale factor duality for conformal cyclic cosmologies
Camara da Silva, U.; Alves Lima, A. L.; Sotkov, G. M.
2016-11-01
The scale factor duality is a symmetry of dilaton gravity which is known to lead to pre-big-bang cosmologies. A conformal time version of the scale factor duality (SFD) was recently implemented as a UV/IR symmetry between decelerated and accelerated phases of the post-big-bang evolution within Einstein gravity coupled to a scalar field. The problem investigated in the present paper concerns the employment of the conformal time SFD methods to the construction of pre-big-bang and cyclic extensions of these models. We demonstrate that each big-bang model gives rise to two qualitatively different pre-big-bang evolutions: a contraction/expansion SFD model and Penrose's Conformal Cyclic Cosmology (CCC). A few examples of SFD symmetric cyclic universes involving certain gauged Kähler sigma models minimally coupled to Einstein gravity are studied. We also describe the specific SFD features of the thermodynamics and the conditions for validity of the generalized second law in the case of Gauss-Bonnet (GB) extension of these selected CCC models.
Scale factor duality for conformal cyclic cosmologies
Energy Technology Data Exchange (ETDEWEB)
Silva, University Camara da; Lima, A.L. Alves; Sotkov, G.M. [Departamento de Física - CCE,Universidade Federal de Espirito Santo, 29075-900, Vitoria ES (Brazil)
2016-11-16
The scale factor duality is a symmetry of dilaton gravity which is known to lead to pre-big-bang cosmologies. A conformal time version of the scale factor duality (SFD) was recently implemented as a UV/IR symmetry between decelerated and accelerated phases of the post-big-bang evolution within Einstein gravity coupled to a scalar field. The problem investigated in the present paper concerns the employment of the conformal time SFD methods to the construction of pre-big-bang and cyclic extensions of these models. We demonstrate that each big-bang model gives rise to two qualitatively different pre-big-bang evolutions: a contraction/expansion SFD model and Penrose’s Conformal Cyclic Cosmology (CCC). A few examples of SFD symmetric cyclic universes involving certain gauged Kähler sigma models minimally coupled to Einstein gravity are studied. We also describe the specific SFD features of the thermodynamics and the conditions for validity of the generalized second law in the case of Gauss-Bonnet (GB) extension of these selected CCC models.
Fricke S-duality in CHL models
Energy Technology Data Exchange (ETDEWEB)
Persson, Daniel [Fundamental Physics, Chalmers University of Technology,412 96, Gothenburg (Sweden); Volpato, Roberto [Theory Group, SLAC National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025 (United States); Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo Mall, Stanford, CA 94305 (United States)
2015-12-23
We consider four dimensional CHL models with sixteen spacetime supersymmetries obtained from orbifolds of type IIA superstring on K3×T{sup 2} by a ℤ{sub N} symmetry acting (possibly) non-geometrically on K3. We show that most of these models (in particular, for geometric symmetries) are self-dual under a weak-strong duality acting on the heterotic axio-dilaton modulus S by a “Fricke involution” S→−1/NS. This is a novel symmetry of CHL models that lies outside of the standard SL(2,ℤ)-symmetry of the parent theory, heterotic strings on T{sup 6}. For self-dual models this implies that the lattice of purely electric charges is N-modular, i.e. isometric to its dual up to a rescaling of its quadratic form by N. We verify this prediction by determining the lattices of electric and magnetic charges in all relevant examples. We also calculate certain BPS-saturated couplings and verify that they are invariant under the Fricke S-duality. For CHL models that are not self-dual, the strong coupling limit is dual to type IIA compactified on T{sup 6}/ℤ{sub N}, for some ℤ{sub N}-symmetry preserving half of the spacetime supersymmetries.
Reynolds, Helen
2000-03-01
The Odd Quantum is aiming to be odd. Falling between being a quantum mechanics textbook and a `popular' science book, it aims to convey something of the substance of quantum mechanics without being overly technical or professional. It does not shy away from the mathematics of the subject or resort solely to analogy and metaphor, as so often is the case. Books aimed at the lay reader tend to take on a particular aspect of quantum mechanics, for example, wave-particle duality, and can do little more than hint at the complexity of the subject. This book is more than a textbook on quantum mechanics; it gives the reader a comprehensive account of history and an appreciation of the nature of quantum mechanics. The introductory chapters deal with the earlier part of the century and the thinking of that time. The approach is familiar, as are the stories that Treiman tells, but he also manages to convey the speed with which ideas changed and the excitement this brought to the physics community. Classical ideas of force and energy are dealt with succinctly but with sufficient depth to set up the reader for what is to come; Maxwell's equations and a brief glimpse at relativity are included. This is followed by a brief description of what the author terms the `old' quantum mechanics, in effect a highly readable tour around black body radiation and spectroscopy and the models of the atom that emerged from them. The `new' quantum mechanics begins about a third of the way through the book, and in a chapter entitled `Foundations' starts gently but rapidly moves into a detailed mathematical treatment. This section, of necessity, relapses into the style of a textbook and covers a lot of ground quickly. It is at this point that the non-specialist popular science readers for whom Treiman has written this book may become a little bemused. Concepts such as non-degeneracy and operators come thick and fast. It is difficult to imagine an educated non-physicist with little mathematical
On T-duality transformations for the three-sphere
Directory of Open Access Journals (Sweden)
Erik Plauschinn
2015-04-01
Full Text Available We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with H-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus. However, the resulting backgrounds turn out to be geometric in nature. To perform the duality transformations, we develop a novel procedure for non-abelian T-duality, which follows a route different compared to the known literature, and which highlights the underlying structure from an alternative point of view.
On T-duality transformations for the three-sphere
Energy Technology Data Exchange (ETDEWEB)
Plauschinn, Erik, E-mail: erik.plauschinn@pd.infn.it [Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova (Italy)
2015-04-15
We study collective T-duality transformations along one, two and three directions of isometry for the three-sphere with H-flux. Our aim is to obtain new non-geometric backgrounds along lines similar to the example of the three-torus. However, the resulting backgrounds turn out to be geometric in nature. To perform the duality transformations, we develop a novel procedure for non-abelian T-duality, which follows a route different compared to the known literature, and which highlights the underlying structure from an alternative point of view.
On Various R-duals and the Duality Principle
DEFF Research Database (Denmark)
Stoeva, Diana T.; Christensen, Ole
2016-01-01
The duality principle states that a Gabor system is a frame if and only if the corresponding adjoint Gabor system is a Riesz sequence. In general Hilbert spaces and without the assumption of any particular structure, Casazza, Kutyniok and Lammers have introduced the so-called R-duals that also lead...... to a characterization of frames in terms of associated Riesz sequences; however, it is still an open question whether this abstract theory is a generalization of the duality principle. In this paper we prove that a modified version of the R-duals leads to a generalization of the duality principle that keeps all...
Duality as a gauge symmetry and topology change
Giveon, Amit
1993-01-01
Duality groups as (spontaneously broken) gauge symmetries for toroidal backgrounds, and their role in ($\\infty$-dimensional) underlying string gauge algebras are reviewed. For curved backgrounds, it is shown that there is a duality in the moduli space of WZNW sigma-models, that can be interpreted as a broken gauge symmetry. In particular, this duality relates the backgrounds corresponding to axially gauged abelian cosets $G/U(1)_a$, to vectorially gauged abelian cosets, $G/U(1)_v$. Finally, topology change in the moduli space of WZNW sigma-models is discussed.
APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES
Institute of Scientific and Technical Information of China (English)
Amir KHOSRAVI; Morteza MIRZAEE AZANDARYANI
2014-01-01
In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.
Murphy, Kyle R; Mann, Ian R; Rae, I Jonathan; Sibeck, David G; Watt, Clare E J
2016-08-01
Wave-particle interactions play a crucial role in energetic particle dynamics in the Earth's radiation belts. However, the relative importance of different wave modes in these dynamics is poorly understood. Typically, this is assessed during geomagnetic storms using statistically averaged empirical wave models as a function of geomagnetic activity in advanced radiation belt simulations. However, statistical averages poorly characterize extreme events such as geomagnetic storms in that storm-time ultralow frequency wave power is typically larger than that derived over a solar cycle and Kp is a poor proxy for storm-time wave power.
Wave-particle and wave-wave interactions in hot plasmas: a French historical point of view
Laval, Guy; Pesme, Denis; Adam, Jean-Claude
2016-11-01
The first researches on nuclear fusion for energy applications marked the entrance of hot plasmas into the laboratory. It became necessary to understand the behavior of such plasmas and to learn how to manipulate them. Theoreticians and experimentalists, building on the foundations of empirical laws, had to construct this new plasma physics from first principles and to explain the results of more and more complicated experiments. Along this line, two important topics emerged: wave-particle and wave-wave interactions. Here, their history is recalled as it has been lived by a French team from the end of the sixties to the beginning of the twenty-first century.
Deymier, Pierre
2017-01-01
This book offers an essential introduction to the notions of sound wave topology, duality, coherence and wave-mixing, which constitute the emerging new science of sound. It includes general principles and specific examples that illuminate new non-conventional forms of sound (sound topology), unconventional quantum-like behavior of phonons (duality), radical linear and nonlinear phenomena associated with loss and its control (coherence), and exquisite effects that emerge from the interaction of sound with other physical and biological waves (wave mixing). The book provides the reader with the foundations needed to master these complex notions through simple yet meaningful examples. General principles for unraveling and describing the topology of acoustic wave functions in the space of their Eigen values are presented. These principles are then applied to uncover intrinsic and extrinsic approaches to achieving non-conventional topologies by breaking the time revers al symmetry of acoustic waves. Symmetry brea...
Kim, Jungmin; Lee, Kimyeong
2015-01-01
We study the 2d N = 4 gauge theory descriptions of little strings on type II NS5- branes. The IIB strings on N NS5-branes are described by the N = (4,4) gauge theories, whose Higgs branch CFTs on U(N) instanton moduli spaces are relevant. The IIA strings are described by N = (4,4) circular A_{N-1} quiver theories, whose Coulomb branch CFTs are relevant. We study new N = (0,4) quiver gauge theories for the IIA strings, which make it easier to study some infrared observables. In particular, we show that the elliptic genera of the IIA / IIB strings precisely map to each other by T-duality.
Liouville mode in Gauge/Gravity Duality
Moskalets, Tatiana
2014-01-01
We establish solutions corresponding to AdS4 static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of 2D constant curvature space, the metric potential of internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of Gauge/Gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in presence of inhomogeneity on black hole horizons with planar, spherical and hyperbolic geometry. We discuss subtleties of the developed approach for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling into the experimentally relevant range. The obtained solutions are also extended to higher-dime...
The duality of computation under focus
Curien, Pierre-Louis
2010-01-01
We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the duality of computation. We use this kit to provide a term language for a presentation of LK (with conjunction, disjunction, and negation), and to transcribe cut elimination as (non confluent) rewriting. A key slogan here, which may appear here in print for the first time, is that commutative cut elimination rules are explicit substitution propagation rules. We then describe the focalised proof search discipline (in the classical setting), and narrow down the language and the rewriting rules to a confluent calculus (a variant of the second author's focalising system L). We then define a game of patterns and counterpatterns, leading us to a fully focalised finitary syntax for a synthetic presentation of classical logic, that provides a quotient on (focalised) proofs, abstracting ou...
Some Generalizations of Fedorchuk Duality Theorem -- II
Dimov, Georgi Dobromirov
2007-01-01
As it was shown in the first part of this paper, there exists a duality between the category DSkeLC (introduced there) and the category SkeLC of locally compact Hausdorff spaces and continuous skeletal maps. We describe here the subcategories of the category DSkeLC which are dually equivalent to the following eight categories: all of them have as objects the locally compact Hausdorff spaces and their morphisms are, respectively, the injective (respectively, surjective) continuous skeletal maps, the injective (resp., surjective) open maps, the injective (resp., surjective) skeletal perfect maps, the injective (resp., surjective) open perfect maps. The particular cases of these theorems for the full subcategories of the last four categories having as objects all compact Hausdorff spaces are formulated and proved. The DSkeLC-morphisms which are LCA-embeddings and the dense homeomorphic embeddings are characterized through their dual morphisms. For any locally compact space X, a description of the frame of all op...
Duality of Maximum Entropy and Minimum Divergence
Directory of Open Access Journals (Sweden)
Shinto Eguchi
2014-06-01
Full Text Available We discuss a special class of generalized divergence measures by the use of generator functions. Any divergence measure in the class is separated into the difference between cross and diagonal entropy. The diagonal entropy measure in the class associates with a model of maximum entropy distributions; the divergence measure leads to statistical estimation via minimization, for arbitrarily giving a statistical model. The dualistic relationship between the maximum entropy model and the minimum divergence estimation is explored in the framework of information geometry. The model of maximum entropy distributions is characterized to be totally geodesic with respect to the linear connection associated with the divergence. A natural extension for the classical theory for the maximum likelihood method under the maximum entropy model in terms of the Boltzmann-Gibbs-Shannon entropy is given. We discuss the duality in detail for Tsallis entropy as a typical example.
Distance Duality Relation from Strong Gravitational Lensing
Liao, Kai; Cao, Shuo; Biesiada, Marek; Zheng, Xiaogang; Zhu, Zong-Hong
2015-01-01
Under very general assumptions of metric theory of spacetime, photons traveling along null geodesics and photon number conservation, two observable concepts of cosmic distance, i.e. the angular diameter and the luminosity distances are related to each other by the so called distance duality relation (DDR) $D^L=D^A(1+z)^2$. Observational validation of this relation is quite important because any evidence of its violation could be a signal of new physics. In this letter we introduce a new method to test DDR based on strong gravitational lensing systems and supernovae Ia. Using a new compilation of strong lensing systems and JLA compilation of SNe Ia we found no evidence of DDR violation. However, not so much the final result but the method itself is worth attention, because unlike previously proposed techniques, it does not depend on prior assumptions concerning the details of cosmological model and galaxy cluster modelling.
Schur-Weyl Duality for Heisenberg Cosets
Creutzig, Thomas; Linshaw, Andrew R; Ridout, David
2016-01-01
Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C=\\text{Com}\\left( {H}, {V}\\right)$ be the coset of ${H}$ in ${V}$. Assuming that the representation categories of interest are vertex tensor categories in the sense of Huang, Lepowsky and Zhang, a Schur-Weyl type duality for both simple and indecomposable but reducible modules is proven. Families of vertex algebra extensions of ${C}$ are found and every simple ${C}$-module is shown to be contained in at least one ${V}$-module. A corollary of this is that if ${V}$ is rational and $C_2$-cofinite and CFT-type, and $\\text{Com}\\left( {C}, {V}\\right)$ is a rational lattice vertex operator algebra, then so is ${C}$. These results are illustrated with many examples and the $C_1$-cofiniteness of certain interesting classes of modules is established.
Duality of Health Promotion and Sustainable Development
DEFF Research Database (Denmark)
Pedersen, Kirsten Bransholm; Land, Birgit; Kjærgård, Bente
2015-01-01
sustainability and, vice versa, sustainability conditions health. Thus, to avoid unintended, negative effects the strategies directed towards sustainable development must be correlated with strategies for health promotion. The conceptual model is used to take a closer look at the complexities of food waste......A In this article we introduce the concept of duality of structures as our starting point for understanding the linkages between sustainability and health. We argue that the two concepts cannot be separated but must be understood as mutually dependent in the sense that health conditions...... reduction and how these strategies affect the prospects for promoting health and sustainable food production and consumption. Danish food waste reduction strategies are used as examples with references to selected policy documents on food waste reduction strategies launched by international organisations...
Duality in deformed coset fermionic models
Cabra, D C
1996-01-01
We study the SU(2)_k/U(1)-parafermion model perturbed by its first thermal operator. By formulating the theory in terms of a (perturbed) fermionic coset model we show that the model is equivalent to interacting WZW fields modulo free fields. In this scheme, the order and disorder operators of the Z_k parafermion theory are constructed as gauge invariant composites. We find that the theory presents a duality symmetry that interchanges the roles of the spin and dual spin operators. For two particular values of the coupling constant we find that the theory recovers conformal invariance and the gauge symmetry is enlarged. We also find a novel self-dual point.
T-duality and $\\alpha'$-corrections
Marques, Diego
2015-01-01
We construct an $O(d,d)$ invariant universal formulation of the first-order $\\alpha'$-corrections of the string effective actions involving the dilaton, metric and two-form fields. Two free parameters interpolate between four-derivative terms that are even and odd with respect to a $Z_2$-parity transformation that changes the sign of the two-form field. The $Z_2$-symmetric model reproduces the closed bosonic string, and the heterotic string effective action is obtained through a $Z_2$-parity-breaking choice of parameters. The theory is an extension of the generalized frame formulation of Double Field Theory, in which the gauge transformations are deformed by a first-order generalized Green-Schwarz transformation. This deformation defines a duality covariant gauge principle that requires and fixes the four-derivative terms. We discuss the $O(d,d)$ structure of the theory and the (non-)covariance of the required field redefinitions.
Ketov, S V
1996-01-01
The (2,2) world-sheet supersymmetric string theory is discussed from the viewpoint of string/membrane unification. The effective field theory in the closed string target space is known to be the 2+2 dimensional (integrable) theory of self-dual gravity (SDG). A world-volume supersymmetrization of the Pleba'nski action for SDG naturally implies the maximal N=8 world-volume supersymmetry, while the maximal supersymmetrization of the dual covariant K"ahler-Lorentz-Chern-Simons action for SDG implies gauging a self-dual part of the super-Lorentz symmetry in 2+10 dimensions. The proposed OSp(32|1) supersymmetric action for the M-brane may be useful for a fundamental formulation of uncompactified F theory, with the self-duality being playing the central role both in the world-volume and in the target space of the M-brane.
Quark-hadron duality: pinched kernel approch
Dominguez, C A; Schilcher, K; Spiesberger, H
2016-01-01
Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark-hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to $s = 10\\; {\\mbox{GeV}^2}$ by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using $e^+ e^-$ annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.
Duality properties of indicatrices of knots
Adams, Colin; Hawkins, Katherine; Sia, Charmaine; Silversmith, Robert; Tshishiku, Bena
2012-01-01
The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.
Gauge/string duality in confining theories
Energy Technology Data Exchange (ETDEWEB)
Edelstein, J.D. [Departamento de Fi sica de Particulas, Universidade de Santiago de Compostela and Instituto Galego de Fisica de Altas Enerxias (IGFAE), 15782 Santiago de Compostela (Spain); Instituto de Fisica de La Plata (IFLP), Universidad Nacional de La Plata, La Plata (Argentina); Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile); Portugues, R. [Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)
2006-07-03
This is the content of a set of lectures given at the ''XIII Jorge Andre Swieca Summer School on Particles and Fields'', Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Gauge/String Duality in Confining Theories
Edelstein, J D; Edelstein, Jose D.; Portugues, Ruben
2006-01-01
This is the content of a set of lectures given at the XIII Jorge Andre Swieca Summer School on Particles and Fields, held in Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity.
Wronskians, dualities and FZZT-Cardy branes
Chan, Chuan-Tsung; Niedner, Benjamin; Yeh, Chi-Hsien
2016-01-01
The resolvent operator plays a central role in matrix models. For instance, with utilizing the loop equation, all of the perturbative amplitudes including correlators, the free-energy and those of instanton corrections can be obtained from the spectral curve of the resolvent operator. However, at the level of non-perturbative completion, the resolvent operator is generally not sufficient to recover all the information from the loop equations. Therefore it is necessary to find a sufficient set of operators which provide the missing non-perturbative information. In this paper, we study generalized Wronskians of the Baker-Akhiezer systems as a manifestation of these new degrees of freedom. In particular, we derive their isomonodromy systems and then extend several spectral dualities to these systems. In addition, we discuss how these Wronskian operators are naturally aligned on the Kac table. Since they are consistent with the Seiberg-Shih relation, we propose that these new degrees of freedom can be identified ...
Holographic duality from random tensor networks
Hayden, Patrick; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao
2016-01-01
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit simple models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models obey the Ryu-Takayanagi entropy formula for all boundary regions, whether connected or not, a fact closely related to known properties of the multipartite entanglement of assistance. Moreover, we find that all boundary regions faithfully encode the physics of their entire bulk entanglement wedges, not just their smaller causal wedges. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bu...
Lefschetz-Pontrjagin duality for differential characters
Directory of Open Access Journals (Sweden)
REESE HARVEY
2001-06-01
Full Text Available A theory of differential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a Lefschetz-Pontrjagin Duality Theorem, which asserts that the pairing given by (alpha, beta (alpha * beta [X] induces isomorphisms onto the smooth Pontrjagin duals. In particular, and are injective with dense range in the group of all continuous homomorphisms into the circle. A coboundary map is introduced which yields a long sequence for the character groups associated to the pair (X, X. The relation of the sequence to the duality mappings is analyzed.Uma teoria de caracteres diferenciais é aqui desenvolvida para variedades com bordo. Isto é feito tanto do ponto de vista de Cheeger-Simons como do deRham-Federer. O resultado central deste artigo é a formulação e a prova de um teorema da dualidade de Lefschetz-Pontrjagin, que afirma que o pareamento dado por (alfa,beta (alfa * beta [X] induz isomorfismos sobre os duais diferenciáveis de Pontrjagin. Em particular, e são injetivos com domínios densos no grupo de todos os homeomorfismos contínuos no círculo. Uma aplicação de cobordo é introduzida, a qual fornece uma sequência longa para os grupos de caracteres associados ao par ( X, X. A relação desta sequência com as aplicações de dualidade é analisada.
El Naschie's cantorian strings and duality in Weyl-Dirac theory
Energy Technology Data Exchange (ETDEWEB)
Agop, M.; Ioannou, P.D.; Nica, P. E-mail: pnica@ch.tuiasi.ro
2004-03-01
In the weak-field approximation, some implications of duality in the Weyl-Dirac (WD) theory, using the Gregorash-Papini-Wood approach, are investigated. Any particle is in a permanent interaction with the 'subquantic level' (Madelung's fluid) and, as a result of this interaction, the particle acquires the proper fluctuation curvature and the proper fluctuation energy, respectively. By fixing the fluctuations scale, the quantum fluid orders either by means of bright cnoidal oscillation modes inducing causality, or by means of dark cnoidal oscillation modes inducing acausality, and non-linear effects, respectively. The periodic mode is associated with the undulatory characteristic, and the solitonic one with the corpuscular one. By not fixing the fluctuations scale and keeping the symmetry, the quantum fluid orders like a two-dimensional (2D) lattice of vortices, so that the duality needs coherence. In the compatibility between quantum hydrodynamics in the Madelung's representation and the wave mechanics, the self-gravitational field of the Weyl-Dirac type physical object is generated. El Naschie's space-time implies, by means of transfinite heterotic string theory, the masses of nucleons, and, by the gravitational fractional quantum Hall effect, the dispersion of the wave-packet on the particle. The analysis of the fractal dimension of the physical object described by the WD theory shows that the waves, and corpuscle, respectively are 2D projections of a higher dimensional special string in El Naschie's space-time (El Naschie's string)
New Evidence for (0,2) Target Space Duality
Anderson, Lara B
2016-01-01
In the context of (0,2) gauged linear sigma models, we explore chains of perturbatively dual heterotic string compactifications. The notion of target space duality originates in non-geometric phases and can be used to generate distinct GLSMs with shared geometric phases leading to apparently identical target space theories. To date, this duality has largely been studied at the level of counting states in the effective theories. We extend this analysis to the effective potential and loci of enhanced symmetry in dual theories. By engineering vector bundles with non-trivial constraints arising from slope-stability (i.e. D-terms) and holomorphy (i.e. F-terms) the detailed structure of the vacuum space of the dual theories can be explored. Our results give new evidence that GLSM target space duality may provide important hints towards a more complete understanding of (0,2) string dualities.
New evidence for (0,2) target space duality
Anderson, Lara B.; Feng, He
2017-02-01
In the context of (0, 2) gauged linear sigma models, we explore chains of perturbatively dual heterotic string compactifications. The notion of target space duality originates in non-geometric phases and can be used to generate distinct GLSMs with shared geometric phases leading to apparently identical target space theories. To date, this duality has largely been studied at the level of counting states in the effective theories. We extend this analysis to the effective potential and loci of enhanced symmetry in dual theories. By engineering vector bundles with non-trivial constraints arising from slope-stability (i.e. D-terms) and holomorphy (i.e. F-terms) the detailed structure of the vacuum space of the dual theories can be explored. Our results give new evidence that GLSM target space duality may provide important hints towards a more complete understanding of (0, 2) string dualities.
A duality theorem of crossed coproduct for Hopf algebras
Institute of Scientific and Technical Information of China (English)
王栓宏
1995-01-01
A duality theorem for Hopf crossed coproduct is proved. This theorem plays a role similar to that appearing in the work of Koppinen (which generalized the corresponding results of group grraded ring).
Spinor-vector duality in heterotic SUSY vacua
Energy Technology Data Exchange (ETDEWEB)
Catelin-Jullien, Tristan [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, F-75231 Paris cedex 05 (France)], E-mail: catelin@lpt.ens.fr; Faraggi, Alon E. [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom)], E-mail: alon.faraggi@liv.ac.uk; Kounnas, Costas [Laboratoire de Physique Theorique, Ecole Normale Superieure, 24 rue Lhomond, F-75231 Paris cedex 05 (France)], E-mail: costas.kounnas@lpt.ens.fr; Rizos, John [Department of Physics, University of Ioannina, GR45110 Ioannina (Greece)], E-mail: irizos@uoi.gr
2009-05-01
We elaborate on the recently discovered spinor-vector duality in realistic free fermionic heterotic vacua. We emphasize the interpretation of the freely-acting orbifolds carried out on the six internal dimensions as coordinate-dependent compactifications; they play a central role in the duality, especially because of their ability to break the right-moving superconformal algebra of the space-time supersymmetric heterotic vacua. These considerations lead to a simple and intuitive proof of the spinor-vector duality, and to the formulation of explicit rules to find the dual of a given model. We discuss the interest of such a duality, notably concerning the structure of the space of vacua of superstring theory.
On Duality Symmetry in Charged P-Form Theories
Menezes, R; Menezes, Roberto; Wotzasek, Clovis
2004-01-01
We study duality transformation and duality symmetry in the the electromagnetic-like charged p-form theories. It is shown that the dichotomic characterization of duality groups as $Z_2$ or SO(2) remains as the only possibilities but are now present in all dimensions even and odd. This is a property defined in the symplectic sector of the theory both for massive and massless tensors. It is shown that the duality groups depend, in general, both on the ranks of the fields and on the dimension of the spacetime. We search for the physical origin of this two-fold property and show that it is traceable to the dimensional and rank dependence of the parity of certain operator (a generalized-curl) that naturally decomposes the symplectic sector of the action. These operators are only slightly different in the massive and in the massless cases but their physical origin are quite distinct.
Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function
Zhou, Da; He, Yang-Hui
2015-01-01
We study Ihara zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara zeta function to be the generating function for the generic superpotential of the gauge theory.
Matrix-model dualities in the collective field formulation
Andric, I
2005-01-01
We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field formulation, the duality is displayed in terms of the generators of the conformal group. The conformally invariant master Hamiltonian is constructed and we conjecture that the master Hamiltonian corresponds to the hermitian matrix model.
Single Molecule Experiments Challenge the Strict Wave-Particle Dualism of Light
Directory of Open Access Journals (Sweden)
Karl Otto Greulich
2010-01-01
Full Text Available Single molecule techniques improve our understanding of the photon and light. If the single photon double slit experiment is performed at the “single photon limit” of a multi-atom light source, faint light pulses with more than one photon hamper the interpretation. Single molecules, quantum dots or defect centres in crystals should be used as light source. “Single photon detectors” do not meet their promise―only “photon number resolving single photon detectors” do so. Particularly, the accumulation time argument, the only safe basis for the postulate of a strictly particle like photon, has so far not yet been verified.
Single molecule experiments challenge the strict wave-particle dualism of light.
Greulich, Karl Otto
2010-01-21
Single molecule techniques improve our understanding of the photon and light. If the single photon double slit experiment is performed at the "single photon limit" of a multi-atom light source, faint light pulses with more than one photon hamper the interpretation. Single molecules, quantum dots or defect centres in crystals should be used as light source. "Single photon detectors" do not meet their promise-only "photon number resolving single photon detectors" do so. Particularly, the accumulation time argument, the only safe basis for the postulate of a strictly particle like photon, has so far not yet been verified.
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.
Holographic duality from random tensor networks
Energy Technology Data Exchange (ETDEWEB)
Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-11-02
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main
2012-11-19
expansion of the conserved currents. The ratio of the O(v) to O(∂v) terms in the stress tensor is known as the Reynolds number, Re = vLmn/η. Validity of...the gradient expansion requires that the Reynolds number be large. New Journal of Physics 14 (2012) 115009 (http://www.njp.org/) 23 Fermi temperature...John McGreevy, Jessie Petricka, Michael Wall, Haibin Wu and Martin Zwierlein for useful discussions. References [1] Linstrom P J and Mallard W G 2011
Reggeon exchange from gauge/gravity duality
Giordano, M
2011-01-01
We perform the analysis of quark-antiquark Reggeon exchange in meson-meson scattering, in the framework of the gauge/gravity correspondence in a confining background. On the gauge theory side, Reggeon exchange is described as quark-antiquark exchange in the t channel between fast projectiles. The corresponding amplitude is represented in terms of Wilson loops running along the trajectories of the constituent quarks and antiquarks. The paths of the exchanged fermions are integrated over, while the "spectator" fermions are dealt with in an eikonal approximation. On the gravity side, we follow a previously proposed approach, and we evaluate the Wilson-loop expectation value by making use of gauge/gravity duality for a generic confining gauge theory. The amplitude is obtained in a saddle-point approximation through the determination near the confining horizon of a Euclidean "minimal surface with floating boundaries", i.e., by fixing the trajectories of the exchanged quark and antiquark by means of a minimisation ...
Seiberg duality versus hidden local symmetry
Abel, Steven
2012-01-01
It is widely believed that the emergent magnetic gauge symmetry of SQCD is analogous to a hidden local symmetry (HLS). We explore this idea in detail, deriving the entire (spontaneously broken) magnetic theory by applying the HLS formalism to spontaneously broken SU(N) SQCD. We deduce the K\\"ahler potential in the HLS description, and show that gauge and flavour symmetry are smoothly restored along certain scaling directions in moduli space. We propose that it is these symmetry restoring directions, associated with the R-symmetry of the theory, that allow full Seiberg duality. Reconsidering the origin of the magnetic gauge bosons as the rho-mesons of the electric theory, colour-flavour locking allows a simple determination of the parameter "a". Its value continuously interpolates between a=2 on the baryonic branch of moduli space - corresponding to "vector meson dominance" - and a=1 on the mesonic branch. Both limiting values are consistent with previous results in the literature. The HLS formalism is further...
A test for cosmic distance duality
Energy Technology Data Exchange (ETDEWEB)
Holanda, R.F.L.; Gonçalves, R.S.; Alcaniz, J.S., E-mail: holanda@on.br, E-mail: rsousa@on.br, E-mail: alcaniz@on.br [Departamento de Astronomia, Observatório Nacional, 20921-400, Rio de Janeiro - RJ (Brazil)
2012-06-01
Testing the cosmic distance duality relation (CDDR) constitutes an important task for cosmology and fundamental physics since any violation of it would be a clear evidence of new physics. In this paper, we propose a new test for the CDDR using only current measurements of the gas mass fraction of galaxy clusters from Sunyaev-Zeldovich (f{sub SZE}) and X-ray surface brightness (f{sub X−ray}) observations. We show that the relation between f{sub X−ray} and f{sub SZE} observations is given by f{sub SZE} = ηf{sub X−ray}, where η quantifies deviations from the CDDR. Since this latter expression is valid for the same object in a given galaxy cluster sample, the method proposed removes possible contaminations from different systematics error sources and redshift differences involved in luminosity and angular diameter distance measurements. We apply this cosmological model-independent methodology to the most recent f{sub X−ray} and f{sub SZE} data and show that no significant violation of the CDDR is found.
A test for cosmic distance duality
Holanda, R F L; Alcaniz, J S
2012-01-01
Testing the cosmic distance duality relation (CDDR) constitutes an important task for cosmology and fundamental physics since any violation of it would be a clear evidence of new physics. In this {\\it Letter}, we propose a new test for the CDDR using only measurements of the gas mass fraction of galaxy clusters from Sunyaev-Zeldovich ($f_{SZE}$) and X-ray surface brightness ($f_{X-ray}$) observations. We show that the relation between current $f_{X-ray}$ and $f_{SZE}$ observations is given by $f_{SZE}=\\eta f_{X-ray}$, where $\\eta$ quantifies deviations from the CDDR. Since this latter expression is valid for the same object in a given galaxy cluster sample, the method proposed removes possible contaminations from different systematics error sources and redshift differences involved in luminosity and angular diameter distance measurements. We apply this cosmological model-independent methodology to the most recent $f_{X-ray}$ and $f_{SZE}$ data and show that no significant violation of the CDDR is found.
Residues and duality for Cousin complexes
Lipman, J; Lipman, Joseph; Sastry, Pramathanath
1996-01-01
We construct a canonical pseudofunctor ^# on the category of finite-type maps of (say) connected noetherian universally catenary finite-dimensional separated schemes, taking values in the category of Cousin complexes. This pseudofunctor is a concrete approximation to the restriction of the Grothendieck Duality pseudofunctor ^! to the full subcategory of the derived category having Cohen-Macaulay complexes as objects (a subcategory equivalent to the category of Cousin complexes, once a codimension function has been fixed). Specifically, for Cousin complexes M and any scheme map f:X -> Y as above, there is a functorial derived-category map \\gamma: f^# M -> f^! M inducing a functorial isomorphism in the category of Cousin complexes f^# M \\iso E(f^! M) (where E is the Cousin functor). \\gamma itself is an isomorphism if the complex f^! M is Cohen-Macaulay--which will be so whenever the map f is Cohen-Macaulay or whenever the complex M is injective. Also, f^# takes residual (resp. injective) complexes on Y to resid...
Disentangling the $f(R)$ Duality
Broy, Benedict J; Westphal, Alexander
2015-01-01
Motivated by UV realisations of Starobinsky-like inflation models, we study generic exponential plateau-like potentials to understand whether an exact $f(R)$-formulation may still be obtained when the asymptotic shift-symmetry of the potential is broken for larger field values. Potentials which break the shift symmetry with rising exponentials at large field values only allow for corresponding $f(R)$-descriptions with a leading order term $R^{n}$ with $1
Yang-Baxter deformations and string dualities
Energy Technology Data Exchange (ETDEWEB)
Matsumoto, Takuya [Institute for Advanced Research and Department of Mathematics, Nagoya University,Nagoya 464-8602 (Japan); Yoshida, Kentaroh [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan)
2015-03-25
We further study integrable deformations of the AdS{sub 5}×S{sup 5} superstring by following the Yang-Baxter sigma model approach with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). Deformed string backgrounds specified by r-matrices are considered as solutions of type IIB supergravity, and therefore the relation between gravitational solutions and r-matrices may be called the gravity/CYBE correspondence. In this paper, we present a family of string backgrounds associated with a classical r-matrices carrying two parameters and its three-parameter generalization. The two-parameter case leads to the metric and NS-NS two-form of a solution found by Hubeny-Rangamani-Ross [hep-th/0504034] and another solution in [arXiv:1402.6147]. For all of the backgrounds associated with the three-parameter case, the metric and NS-NS two-form are reproduced by performing TsT transformations and S-dualities for the undeformed AdS{sub 5}×S{sup 5} background. As a result, one can anticipate the R-R sector that should be reproduced via a supercoset construction.
Stringy horizons and generalized FZZ duality in perturbation theory
Giribet, Gaston
2017-02-01
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n - 2 winding modes actually coincide with the correlation functions in the SL(2,R)/U(1) gauged WZW model that include n - 2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference [1]. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.
Spinor-vector duality in N=2 heterotic string vacua
Energy Technology Data Exchange (ETDEWEB)
Faraggi, Alon E. [Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL (United Kingdom)], E-mail: faraggi@amtp.liv.ac.uk; Kounnas, Costas [Laboratoire Physique Theorique, Ecole Normale Superieure, F-75231 Paris 05 (France); Rizos, John [Department of Physics, University of Ioannina, GR45110 Ioannina (Greece)
2008-08-11
Classification of the N=1 space-time supersymmetric fermionic Z{sub 2}xZ{sub 2} heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S{sub t}{r_reversible}V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z{sub 2} heterotic string models, which preserve N=2 space-time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S{sub t}{r_reversible}V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.
Spin duality in the nucleon: Measurements at Jefferson Lab Hall A
Energy Technology Data Exchange (ETDEWEB)
Nilanga Liyanage
2005-02-01
The current experimental status of quark-hadron duality is discussed with particular emphasis on separated longitudinal and transverse structure functions. In addition, current and future experiments, which could help elucidate the nature of duality, are briefly discussed.
4D/3D reduction of dualities: mirrors on the circle
Energy Technology Data Exchange (ETDEWEB)
Amariti, Antonio [LPTENS - UMR CNRS 8549,24, rue Lhomond, 75231 Paris (France); Forcella, Davide [Physique Théorique et Mathématique and International Solvay Institutes, ULB,C.P. 231, 1050 Bruxelles (Belgium); Klare, Claudius [IPHT, CEA/Saclay,91191 Gif-sur-Yvette (France); IHES,35, Route de Chartres, 91440 Bures-sur-Yvette (France); Orlando, Domenico [LPTENS - UMR CNRS 8549,24, rue Lhomond, 75231 Paris (France); IPT Ph. Meyer,24, rue Lhomond, 75231 Paris (France); Reffert, Susanne [ITP - AEC, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland)
2015-10-08
We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a sector of interacting singlets, giving a unified mechanism for the brane reduction of dualities.
Quantum gravity via supersymmetry and holography
Elvang, Henriette; Horowitz, Gary T.
2013-01-01
We review the approach to quantum gravity based on supersymmetry, strings, and holography. This includes a survey of black holes in higher-dimensions, supersymmetry and supergravity, as well as string theory, black hole microstates, and the gauge/gravity duality. This presentation will appear as a chapter in "General Relativity and Gravitation: A Centennial Perspective", to be published by Cambridge University Press.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Single Photon Experiments and Quantum Complementarity
Directory of Open Access Journals (Sweden)
Georgiev D. D.
2007-04-01
Full Text Available Single photon experiments have been used as one of the most striking illustrations of the apparently nonclassical nature of the quantum world. In this review we examine the mathematical basis of the principle of complementarity and explain why the Englert-Greenberger duality relation is not violated in the configurations of Unruh and of Afshar.
Chiral observables and S-duality in N = 2* U(N) gauge theories
Ashok, S K; Dell'Aquila, E; Frau, M; Lerda, A; Moskovic, M; Raman, M
2016-01-01
We study N = 2* theories with gauge group U(N) and use equivariant localization to calculate the quantum expectation values of the simplest chiral ring elements. These are expressed as an expansion in the mass of the adjoint hypermultiplet, with coefficients given by quasi-modular forms of the S-duality group. Under the action of this group, we construct combinations of chiral ring elements that transform as modular forms of definite weight. As an independent check, we confirm these results by comparing the spectral curves of the associated Hitchin system and the elliptic Calogero-Moser system. We also propose an exact and compact expression for the 1-instanton contribution to the expectation value of the chiral ring elements.
Duality of a compact topological superconductor model and the Witten effect
Nogueira, Flavio S.; Nussinov, Zohar; van den Brink, Jeroen
2016-10-01
We consider a compact Abelian Higgs model in 3 +1 dimensions with a topological axion term and construct its dual theories for both bulk and boundary at strong coupling. The model may be viewed as describing a superconductor with magnetic monopoles, which can also be interpreted as a field theory of a topological Mott insulator. We show that this model is dual to a noncompact topological field theory of particles and vortices. It has exactly the same form as a model for superconducting cosmic strings with an axion term. We consider the duality of the boundary field theory at strong coupling and show that in this case θ is quantized as -8 π n /m , where n and m are the quantum numbers associated with electric and magnetic charges. These topological states lack a noninteracting equivalent.
Precision lattice test of the gauge/gravity duality at large N
Berkowitz, Evan; Rinaldi, Enrico; Hanada, Masanori; Ishiki, Goro; Shimasaki, Shinji; Vranas, Pavlos; Monte Carlo String/M-Theory Collaboration McSmc
2016-11-01
We perform a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-N and continuum limits of the gauge theory are taken for the first time at various temperatures 0.4 ≤T ≤1.0 . As a way to test the gauge/gravity duality conjecture we compute the internal energy of the black hole as a function of the temperature directly from the gauge theory. We obtain a leading behavior that is compatible with the supergravity result E /N2=7.41 T14 /5 : the coefficient is estimated to be 7.4 ±0.5 when the exponent is fixed and stringy corrections are included. This is the first confirmation of the supergravity prediction for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. We also constrain stringy corrections to the internal energy.
Kramers-Wannier duality applied to the boolean satifiability problem
Mitchell, Joe; Hsu, Benjamin; Galitski, Victor
2014-03-01
Kramers-Wannier duality, first considered in 1941, is an exact technique used in statistical mechanics to relate two models together through an order-disorder transformation, and thereby study their structure and critical phenomena. The boolean satisfiability problem is one of the most important problems in computer science, specifically complexity theory; it is the first proven NP-complete problem. Using a mapping to a multi-spin Ising model in the limit of zero temperature, we present an application of Kramers-Wannier duality to this problem. This results in a novel relationship between solving the boolean satisfiability counting problem and a different computational problem: listing the non-negative solutions to a particular system of linear integer equations. This mapping relates the complexity of the two problems. We discuss the generality of Kramers-Wannier duality and its possible application to other computational problems. This research was supported by NSF-CAREER award No. DMR-0847224 and Simons Foundation.
Spectral Duality Between Heisenberg Chain and Gaudin Model
Mironov, A; Runov, B; Zenkevich, Y; Zotov, A
2012-01-01
In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.
Duality and Topological Mass Generation in Diverse Dimensions
Wotzasek, C
2004-01-01
We shall discuss issues of duality and topological mass generation in diverse dimensions. Particular emphasis will be given to the mass generation mechanism from interference between self and anti self-dual components, as disclosed by the soldering formalism. This is a gauge embedding procedure derived from an old algorithm of second-class constraint conversion used by the author to approach anomalous gauge theories. The problem of classification of the electromagnetic duality groups, both massless and massive, that is closely related will be discussed. Particular attention will be paid to a new approach to duality based on the soldering embedding to tackle the problem of mass generation by topological mechanisms in arbitrary dimensions including the couplings to dynamical matter, nonlinear cases and nonabelian symmetries.
N = (4,4 Supersymmetry and T-Duality
Directory of Open Access Journals (Sweden)
Malin Göteman
2012-10-01
Full Text Available A sigma model with four-dimensional target space parametrized by chiral and twisted chiral N =(2,2 superfields can be extended to N =(4,4 supersymmetry off-shell, but this is not true for a model of semichiral fields, where the N = (4,4 supersymmetry can only be realized on-shell. The two models can be related to each other by T-duality. In this paper we perform a duality transformation from a chiral and twisted chiral model with off-shell N = (4,4 supersymmetry to a semichiral model. We find that additional non-linear terms must be added to the original transformations to obtain a semichiral model with N =(4,4 supersymmetry, and that the algebra closes on-shell as a direct consequence of the T-duality.
New localization mechanism and Hodge duality for q -form field
Fu, Chun-E.; Liu, Yu-Xiao; Guo, Heng; Zhang, Sheng-Li
2016-03-01
In this paper, we investigate the problem of localization and the Hodge duality for a q -form field on a p -brane with codimension one. By a general Kaluza-Klein (KK) decomposition without gauge fixing, we obtain two Schrödinger-like equations for two types of KK modes of the bulk q -form field, which determine the localization and mass spectra of these KK modes. It is found that there are two types of zero modes (the 0-level modes): a q -form zero mode and a (q -1 )-form one, which cannot be localized on the brane at the same time. For the n -level KK modes, there are two interacting KK modes, a massive q -form KK mode and a massless (q -1 )-form one. By analyzing gauge invariance of the effective action and choosing a gauge condition, the n -level massive q -form KK mode decouples from the n -level massless (q -1 )-form one. It is also found that the Hodge duality in the bulk naturally becomes two dualities on the brane. The first one is the Hodge duality between a q -form zero mode and a (p -q -1 )-form one, or between a (q -1 )-form zero mode and a (p -q )-form one. The second duality is between two group KK modes: one is an n -level massive q -form KK mode with mass mn and an n -level massless (q -1 )-form mode; another is an n -level (p -q )-form one with the same mass mn and an n -level massless (p -q -1 )-form mode. Because of the dualities, the effective field theories on the brane for the KK modes of the two dual bulk form fields are physically equivalent.
Experimental probes of emergent symmetries in the quantum Hall system
Lutken, C A
2011-01-01
Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry Gamma(0)(2). We briefly review this evidence and show that, for the lowest temperatures, the experimental determination of the position of the quantum critical points agrees to the parts per mille level with the prediction from Gamma(0)(2). We present evidence that experiments giving results that deviate substantially from the symmetry predictions are not cold enough to be in the quantum critical domain. We show how the modular symmetry extended by a non-holomorphic particle hole duality leads to an extensive web of dualities related to those in plateau insulator transitions, and we derive a formula relating dual pairs (B, B(d)) of magnetic field strengths across any transition. The experimental data obtained for the transition studied so far is in excellent agreement with the duality relations following from this emergent symmetry, and rule out...
A Remark on Gelfand Duality for Spectral Triples
Bertozzini, Paolo; Lewkeeratiyutkul, Wicharn
2008-01-01
We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative pre-C*-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in arXiv:math/0502583v1 into the latter metric category. Finally we discuss a further related duality in the case of orientation and spin-preserving maps between manifolds of fixed dimension.
Non-abelian T-duality, generalised geometry and holography
Macpherson, Niall T
2013-01-01
Recent progress which relates non-abelian T-duality of $\\mathcal{N}=1$ SuGra solutions to the powerful techniques of Generalised geometry is reviewed. It is shown that SU(3) structure solutions are mapped to SU(2) structures and the transformation rule of the corresponding pure spinors is presented. This constitutes an important step on the road towards the utility of the duality within holography, showing for example, how smeared sources must transform and so how to add flavour to the T-duals.
New Correlation Duality Relations for the Planar Potts Model
King, C.; Wu, F. Y.
2002-05-01
We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. We show that generally it is linear combinations of correlation functions, not the individual correlations, that are related by dualities. The method is illustrated in several non-trivial cases, and the relation to earlier results is explained. A graph-theoretical formulation of our results in terms of rooted dichromatic, or Tutte, polynomials is also given.
Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
Bjerrum-Bohr, N E J; Damgaard, Poul H; Feng, Bo
2016-01-01
We prove that the scattering equation formalism for Yang-Mills amplitudes can be used to make manifest the theory's color-kinematics duality. This is achieved through a concrete reduction algorithm which renders this duality manifest term-by-term. The reduction follows from the recently derived set of identities for amplitudes expressed in the scattering equation formalism that are analogous to monodromy relations in string theory. A byproduct of our algorithm is a generalization of the identities among gravity and Yang-Mills amplitudes.
Higher Derivative Brane Couplings from T-Duality
Becker, Katrin; Robbins, Daniel
2010-01-01
The Wess-Zumino coupling on D-branes in string theory is known to receive higher derivative corrections which couple the Ramond-Ramond potential to terms involving the square of the spacetime curvature tensor. Consistency with T-duality implies that the branes should also have four-derivative couplings that involve the NS-NS B-field. We use T-duality to predict some of these couplings. We then confirm these results with string worldsheet computations by evaluating disc amplitudes with insertions of one R-R and two NS-NS vertex operators.
A duality theorem by means of Riemann Stieltjes integral
Directory of Open Access Journals (Sweden)
Ottavio Caligaris
1993-05-01
Full Text Available Duality between the space of continuous functions and the space of bounded variations functions can be easily characterized by means of Riemann-Stieltjes integrals when we consider real valued functions defined, e.g., on [0,1]; here we give a self-contained exposition of Riemann-Stieltjes integration theory for functions which assumes values in infinite dimensional vector spaces and we show as the duality between the space of continuous functions and the space of bounded variation functions can be represented by means of such theory.
Vector optimization and monotone operators via convex duality recent advances
Grad, Sorin-Mihai
2014-01-01
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
Duality invariance of s≥32 fermions in AdS
Directory of Open Access Journals (Sweden)
S. Deser
2014-11-01
Full Text Available We show that in D=4 AdS, s≥3/2 partially massless (PM fermions retain the duality invariances of their flat space massless counterparts. They have tuned ratios m2/M2≠0 that turn them into sums of effectively massless unconstrained helicity ±(s,⋯,32 excitations, shorn of the lowest (non-dual helicity ±12-rung and — more generally — of succeeding higher rung as well. Each helicity mode is separately duality invariant, like its flat space counterpart.
Black hole thermodynamics, stringy dualities and double field theory
Arvanitakis, Alex S.; Blair, Chris D. A.
2017-03-01
We discuss black hole thermodynamics in the manifestly duality invariant formalism of double field theory (DFT). We reformulate and prove the first law of black hole thermodynamics in DFT, using the covariant phase space approach. After splitting the full O(D, D) invariant DFT into a Kaluza–Klein-inspired form where only n coordinates are doubled, our results provide explicit duality invariant mass and entropy formulas. We illustrate how this works by discussing the black string solution and its T-duals.
Black hole thermodynamics, stringy dualities and double field theory
Arvanitakis, Alex S
2016-01-01
We discuss black hole thermodynamics in the manifestly duality invariant formalism of double field theory (DFT). We reformulate and prove the first law of black hole thermodynamics in DFT, using the covariant phase space approach. After splitting the full O(D, D) invariant DFT into a Kaluza-Klein-inspired form where only n coordinates are doubled, our results provide explicit duality invariant mass and entropy formulas. We illustrate how this works by discussing the black fundamental string solution and its T-duals.
Entanglement entropy and duality in AdS4
Directory of Open Access Journals (Sweden)
Ioannis Bakas
2015-07-01
Full Text Available Small variations of the entanglement entropy δS and the expectation value of the modular Hamiltonian δE are computed holographically for circular entangling curves in the boundary of AdS4, using gravitational perturbations with general boundary conditions in spherical coordinates. Agreement with the first law of thermodynamics, δS=δE, requires that the line element of the entangling curve remains constant. In this context, we also find a manifestation of electric–magnetic duality for the entanglement entropy and the corresponding modular Hamiltonian, following from the holographic energy–momentum/Cotton tensor duality.
Color-kinematic duality in ABJM theory without amplitude relations
Sivaramakrishnan, Allic
2017-01-01
We explicitly show that the Bern-Carrasco-Johansson color-kinematic duality holds at tree level through at least eight points in Aharony-Bergman-Jafferis-Maldacena theory with gauge group SU(N) × SU(N). At six points we give the explicit form of numerators in terms of amplitudes, displaying the generalized gauge freedom that leads to amplitude relations. However, at eight points no amplitude relations follow from the duality, so the diagram numerators are fixed unique functions of partial amplitudes. We provide the explicit amplitude-numerator decomposition and the numerator relations for eight-point amplitudes.
A Continuing Duality: Physics and Philosophy.
Larson, James H.
1984-01-01
Discusses need for introducing material to educate students about the relationship of philosophy to physics and science in general, particularly in light of quantum mechanics. Suggesting the dual nature of electrons as a starting point and citing several supplemental texts, a demonstration is described to be used to introduce the topic. (JM)
Quantum mechanics: why complex Hilbert space?
Cassinelli, G; Lahti, P
2017-11-13
We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).
Knot polynomial identities and quantum group coincidences
Morrison, Scott; Snyder, Noah
2010-01-01
We construct link invariants using the D_2n subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories involving the even parts of the D_2n planar algebras. We discuss the origins of these coincidences, explaining the role of SO level-rank duality, Kirby-Melvin symmetry, and properties of small Dynkin diagrams. One of these coincidences involves G_2 and does not appear to be related to level-rank duality.
Geons and the quantum information metric
Sinamuli, Musema; Mann, Robert B.
2017-07-01
We investigate the proposed duality between a quantum information metric in a CFTd +1 and the volume of a maximum time slice in the dual AdSd +2 for topological geons. Examining the specific cases of Banados-Teitelboim-Zannelli (BTZ) black holes and planar Schwarzschild-anti-de Sitter black holes, along with their geon counterparts, we find that the proposed duality relation for geons is the same apart from a factor of 4. The information metric therefore provides a probe of the topology of the bulk spacetime.
Pro-Torus Actions on Poincaré Duality Spaces
Indian Academy of Sciences (India)
Ali Özkurt; Doğan Dönmez
2006-08-01
In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if `torus’ is replaced by `pro-torus’.
Strong Duality and Optimality Conditions for Generalized Equilibrium Problems
Directory of Open Access Journals (Sweden)
D. H. Fang
2013-01-01
Full Text Available We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.
On R-duals and the duality principle
DEFF Research Database (Denmark)
Christensen, Ole; Stoeva, Diana
2015-01-01
. In this paper we discuss the relationship between the R-duals and a variant, called R-duals of type III, introduced in 2014. In contrast to the original R-duals, it is known that the R-duals of type III generalize the duality principle for all Gabor frames, but we believe that a smaller and more convenient...
Piezoelectricity and Piezomagnetism: Duality in two-dimensional checkerboards
Fel, Leonid G.
2002-05-01
The duality approach in two-dimensional two-component regular checkerboards is extended to piezoelectricity and piezomagnetism. The relation between the effective piezoelectric and piezomagnetic moduli is found for a checkerboard with the p6'mm'-plane symmetry group (dichromatic triangle).
Non-uniform horizons in Gauge/Gravity Duality
Moskalets, T M
2015-01-01
In this communication, based on our paper http://arxiv.org/abs/1409.4186, we discuss a way of enhancing Gauge/Gravity Duality and response of a dual strongly coupled medium on placing the inhomogeneity on the gravity side.
Stringy horizons and generalized FZZ duality in perturbation theory
Giribet, Gaston
2016-01-01
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n-2 winding modes actually coincide with the correlation functions in the SL(2,R)/U(1) gauged WZW model ...
Some Duality Results for Fuzzy Nonlinear Programming Problem
Sangeeta Jaiswal; Geetanjali Panda
2012-01-01
The concept of duality plays an important role in optimization theory. This paper discusses some relations between primal and dual nonlinear programming problems in fuzzy environment. Here, fuzzy feasible region for a general fuzzy nonlinear programming is formed and the concept of fuzzy feasible solution is defined. First order dual relation for fuzzy nonlinear programming problem is studied.
On Duality in the Born-Infeld Theory
Khoudeir, Adel; Parra, Yoan
1997-01-01
The $SL(2,R)$ duality symmetric action for the Born-Infeld theory in terms of two potentials, coupled with non-trivial backgroud fields in four dimensions is established. This construction is carried out in detail by analysing the hamiltonian structure of the Born-Infeld theory. The equivalence with the usual Born-Infeld theory is shown.
Softer Hard Scattering and Noncommutative Gauge-String Duality
Rey, S J; Rey, Soo-Jong; Yee, Jung-Tay
2003-01-01
We study exclusive scattering of `hadrons' at high energy and fixed angle in (nonconformal) noncommutative gauge theories. Via gauge-string duality, we show that the noncommutativity renders the scattering soft, leading to exponential suppression. The result fits with the picture that, in noncommutative gauge theory, fundamental parton contents constitute wee-partons only and `hadrons' are made out of open Wilson lines.
Spinor-Vector Duality in N=2 Heterotic String Vacua
Faraggi, Alon E; Rizos, John
2007-01-01
Classification of the N=1 space-time supersymmetric fermionic Z2XZ2 heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor--vector duality exists also in fermionic Z2 heterotic string models, which preserve N=2 space-time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t V duality map. We present a novel basis to generate the free fermionic models in which the ten dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non--trivial sectors, and due to the triality property of the SO(...
Resummation and S-duality in N=4 SYM
Beem, Christopher; Sen, Ashoke; van Rees, Balt C
2013-01-01
We consider the problem of resumming the perturbative expansions for anomalous dimensions of low twist, non-BPS operators in four dimensional N=4 supersymmetric Yang-Mills theories. The requirement of S-duality invariance imposes considerable restrictions on any such resummation. We introduce several prescriptions that produce interpolating functions on the upper half plane that are compatible with a subgroup of the full duality group. These lead to predictions for the anomalous dimensions at all points in the fundamental domain of the complex gauge coupling, and in particular at the duality-invariant values \\tau=i and \\tau=exp(i\\pi/3). For low-rank gauge groups, the predictions are compatible with the bounds derived by conformal bootstrap methods for these anomalous dimensions; within numerical errors, they are in good agreement with the conjecture that said bounds are saturated at a duality-invariant point. We also find that the anomalous dimensions of the lowest twist operators lie within an extremely narr...
Dualities in 3D large N vector models
Muteeb, Nouman; Zayas, Leopoldo A. Pando; Quevedo, Fernando
2016-05-01
Using an explicit path integral approach we derive non-abelian bosonization and duality of 3D systems in the large N limit. We first consider a fermionic U( N) vector model coupled to level k Chern-Simons theory, following standard techniques we gauge the original global symmetry and impose the corresponding field strength F μν to vanish introducing a Lagrange multiplier Λ. Exchanging the order of integrations we obtain the bosonized theory with Λ as the propagating field using the large N rather than the previously used large mass limit. Next we follow the same procedure to dualize the scalar U ( N) vector model coupled to Chern-Simons and find its corresponding dual theory. Finally, we compare the partition functions of the two resulting theories and find that they agree in the large N limit including a level/rank duality. This provides a constructive evidence for previous proposals on level/rank duality of 3D vector models in the large N limit. We also present a partial analysis at subleading order in large N and find that the duality does not generically hold at this level.
Dualities in 3D large N vector models
Energy Technology Data Exchange (ETDEWEB)
Muteeb, Nouman [The Abdus Salam International Centre for Theoretical Physics, ICTP,Strada Costiera 11, 34014 Trieste (Italy); SISSA,Via Bonomea 265, 34136 Trieste (Italy); Zayas, Leopoldo A. Pando [The Abdus Salam International Centre for Theoretical Physics, ICTP,Strada Costiera 11, 34014 Trieste (Italy); Michigan Center for Theoretical Physics, Department of Physics,University of Michigan, Ann Arbor, MI 48109 (United States); Quevedo, Fernando [The Abdus Salam International Centre for Theoretical Physics, ICTP,Strada Costiera 11, 34014 Trieste (Italy); DAMTP, CMS, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2016-05-09
Using an explicit path integral approach we derive non-abelian bosonization and duality of 3D systems in the large N limit. We first consider a fermionic U(N) vector model coupled to level k Chern-Simons theory, following standard techniques we gauge the original global symmetry and impose the corresponding field strength F{sub μν} to vanish introducing a Lagrange multiplier Λ. Exchanging the order of integrations we obtain the bosonized theory with Λ as the propagating field using the large N rather than the previously used large mass limit. Next we follow the same procedure to dualize the scalar U(N) vector model coupled to Chern-Simons and find its corresponding dual theory. Finally, we compare the partition functions of the two resulting theories and find that they agree in the large N limit including a level/rank duality. This provides a constructive evidence for previous proposals on level/rank duality of 3D vector models in the large N limit. We also present a partial analysis at subleading order in large N and find that the duality does not generically hold at this level.
Puzzles on the duality between heterotic and type IIA strings
Abe, M; Abe, Mitsuko; Sato, Masamichi
1999-01-01
We discuss the possibility of the extension of the duality between the webs of heterotic string and the type IIA string to Calabi-Yau 3-folds with another K3 fiber by comparing the dual polyhedron of Calabi-Yau 3-folds given by Candelas, Perevalov and Rajesh.
S-duality invariant dilaton couplings at order $\\alpha'^3$
Garousi, Mohammad R
2013-01-01
The Riemann curvature correction to the type II supergravity at eight-derivative level is given schematically as $(t_8t_8+{1}{8}\\eps_{10}\\eps_{10})R^4$ at tree-level. The replacement of the generalized Riemann curvature in $t_8t_8R^4$, proposed by Gross and Sloan, produces various NS-NS couplings which are invariant under T-duality. Recently, using the combination of S-duality and T-duality transformations on these couplings, we have found groups of couplings which are invariant under the S-duality transformation. In this paper, we have examined the couplings involving the dilaton with direct scattering amplitude calculations of four NS-NS vertex operators in the superstring theory and found exact agreement. The coupling $\\eps_{10}\\eps_{10}R^4$ is a total derivative term at four-field level. The $\\sigma$-model beta function approach implies the presence of this term at the tree-level. By examining the sphere-level scattering amplitude of five gravitons, we have also confirmed the presence of this term in the ...
On the Duality Mapping Sets in Orlicz Sequence Spaces
Institute of Scientific and Technical Information of China (English)
Bao Xiang WANG
2001-01-01
The criteria for the weak compactness of duality mapping sets J(x) = {f ∈ X*:
Topics On Ads/cft Duality And Holography
Lin, F
2000-01-01
This dissertation presents our study on various aspects of Maldacena's AdS/CFT duality and on a generalization of it from the point of view of holography. The AdS/CFT duality states that supergravity on anti-de Sitter (AdS) background is equivalent to a local conformal field theory (CFT) on the boundary at infinity of AdS space. One way to generalize the AdS/CFT duality is to turn on more background fields of supergravity such as the r-form fields. The bulk geometry is no longer AdS, and one finds that in the spirit of AdS/CFT duality, it corresponds to a nonconformal field theory with the radial position of the boundary as the energy scale and with the boundary at infinity as the ultraviolet fixed point. Moreover, one can derive the holographic renormalization group (RG) flows of the field theory from its gravity dual. A specific case of interest is the Neveu-Schwarz 2-form potential on the world volume of a D-brane, the resulting open-string low energy effective field theory has been shown to be a Yang-Mill...
Renormalization group flows in gauge-gravity duality
Murugan, Arvind
2016-01-01
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated with the breaking of supersymmetry. Chapter 5 contains new unpublished material on various instabilities of the weakly curved non-supersymmetric $AdS_4$ backgrounds of M-theory.
A D-induced duality and its applications
J. Brinkhuis (Jan); S. Zhang (Shuzhong)
2002-01-01
textabstractThis paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a
M-theory duality and BPS-extended supergravity
de Wit, Bernard
2001-01-01
We discuss toroidal compactifications of maximal supergravity coupled to an extended configuration of BPS states which transform consistently under the U-duality group. Under certain conditions this leads to theories that live in more than eleven spacetime dimensions, with maximal supersymmetry but only partial Lorentz invariance. We demonstrate certain features of this construction for the case of nine-dimensional N=2 supergravity.
Some remarks on defects and T-duality
DEFF Research Database (Denmark)
Sarkissian, Gor; Schweigert, Christoph
2009-01-01
conditions. We also exhibit a class of diagonal defects that induce a shift of the B-field. We finally study T-dualities for S1 -fibrations in the example of the Wess–Zumino–Witten model on SU(2) and lens spaces. Using standard techniques from D-branes, we derive from algebraic data in rational conformal...
Doveil, Fabrice; Guyomarc'h, Didier; Caetano da Sousa, Meirielen; Elskens, Yves
2016-10-01
Beside industrial uses, Traveling Wave Tubes (TWT) are useful to mimic and study plasma-like wave-particle interaction. We upgraded a TWT, whose slow wave structure is a 4 m long helix (diameter 3.4 cm, pitch 1 mm) of Be-Cu wire in a vacuum glass tube. At one end, a cathode injects electrons, radially confined by a constant axial magnetic field. Movable probes, capacitively coupled to the helix, launch and monitor waves with an arbitrary waveform at a few tens of MHz. At the other end of the helix, a trochoidal analyzer allows to reconstruct the beam electron distribution function after its self-consistent interaction with the waves. The new device's observed dispersion relation agrees very well with a sheath model. The measured probe-helix coupling coefficients are used to reconstruct the spatial evolution of a launched wave as it interacts with the beam. For low beam intensity, chaotic effects are observed on the beam. For larger beam intensity, growth and saturation of a launched wave is observed.
Barbosa, D. D.
1986-01-01
A theory of medium-energy (about keV) electrons and heavy ions in Jupiter's magnetosphere is presented. Lower hybrid waves are generated by the combined effects of a ring instability of neutral wind pickup ions and the modified two-stream instability associated with transport of cool Iogenic plasma. The quasi-linear energy diffusion coefficient for lower hybrid wave-particle interactions is evaluated, and several solutions to the diffusion equation are given. Calculations based on measured wave properties show that the noise substantially modifies the particle distribution functions. The effects are to accelerate superthermal ions and electrons to keV energies and to thermalize the pickup ions on time scales comparable to the particle residence time. The S(2+)/S(+) ratio at medium energies is a measure of the relative contribution from Iogenic thermal plasma and neutral wind ions, and this important quantity should be determined from future measurements. The theory also predicts a preferential acceleration of heavy ions with an accleration time that scales inversely with the root of the ion mass. Electrons accelerated by the process contribute to further reionization of the neutral wind by electron impact, thus providing a possible confirmation of Alfven's critical velocity effect in the Jovian magnetosphere.
Bounce-resonance wave-particle interactions involving energetic ions and 2nd-harmonic ULF waves
Rankin, Robert; Sydorenko, Dmytro; Wang, Chengrui
2016-07-01
Multi-point observations from Cluster show clear evidence of acceleration of H+ and O+ ions by large azimuthal mode number ULF waves. In this paper we present a quantitative comparison between these observations and results from a numerical model. The methodology consists of large-scale test-particle simulations of bounce-resonance wave-particle interactions in fields of second harmonic standing ULF waves. The ULF waves are specified using a recently developed three-dimensional model that can take dipolar and compressed dipole magnetic field configurations. Our test particle simulations confirm the theoretical treatment of bounce-resonance developed by Southwood and Kivelson, including the resonance condition that must be satisfied, as well as a phase change of Pi in the energy spectrum. We also find strong nonlinear behaviour for m-numbers between 40-100, and for azimuthal electric field strengths of a few tens of millivolts per metre. The test-particle simulations are able to reproduce energy-dispersed ion signatures observed by Cluster, opening the possibility to more fully understand the inter-relationship between ULF waves and ion energization and transport in the inner magnetosphere.
Are All Probabilities Fundamentally Quantum Mechanical?
Pradhan, Rajat Kumar
2011-01-01
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated that all probabilities may be fundamentally quantum mechanical in the sense that they may all be derived from the corresponding amplitudes. The classical coin-toss and the quantum double slit interference experiments are discussed as illustrative prototype examples. Absence of multi-order quantum interference effects in multiple-slit experiments and the Experimental tests of complementarity in Wheeler's delayed-choice type experiments are explained using the involvement of the observer.
Holographic Duality in Condensed Matter Physics
Zaanen, Jan; Liu, Yan; Sun, Ya-Wen; Schalm, Koenraad
2015-11-01
Preface; 1. Introduction; 2. Condensed matter: the charted territory; 3. Condensed matter: the challenges; 4. Large N field theories for holography and condensed matter; 5. The AdS/CFT correspondence as computational device: the dictionary; 6. Finite temperature magic: black holes and holographic thermodynamics; 7. Holographic hydrodynamics; 8. Finite density: the Reissner-Nordström black hole and strange metals; 9. Holographic photoemission and the RN metal: the fermions as probes; 10. Holographic superconductivity; 11. Holographic Fermi liquids; 12. Breaking translational invariance; 13. AdS/CMT from the top down; 14. Outlook: holography and quantum matter; References; Index.
Camporeale, Enrico; Zimbardo, G.
2015-01-01
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earths radiation belt. By tracking PIC particles, and comparing with test-particle simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi- linear theory routinely used in ...
Vector Potential Quantization and the Quantum Vacuum
Directory of Open Access Journals (Sweden)
Constantin Meis
2014-01-01
Full Text Available We investigate the quantization of the vector potential amplitude of the electromagnetic field to a single photon state starting from the fundamental link equations between the classical electromagnetic theory and the quantum mechanical expressions. The resulting wave-particle formalism ensures a coherent transition between the classical electromagnetic wave theory and the quantum representation. A quantization constant of the photon vector potential is defined. A new quantum vacuum description results directly in having very low energy density. The calculated spontaneous emission rate and Lambs shift for the nS states of the hydrogen atom are in agreement with quantum electrodynamics. This low energy quantum vacuum state might be compatible with recent astrophysical observations.