Modern Canonical Quantum General Relativity
NASA Astrophysics Data System (ADS)
Thiemann, Thomas
2007-09-01
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. Implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics; Bibliography; Index.
Modern Canonical Quantum General Relativity
NASA Astrophysics Data System (ADS)
Thiemann, Thomas
2008-11-01
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. Implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics; Bibliography; Index.
BOOK REVIEW: Modern Canonical Quantum General Relativity
NASA Astrophysics Data System (ADS)
Kiefer, Claus
2008-06-01
The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly divided into two classes: either one seeks a unified quantum framework of all interactions or one starts with a direct quantization of general relativity. In the first class, string theory (M-theory) is the only known example. In the second class, one can make an additional methodological distinction: while covariant approaches such as path-integral quantization use the four-dimensional metric as an essential ingredient of their formalism, canonical approaches start with a foliation of spacetime into spacelike hypersurfaces in order to arrive at a Hamiltonian formulation. The present book is devoted to one of the canonical approaches—loop quantum gravity. It is named modern canonical quantum general relativity by the author because it uses connections and holonomies as central variables, which are analogous to the variables used in Yang Mills theories. In fact, the canonically conjugate variables are a holonomy of a connection and the flux of a non-Abelian electric field. This has to be contrasted with the older geometrodynamical approach in which the metric of three-dimensional space and the second fundamental form are the fundamental entities, an approach which is still actively being pursued. It is the author's ambition to present loop quantum gravity in a way in which every step is formulated in a mathematically rigorous form. In his own words: 'loop quantum gravity is an attempt to construct a mathematically rigorous, background-independent, non-perturbative quantum field theory of Lorentzian general relativity and all known matter in four spacetime dimensions, not more and not less'. The formal Leitmotiv of loop quantum gravity is background independence. Non-gravitational theories are usually quantized on a given non-dynamical background. In contrast, due to
Complexifier coherent states for quantum general relativity
NASA Astrophysics Data System (ADS)
Thiemann, T.
2006-03-01
Recently, substantial amount of activity in quantum general relativity (QGR) has focused on the semiclassical analysis of the theory. In this paper, we want to comment on two such developments: (1) polymer-like states for Maxwell theory and linearized gravity constructed by Varadarajan which use much of the Hilbert space machinery that has proved useful in QGR, and (2) coherent states for QGR, based on the general complexifier method, with built-in semiclassical properties. We show the following. (A) Varadarajan's states are complexifier coherent states. This unifies all states constructed so far under the general complexifier principle. (B) Ashtekar and Lewandowski suggested a non-Abelian generalization of Varadarajan's states to QGR which, however, are no longer of the complexifier type. We construct a new class of non-Abelian complexifiers which come close to that underlying Varadarajan's construction. (C) Non-Abelian complexifiers close to Varadarajan's induce new types of Hilbert spaces which do not support the operator algebra of QGR. The analysis suggests that if one sticks to the present kinematical framework of QGR and if kinematical coherent states are at all useful, then normalizable, graph-dependent states must be used which are produced by the complexifier method as well. (D) Present proposals for states with mildened graph dependence, obtained by performing a graph average, do not approximate well coordinate-dependent observables. However, graph-dependent states, whether averaged or not, seem to be well suited for the semiclassical analysis of QGR with respect to coordinate-independent operators.
Harmonizing General Relativity with Quantum Mechanics
NASA Astrophysics Data System (ADS)
Alfonso-Faus, Antonio
2007-04-01
Gravitation is the common underlying texture between General Relativity and Quantum Mechanics. We take gravitation as the link that can make possible the marriage between these two sciences. We use here the duality of Nature for gravitation: A continuous warped space, wave-like, and a discrete quantum gas, particle-like, both coexistent and producing an equilibrium state in the Universe. The result is a static, non expanding, spherical, unlimited and finite Universe, with no cosmological constant and no dark energy. Macht's Principle is reproduced here by the convergence of the two cosmological equations of Einstein. From this a Mass Boom concept is born given by M = t, M the mass of the Universe and t its age. Also a decreasing speed of light is the consequence of the Mass Boom, c = 1/t, which explains the Supernovae Type Ia observations without the need of expansion (nor, of course, accelerated expansion). Our Mass Boom model completely wipes out the problems and paradoxes built in the Big Bang model, like the horizon, monopole, entropy, flatness, fine tuning, etc. It also eliminates the need for inflation.
Minimum length from quantum mechanics and classical general relativity.
Calmet, Xavier; Graesser, Michael; Hsu, Stephen D H
2004-11-19
We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order lP. Our results imply a device independent limit on possible position measurements.
Generalized Orthogonality Relations and SU(1,1)-Quantum Tomography
NASA Astrophysics Data System (ADS)
Carmeli, C.; Cassinelli, G.; Zizzi, F.
2009-06-01
We present a mathematically precise derivation of some generalized orthogonality relations for the discrete series representations of SU(1,1). These orthogonality relations are applied to derive tomographical reconstruction formulas. Their physical interpretation is also discussed.
Extended theory of harmonic maps connects general relativity to chaos and quantum mechanism
NASA Astrophysics Data System (ADS)
Ren, Gang; Duan, Yi-Shi
2017-10-01
General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the line between classical and quantum physics by connecting chaos and entanglement. Here, we showed the early reported extended HM theory that included the general relativity can also be used to recover the classic chaos equations and even the Schrodinger equation in quantum physics, suggesting the extended theory of harmonic maps may act as a universal theory of physics.
The interface between quantum mechanics and general relativity
NASA Astrophysics Data System (ADS)
Chiao, R. Y.
The generation, as well as the detection, of gravitational radiation by means of charged superfluids is considered. One example of such a “charged superfluid” consists of a pair of Planck-mass-scale, ultracold “Millikan oil drops”, each with a single electron on its surface in a strong magnetic field, in which the oil of the drop is replaced by superfluid helium. When levitated in a magnetic trap, and subjected to microwave-frequency electromagnetic radiation, a pair of such “Millikan oil drops” separated by a microwave wavelength can become an efficient quantum transducer between quadrupolar electromagnetic and gravitational radiation. This leads to the possibility of a Hertz-like experiment, in which the source of microwave-frequency gravitational radiation consists of one pair of “Millikan oil drops” driven by microwaves, and the receiver of such radiation consists of another pair of “Millikan oil drops” in the far field driven by the gravitational radiation generated by the first pair. The second pair then back-converts the gravitational radiation into detectable microwaves. The enormous enhancement of the conversion efficiency for these quantum transducers over that for electrons arises from the fact that there exists macroscopic quantum phase coherence in these charged superfluid systems.
Comment on 'Immirzi parameter in quantum general relativity'
Samuel, Joseph
2001-08-15
The Immirzi parameter is a free parameter which appears in the physical predictions of loop quantum gravity and is sometimes viewed as a quantization ambiguity. Interpretations have been offered for the Immirzi ambiguity, but there does not appear to be a clear understanding or even a consensus about its origin and significance. We show that a previously discussed example containing a 'finite dimensional analogue' of the Immirzi ambiguity is fallacious, in the sense that the ambiguity in this example is not intrinsic to the system, but introduced artificially by compactifying the configuration space.
Chapter 10 Quantum Mechanics and the Special and General Theory of Relativity
NASA Astrophysics Data System (ADS)
Brändas, Erkki J.
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered. A first principles relativistically invariant theory will be provided through a model, which is basically quantum mechanical. Moreover, by analytically extending quantum mechanics into the complex plane, it is possible to include dynamical features such as time-, length-, and temperature-scales into the theory. The flexibility of including complex symmetric interactions will in the same way support a transition from firmly quantum mechanical non-local behaviour to a decidedly classical-local appearance. Furthermore, the extended formulation gives rise to so-called Jordan blocks. They will be shown to appear logically in the present generalized dynamical picture and a compelling interpretation is microscopic self-organization (MSO). Not only have the manifestation of quantum-thermal correlations, and the emergence of generic time scales been established, but the present viewpoint also appears to throw new light on the age-old problem of quantum mechanics versus relativity. To bring all these ideas together, we will demonstrate that our model (i) displays the simple occurrence of such a degenerate unit, (ii) demonstrates the link with the Klein-Gordon-Dirac relativistic theory and (iii) provides dynamical features of both special and general relativity theory.
Relating different quantum generalizations of the conditional Rényi entropy
Tomamichel, Marco; Berta, Mario; Hayashi, Masahito
2014-08-15
Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here, we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Rényi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Rényi entropies and derive a new entropic uncertainty relation.
Generalized concatenated quantum codes
Grassl, Markus; Shor, Peter; Smith, Graeme; Smolin, John; Zeng Bei
2009-05-15
We discuss the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we construct families of single-error-correcting nonadditive quantum codes, in both binary and nonbinary cases, which not only outperform any stabilizer codes for finite block length but also asymptotically meet the quantum Hamming bound for large block length.
The general dispersion relation of induced streaming instabilities in quantum outflow systems
Mehdian, H. Hajisharifi, K.; Hasanbeigi, A.
2015-11-15
In this manuscript the dispersion relations of streaming instabilities, by using the unique property (neutralized in charge and current by default) of plasma shells colliding, have been generalized and studied. This interesting property for interpenetrating beams enables one to find the general dispersion relations without any restrictions used in the previous works in this area. In our previous work [H. Mehdian et al., ApJ. 801, 89 (2015)], employing the plasma shell concept and boost frame method, the general dispersion relation for filamentation instability has been derived in the relativistic classical regime. But in this paper, using the above mentioned concepts, the general dispersion relations (for each of streaming instabilities, filamentation, two-stream and multi-stream) in the non-relativistic quantum regime have been derived by employing the quantum fluid equations together with Maxwell equations. The derived dispersion relations enable to describe any arbitrary system of interacting two and three beams, justified neutralization condition, by choosing the inertial reference frame embedded on the one of the beams. Furthermore, by the numerical and analytical study of these dispersion relations, many new features of streaming instabilities (E.g. their cut-off wave numbers and growth rates) in terms of all involved parameters have been illustrated. The obtained results in this paper can be used to describe many astrophysical systems and laboratory astrophysics setting, such as collision of non-parallel plasma shells over a background plasma or the collision of three neutralized plasma slabs, and justifying the many plasma phenomena such as particle accelerations and induced fields.
Bays, Harold
2005-05-01
Excessive fat (adiposity) and dysfunctional fat (adiposopathy) constitute the most common worldwide epidemics of our time -- and perhaps of all time. Ongoing efforts to explain how the micro (adipocyte) and macro (body organ) biologic systems interact through function and dysfunction in promoting Type 2 diabetes mellitus, hypertension and dyslipidemia are not unlike the mechanistic and philosophical thinking processes involved in reconciling the micro (quantum physics) and macro (general relativity) theories in physics. Currently, the term metabolic syndrome refers to a constellation of consequences often associated with excess body fat and is an attempt to unify the associations known to exist between the four fundamental metabolic diseases of obesity, hyperglycemia (including Type 2 diabetes mellitus), hypertension and dyslipidemia. However, the association of adiposity with these metabolic disorders is not absolute and the metabolic syndrome does not describe underlying causality, nor does the metabolic syndrome necessarily reflect any reasonably related pathophysiologic process. Just as with quantum physics, general relativity and the four fundamental forces of the universe, the lack of an adequate unifying theory of micro causality and macro consequence is unsatisfying, and in medicine, impairs the development of agents that may globally improve both obesity and obesity-related metabolic disease. Emerging scientific and clinical evidence strongly supports the novel concept that it is not adiposity alone, but rather it is adiposopathy that is the underlying cause of most cases of Type 2 diabetes mellitus, hypertension and dyslipidemia. Adiposopathy is a plausible Theory of Everything for mankind's greatest metabolic epidemics.
Exactly solvable quantum cosmologies from two killing field reductions of general relativity
NASA Astrophysics Data System (ADS)
Husain, Viqar; Smolin, Lee
1989-11-01
An exact and, possibly, general solution to the quantum constraints is given for the sector of general relativity containing cosmological solutions with two space-like, commuting, Killing fields. The dynamics of these model space-times, which are known as Gowdy space-times, is formulated in terms of Ashtekar's new variables. The quantization is done by using the recently introduced self-dual and loop representations. On the classical phase space we find four explicit physical observables, or constants of motion, which generate a GL(2) symmetry group on the space of solutions. In the loop representations we find that a complete description of the physical state space, consisting of the simultaneous solutions to all of the constraints, is given in terms of the equivalence classes, under Diff(S1), of a pair of densities on the circle. These play the same role that the link classes play in the loop representation solution to the full 3+1 theory. An infinite dimensional algebra of physical observables is found on the physical state space, which is a GL(2) loop algebra. In addition, by freezing the local degrees of freedom of the model, we find a finite dimensional quantum system which describes a set of degenerate quantum cosmologies on T3 in which the length of one of the S1's has gone to zero, while the area of the remaining S1×S1 is quantized in units of the Planck area. The quantum kinematics of this sector of the model is identical to that of a one-plaquette SU(2) lattice gauge theory.
The Present Situation in Quantum Theory and its Merging with General Relativity
NASA Astrophysics Data System (ADS)
Khrennikov, Andrei
2017-08-01
We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena—a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the most widely known (but, e.g., Bohmian mechanics is also a part of QT). The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement. We compare the QFT and QM based measurement theories by presenting both theoretical and experimental viewpoints. Then we discuss two basic mathematical constraints of both QM and QFT, namely, the use of real (and, hence, complex) numbers and the Hilbert state space. We briefly present non-archimedean and non-hilbertian approaches to QT and their consequences. Finally, we claim that, in spite of the Bell theorem, it is still possible to treat quantum phenomena on the basis of a classical-like causal theory. We present a random field model generating the QM and QFT formalisms. This emergence viewpoint can serve as the basis for unification of novel QT (may be totally different from presently powerful QM and QFT) and GR. (It may happen that the latter would also be revolutionary modified.)
Gambini, R; Pullin, J
2000-12-18
We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the lambda --> infinity limit of general relativity. This allows an explicit perturbative computational setup in which the quantum states of the theory and the classical observables can be explicitly computed. An unexpected relationship arises at a quantum level between the discrete spectrum of the volume operator and the allowed values of the cosmological constant.
Generalized Geometric Quantum Speed Limits
NASA Astrophysics Data System (ADS)
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
Relativity and Quantum Mechanics
NASA Astrophysics Data System (ADS)
Brändas, Erkki J.
2007-12-01
The old dilemma of quantum mechanics versus the theory of relativity is reconsidered via a first principles relativistically invariant theory. By analytic extension of quantum mechanics into the complex plane one may (i) include dynamical features such as time- and length-scales and (ii) examine the possibility and flexibility of so-called general Jordan block formations. The present viewpoint asks for a new perspective on the age-old problem of quantum mechanics versus the theory of relativity. To bring these ideas together, we will establish the relation with the Klein-Gordon-Dirac relativistic theory and confirm some dynamical features of both the special and the general relativity theory.
Generalized uncertainty relations and entanglement dynamics in quantum Brownian motion models
Anastopoulos, C.; Kechribaris, S.; Mylonas, D.
2010-10-15
We study entanglement dynamics in quantum Brownian motion (QBM) models. Our main tool is the Wigner function propagator. Time evolution in the Wigner picture is physically intuitive and it leads to a simple derivation of a master equation for any number of system harmonic oscillators and spectral density of the environment. It also provides generalized uncertainty relations, valid for any initial state, that allow a characterization of the environment in terms of the modifications it causes to the system's dynamics. In particular, the uncertainty relations are very informative about the entanglement dynamics of Gaussian states, and to a lesser extent for other families of states. For concreteness, we apply these techniques to a bipartite QBM model, describing the processes of entanglement creation, disentanglement, and decoherence at all temperatures and time scales.
Generalized quantum secret sharing
Singh, Sudhir Kumar; Srikanth, R.
2005-01-01
We explore a generalization of quantum secret sharing (QSS) in which classical shares play a complementary role to quantum shares, exploring further consequences of an idea first studied by Nascimento, Mueller-Quade, and Imai [Phys. Rev. A 64, 042311 (2001)]. We examine three ways, termed inflation, compression, and twin thresholding, by which the proportion of classical shares can be augmented. This has the important application that it reduces quantum (information processing) players by replacing them with their classical counterparts, thereby making quantum secret sharing considerably easier and less expensive to implement in a practical setting. In compression, a QSS scheme is turned into an equivalent scheme with fewer quantum players, compensated for by suitable classical shares. In inflation, a QSS scheme is enlarged by adding only classical shares and players. In a twin-threshold scheme, we invoke two separate thresholds for classical and quantum shares based on the idea of information dilution.
NASA Astrophysics Data System (ADS)
Heusler, Stefan
2006-12-01
The main focus of the second, enlarged edition of the book Mathematica for Theoretical Physics is on computational examples using the computer program Mathematica in various areas in physics. It is a notebook rather than a textbook. Indeed, the book is just a printout of the Mathematica notebooks included on the CD. The second edition is divided into two volumes, the first covering classical mechanics and nonlinear dynamics, the second dealing with examples in electrodynamics, quantum mechanics, general relativity and fractal geometry. The second volume is not suited for newcomers because basic and simple physical ideas which lead to complex formulas are not explained in detail. Instead, the computer technology makes it possible to write down and manipulate formulas of practically any length. For researchers with experience in computing, the book contains a lot of interesting and non-trivial examples. Most of the examples discussed are standard textbook problems, but the power of Mathematica opens the path to more sophisticated solutions. For example, the exact solution for the perihelion shift of Mercury within general relativity is worked out in detail using elliptic functions. The virial equation of state for molecules' interaction with Lennard-Jones-like potentials is discussed, including both classical and quantum corrections to the second virial coefficient. Interestingly, closed solutions become available using sophisticated computing methods within Mathematica. In my opinion, the textbook should not show formulas in detail which cover three or more pages—these technical data should just be contained on the CD. Instead, the textbook should focus on more detailed explanation of the physical concepts behind the technicalities. The discussion of the virial equation would benefit much from replacing 15 pages of Mathematica output with 15 pages of further explanation and motivation. In this combination, the power of computing merged with physical intuition
Generalized quantum potentials
NASA Astrophysics Data System (ADS)
Nottale, Laurent
2009-07-01
We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (depending on a constant which may be different from the standard quantum constant planck) is equivalent to a generalized Schrödinger equation for a 'wavefunction' whose modulus squared yields the fluid density. Then we show that even in the case of the presence of vorticity, it is also possible to obtain a nonlinear Schrödinger-like equation (now of the vectorial field type) from the continuity and Euler equations including a quantum potential. The same kind of transformation also applies to a classical charged fluid subjected to an electromagnetic field and to an additional potential having the form of a quantum potential. Such a fluid can therefore be described by an equation of the Ginzburg-Landau type, and is expected to show some superconducting-like properties. Moreover, a Schrödinger form can be obtained for a fluctuating rotational motion of a solid. In this case the mass is replaced by the tensor of inertia, and a generalized form of the quantum potential is derived. We finally reconsider the case of a standard diffusion process, and we show that, after a change of variable, the diffusion equation can also be given the form of a continuity and Euler system including an additional potential energy. Since this potential is exactly the opposite of a quantum potential, the quantum behavior may be considered, in this context, as an anti-diffusion.
NASA Technical Reports Server (NTRS)
Li, Xi-Zeng; Su, Bao-Xia
1994-01-01
It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.
General polygamy inequality of multiparty quantum entanglement
NASA Astrophysics Data System (ADS)
Kim, Jeong San
2012-06-01
Using entanglement of assistance, we establish a general polygamy inequality of multiparty entanglement in arbitrary-dimensional quantum systems. For multiparty closed quantum systems, we relate our result with the monogamy of entanglement, and clarify that the entropy of entanglement bounds both monogamy and polygamy of multiparty quantum entanglement.
Generalized teleportation by quantum walks
NASA Astrophysics Data System (ADS)
Wang, Yu; Shang, Yun; Xue, Peng
2017-09-01
We develop a generalized teleportation scheme based on quantum walks with two coins. For an unknown qubit state, we use two-step quantum walks on the line and quantum walks on the cycle with four vertices for teleportation. For any d-dimensional states, quantum walks on complete graphs and quantum walks on d-regular graphs can be used for implementing teleportation. Compared with existing d-dimensional states teleportation, prior entangled state is not required and the necessary maximal entanglement resource is generated by the first step of quantum walk. Moreover, two projective measurements with d elements are needed by quantum walks on the complete graph, rather than one joint measurement with d^2 basis states. Quantum walks have many applications in quantum computation and quantum simulations. This is the first scheme of realizing communicating protocol with quantum walks, thus opening wider applications.
NASA Astrophysics Data System (ADS)
Spaans, M.
2013-08-01
General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian spacetime. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes (BHs)/wormholes. Paths are fundamental and prime three-manifolds like T3, S1 × S2 and S3 are used to construct quantum spacetime. A physical principle is formulated that causes observed paths to multiply: It takes one to know one. So topological fluctuations on the Planck scale take the form of multiple copies of any homeomorphically distinct path through quantum spacetime. The discrete time equation of motion for this topological quantum gravity is derived by counting distinct paths globally. The equation of motion is solved to derive some properties of dark energy and inflation. The dark energy density depends linearly on the number of macroscopic BHs in the universe and is time-dependent in a manner consistent with current astrophysical observations, having an effective equation of state w ≈ -1.1 for redshifts smaller than unity. Inflation driven by mini BHs proceeds over n ≈ 55 e-foldings, without strong inhomogeneity. A discrete time effect visible in the cosmic microwave background is suggested.
Quantum thermodynamics of general quantum processes.
Binder, Felix; Vinjanampathy, Sai; Modi, Kavan; Goold, John
2015-03-01
Accurately describing work extraction from a quantum system is a central objective for the extension of thermodynamics to individual quantum systems. The concepts of work and heat are surprisingly subtle when generalizations are made to arbitrary quantum states. We formulate an operational thermodynamics suitable for application to an open quantum system undergoing quantum evolution under a general quantum process by which we mean a completely positive and trace-preserving map. We derive an operational first law of thermodynamics for such processes and show consistency with the second law. We show that heat, from the first law, is positive when the input state of the map majorizes the output state. Moreover, the change in entropy is also positive for the same majorization condition. This makes a strong connection between the two operational laws of thermodynamics.
General monogamy relations of quantum entanglement for multiqubit W-class states
NASA Astrophysics Data System (ADS)
Zhu, Xue-Na; Fei, Shao-Ming
2017-02-01
Entanglement monogamy is a fundamental property of multipartite entangled states. We investigate the monogamy relations for multiqubit generalized W-class states. Analytical monogamy inequalities are obtained for the concurrence of assistance, the entanglement of formation, and the entanglement of assistance.
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory.
Burgess, Cliff P
2004-01-01
This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems, ideas which provide the theoretical foundations for the modern use of general relativity as a theory from which precise predictions are possible.
New Frontiers at the Interface of General Relativity and Quantum Optics
NASA Astrophysics Data System (ADS)
Feiler, C.; Buser, M.; Kajari, E.; Schleich, W. P.; Rasel, E. M.; O'Connell, R. F.
2009-12-01
In the present paper we follow three major themes: (i) concepts of rotation in general relativity, (ii) effects induced by these generalized rotations, and (iii) their measurement using interferometry. Our journey takes us from the Foucault pendulum via the Sagnac interferometer to manifestations of gravito-magnetism in double binary pulsars and in Gödel’s Universe. Throughout our article we emphasize the emerging role of matter wave interferometry based on cold atoms or Bose-Einstein condensates leading to superior inertial sensors. In particular, we advertise recent activities directed towards the operation of a coherent matter wave interferometer in an extended free fall.
General relativity and cosmology
NASA Astrophysics Data System (ADS)
Bucher, Martin; Ni, Wei-Tou
2015-10-01
This year marks the 100th anniversary of Einstein’s 1915 landmark paper “Die Feldgleichungen der Gravitation” in which the field equations of general relativity were correctly formulated for the first time, thus rendering general relativity a complete theory. Over the subsequent hundred years, physicists and astronomers have struggled with uncovering the consequences and applications of these equations. This paper, which was written as an introduction to six chapters dealing with the connection between general relativity and cosmology that will appear in the two-volume book One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, endeavors to provide a historical overview of the connection between general relativity and cosmology, two areas whose development has been closely intertwined.
NASA Astrophysics Data System (ADS)
Meenakshisundaram, N.
Application of the Hadamard and related transforms on a few generalized quantum baker’s maps have been studied. Effectiveness of the Hadamard transform and a new transform which combines the Fourier and the Hadamard transforms, for simplifying the eigenstates or resonances of the quantization of a few generalized baker’s map namely tetradic baker and lazy baker’s map when the Hilbert space dimension is power of 2 has been done by comparing the participation ratios in the transformed basis with respect to the position basis. Several special family of states based on their maximal compression in either Hadamard transform or the new transform are identified and they are related to the ubiquitous Thue-Morse and allied sequences. Evidence is provided that these special family of states as well as average over all eigenstates exhibits multifractal nature.
Unnikrishnan, C.S.; Gillies, G.T.
2006-05-15
Recently Ehlers, Ozsvath, and Schucking discussed whether pressure contributes to active gravitational mass as required by general relativity. They pointed out that there is no experimental information on this available, though precision measurement of the gravitational constant should provide a test of this foundational aspect of gravity. We had used a similar argument earlier to test the contribution of leptons to the active gravitational mass. In this paper we use the result from the Zuerich gravitational constant experiment to provide the first adequate experimental input regarding the active gravitational mass of Fermi pressure. Apart from confirming the equality of the passive and active gravitational roles of the pressure term in general relativity within an accuracy of 5%, our results are consistent with the theoretical expectation of the cancellation of the gravity of pressure by the gravity of the surface tension of confined matter. This result on the active gravitational mass of the quantum zero-point Fermi pressure in the atomic nucleus is also interesting from the point of view of studying the interplay between quantum physics and classical gravity.
General Relativity and Gravitation
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Berger, Beverly; Isenberg, James; MacCallum, Malcolm
2015-07-01
Part I. Einstein's Triumph: 1. 100 years of general relativity George F. R. Ellis; 2. Was Einstein right? Clifford M. Will; 3. Cosmology David Wands, Misao Sasaki, Eiichiro Komatsu, Roy Maartens and Malcolm A. H. MacCallum; 4. Relativistic astrophysics Peter Schneider, Ramesh Narayan, Jeffrey E. McClintock, Peter Mészáros and Martin J. Rees; Part II. New Window on the Universe: 5. Receiving gravitational waves Beverly K. Berger, Karsten Danzmann, Gabriela Gonzalez, Andrea Lommen, Guido Mueller, Albrecht Rüdiger and William Joseph Weber; 6. Sources of gravitational waves. Theory and observations Alessandra Buonanno and B. S. Sathyaprakash; Part III. Gravity is Geometry, After All: 7. Probing strong field gravity through numerical simulations Frans Pretorius, Matthew W. Choptuik and Luis Lehner; 8. The initial value problem of general relativity and its implications Gregory J. Galloway, Pengzi Miao and Richard Schoen; 9. Global behavior of solutions to Einstein's equations Stefanos Aretakis, James Isenberg, Vincent Moncrief and Igor Rodnianski; Part IV. Beyond Einstein: 10. Quantum fields in curved space-times Stefan Hollands and Robert M. Wald; 11. From general relativity to quantum gravity Abhay Ashtekar, Martin Reuter and Carlo Rovelli; 12. Quantum gravity via unification Henriette Elvang and Gary T. Horowitz.
Measuring our changing Earth by means of General Relativity and quantum sensors
NASA Astrophysics Data System (ADS)
Flury, Jakob
2016-07-01
Breakthroughs in quantum metrology and advanced laser metrology enable new methods for extremely accurate and precise measurements of time, ranging, inertial forces and gravity, in sensor setups that can be very compact. This is relevant for satellite geodesy and geodetic ground networks, which together provide the geometric and gravimetric reference frames and the basis for monitoring processes of global and regional change involving deformation and mass re-distribution. Ultraprecise optical atomic clocks and optical frequency transfer allow measuring the relativistic gravitational frequency redshift and open the perspective of tying height differences and height systems to atomic standards. Satellite gravimetry with laser interferometric ranging, which is demonstrated on LISA Pathfinder and the upcoming GRACE Follow-On, will allow recovering the Earth's large-scale mass redistribution in its water cycle and due to climatic change with better resolution. Interferometry with clouds of cold atoms is the basis for very sensitive and compact gravimeters to monitor local and regional geophysical processes.
Quantum relative Lorenz curves
NASA Astrophysics Data System (ADS)
Buscemi, Francesco; Gour, Gilad
2017-01-01
The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we formulate the framework of quantum relative Lorenz curves, and show how it is able to unify majorization, thermomajorization, and their noncommutative analogs. In doing so, we define the family of Hilbert α divergences and show how it relates with other divergences used in quantum information theory. We then apply these tools to the problem of deciding the existence of a suitable transformation from an initial pair of quantum states to a final one, focusing in particular on applications to the resource theory of athermality, a precursor of quantum thermodynamics.
Generalized uncertainty relations
NASA Astrophysics Data System (ADS)
Herdegen, Andrzej; Ziobro, Piotr
2017-04-01
The standard uncertainty relations (UR) in quantum mechanics are typically used for unbounded operators (like the canonical pair). This implies the need for the control of the domain problems. On the other hand, the use of (possibly bounded) functions of basic observables usually leads to more complex and less readily interpretable relations. In addition, UR may turn trivial for certain states if the commutator of observables is not proportional to a positive operator. In this letter we consider a generalization of standard UR resulting from the use of two, instead of one, vector states. The possibility to link these states to each other in various ways adds additional flexibility to UR, which may compensate some of the above-mentioned drawbacks. We discuss applications of the general scheme, leading not only to technical improvements, but also to interesting new insight.
Kramer, Michael
2011-09-22
The last years have seen continuing activities in the exploration of our understanding of gravity, motivated by results from precision cosmology and new precision astrophysical experiments. At the centre of attention lies the question as to whether general relativity is the correct theory of gravity. In answering this question, we work not only towards correctly interpreting the phenomenon of 'dark energy' but also towards the goal of achieving a quantum theory of gravity. In these efforts, the observations of pulsars, especially those in binary systems, play an important role. Pulsars do not only provide the only evidence for the existence of gravitational waves so far, but they also provide precision tests of general relativity and alternative theories of gravity. This talk summarizes the current state-of-art in these experiments and looks into the future.
Directions in General Relativity
NASA Astrophysics Data System (ADS)
Hu, B. L.; Ryan, M. P., Jr.; Vishveshwara, C. V.
2005-10-01
Preface; Dieter Brill: a spacetime perspective; 1. Thawing the frozen formalism: the difference between observables and what we observe A. Anderson; 2. Jacobi's action and the density of states J. D. Brown and J. W. York; 3. Decoherence of correlation histories E. Calzetta and B. L. Hu; 4. The initial value problem in light of Ashtekar's variables R. Capovilla, J. Dell and T. Jacobson; 5. Status report on an axiomatic basis for functional integration P. Cartier and C. DeWitt-Morette; 6. Solution of the coupled Einstein constraints on asymptotically Euclidean manifolds Y. Choquet-Bruhat; 7. Compact Cauchy horizons and Cauchy surfaces P. Chrusciel and J. Isenberg; 8. The classical electron J. M. Cohen and E. Mustafa; 9. Gauge (in)variance, mass and parity in D=3 revisited S. Deser; 10. Triality, exceptional Lie groups and Dirac operators F. Flaherty; 11. The reduction of the state vector and limitations on measurement in the quantum mechanics of closed systems J. B. Hartle; 12 Quantum linearization instabilities of de Sitter spacetime A. Higuchi; 13. What is the true description of charged black holes? G. T. Horowitz; 14. Limits on the adiabatic index in static stellar models L. Lindblom and A. K. M. Masood-ul-Alam; 15. On the relativity of rotation B. Mashhoon; 16. Recent progress and open problems in linearization stability V. E. Moncrief; 17. Brill waves N. Ó Murchadha; 18. You can't get there from here: constraints on topology change K. Schleich and D. M. Witt; 19. Time, measurement and information loss in quantum cosmology L. Smolin; 20. Impossible measurements on quantum fields R. Sorkin; 21. A new condition implying the existence of a constant mean curvature foliation F. J. Tipler; 22. Maximal slices in stationary spacetimes with ergoregions R. M. Wald; 23. (1 + 1) - Dimensional methods for general relativity J. H. Yoon; 24. Coalescence of primal gravity waves to make cosmological mass without matter D. E. Holz, W. A. Miller, M. Wakano and J. A. Wheeler.
Milestones of general relativity
NASA Astrophysics Data System (ADS)
Pullin, Jorge
2017-02-01
We present a summary for non-specialists of the special issue of the journal Classical and Quantum Gravity on ‘Milestones of general relativity’, commemorating the 100th anniversary of the theory.
Sujata Relativity: Complete Relativity from Gravity to Quantum-Gravity
NASA Astrophysics Data System (ADS)
Sinha, Nilotpal
2009-01-01
Here, we describe gravity as a universal deformation of Minkowski metric depending on a "double-fold" complex number for fourth coordinate within a (3 + 1)D-space. A unification of Special Relativity and General Relativity, induced by Lorentz transformation, gives a Quantum-Gravity Wave Equation, much like as Wheeler-DeWitt equation, without considering Canonical or, Covariant Quantum Relativity. A complete and well-grown ("Sujata") Quantum-Gravity picture satisfies the Quantum Gravitational Field Equation.
Generalized Entanglement and Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Somma, Rolando; Barnum, Howard; Knill, Emanuel; Ortiz, Gerardo; Viola, Lorenzo
2006-07-01
Quantum phase transitions in matter are characterized by qualitative changes in some correlation functions of the system, which are ultimately related to entanglement. In this work, we study the second-order quantum phase transitions present in models of relevance to condensed-matter physics by exploiting the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)]. In particular, we focus on the illustrative case of a one-dimensional spin-1/2 Ising model in the presence of a transverse magnetic field. Our approach leads to tools useful for distinguishing between the ordered and disordered phases in the case of broken-symmetry quantum phase transitions. Possible extensions to the study of other kinds of phase transitions as well as of the relationship between generalized entanglement and computational efficiency are also discussed.
Generalized Entanglement and Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Somma, Rolando; Barnum, Howard; Knill, Emanuel; Ortiz, Gerardo; Viola, Lorenzo
Quantum phase transitions in matter are characterized by qualitative changes in some correlation functions of the system, which are ultimately related to entanglement. In this work, we study the second-order quantum phase transitions present in models of relevance to condensed-matter physics by exploiting the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)]. In particular, we focus on the illustrative case of a one-dimensional spin-1/2 Ising model in the presence of a transverse magnetic field. Our approach leads to tools useful for distinguishing between the ordered and disordered phases in the case of broken-symmetry quantum phase transitions. Possible extensions to the study of other kinds of phase transitions as well as of the relationship between generalized entanglement and computational efficiency are also discussed.
Reexamining the Quantum-Classical Relation
NASA Astrophysics Data System (ADS)
Bokulich, Alisa
2008-10-01
1. Intertheoretic relations: are imperialism and isolationism our only options?; 2. Heisenberg's closed theories and pluralistic realism; 3. Dirac's open theories and the reciprocal correspondence principle; 4. Bohr's generalization of classical mechanics; 5. Semiclassical mechanics: putting quantum flesh on classical bones; 6. Can classical structures explain quantum phenomena?; 7. A structural approach to intertheoretic relations; References; Index.
On a Quantum Theory of Relativity
NASA Astrophysics Data System (ADS)
González-Díaz, Pedro F.; Rozas-Fernández, Alberto
2017-09-01
As expressed in terms of classical coordinates, the inertial spacetime metric that contains quantum corrections deriving from a quantum potential defined from the quantum probability amplitude is obtained to be given as an elliptic integral of the second kind that does not satisfy Lorentz transformations but a generalised invariance quantum group. Based on this result, we introduce a new, alternative procedure to quantise Einstein general relativity where the metric is also given in terms of elliptic integrals and is free from the customary problems of the current quantum models. We apply the procedure to Schwarzschild black holes and briefly analyse the results.
Quantum uncertainty relation using coherence
NASA Astrophysics Data System (ADS)
Yuan, Xiao; Bai, Ge; Peng, Tianyi; Ma, Xiongfeng
2017-09-01
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constraints on the accuracy of two noncommuting observables. The existing uncertainty relations adopt variance or entropic measures, which are functions of observed outcome distributions, to quantify the uncertainty. According to recent studies of quantum coherence, such uncertainty measures contain both classical (predictable) and quantum (unpredictable) components. In order to extract out the quantum effects, we define quantum uncertainty to be the coherence of the state on the measurement basis. We discover a quantum uncertainty relation using coherence between two measurement noncommuting bases. Furthermore, we analytically derive the quantum uncertainty relation for the qubit case with three widely adopted coherence measures, the relative entropy of coherence, the coherence of formation, and the l1 norm of coherence.
Generalized semi-Markov quantum evolution
NASA Astrophysics Data System (ADS)
Chruściński, Dariusz; Kossakowski, Andrzej
2017-04-01
We provide a large class of quantum evolutions governed by the memory kernel master equation. This class defines a quantum analog of so-called semi-Markov classical stochastic dynamics. In this paper we provide a precise definition of quantum semi-Markov evolution, and using the appropriate gauge freedom we propose a suitable generalization which contains a majority of examples considered so far in the literature. The key concepts are quantum counterparts of classical waiting time distribution and survival probability—a quantum waiting time operator and a quantum survival operator, respectively. In particular collision models and their generalizations considered recently are special examples of generalized semi-Markov evolution. This approach allows for an interesting generalization of the trajectory description of the quantum dynamics in terms of positive operator-valued measure densities.
Quantum mechanics and the generalized uncertainty principle
Bang, Jang Young; Berger, Micheal S.
2006-12-15
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalized uncertainty principle results for minimum uncertainty wave packets.
Understanding Quantum Numbers in General Chemistry Textbooks
ERIC Educational Resources Information Center
Niaz, Mansoor; Fernandez, Ramon
2008-01-01
Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…
Understanding Quantum Numbers in General Chemistry Textbooks
ERIC Educational Resources Information Center
Niaz, Mansoor; Fernandez, Ramon
2008-01-01
Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…
NASA Technical Reports Server (NTRS)
Li, Xi-Zeng; Su, Bao-Xia
1996-01-01
It is found that the field of the combined mode of the probe wave and the phase-conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations in this process are also presented.
General Relativity and Gravitation, 1989
NASA Astrophysics Data System (ADS)
Ashby, Neil; Bartlett, David F.; Wyss, Walker
2005-10-01
Part I. Classical Relativity and Gravitation Theory: 1. Global properties of exact solutions H. Friedrich; 2. Numerical relativity T. Nakamura; 3. How fast can a pulsar spin? J. L. Friedman; 4. Colliding waves in general relativity V. Ferrari; Part II. Relativistic Astrophysics, Early Universe, and Classical Cosmology: 5. Observations of cosmic microwave radiation R. B. Partridge; 6. Cosmic microwave background radiation (theory) M. Panek; 7. Inflation and quantum cosmology A. D. Linde; 8. Observations of lensing B. Fort; 9. Gravitational lenses: theory and interpretation R. Blandford; Part III. Experimental Gravitation and Gravitational Waves: 10. Solar system tests of GR: recent results and present plans I. Shapiro; 11. Laser interferometer detectors R. Weiss; 12. Resonant bar gravitational wave experiments G. Pizzella; 13. A non-inverse square law test E. Adelberger; Part IV. Quantum Gravity, Superstrings, Quantum Cosmology: 14. Cosmic strings B. Unruh; 15. String theory as a quantum theory of gravity G. Horowitz; 16. Progress in quantum cosmology J. B. Hartle; 17. Self-duality, quantum gravity, Wilson loops and all that A. V. Ashtekar; Part V. Summary Talk: 18. GR-12 Conference summary J. Ehlers II; Part VI. Reports on Workshops/Symposia: 19. Exact solutions and exact properties of Einstein equations V. Moncrieff; 20. Spinors, twistors and complex methods N. Woodhouse; 21. Alternative gravity theories M. Francaviglia; 22. Asymptotia, singularities and global structure B. G. Schmidt; 23. Radiative spacetimes and approximation methods T. Damour; 24. Algebraic computing M. MacCallum; 25. Numerical relativity J. Centrella; 26. Mathematical cosmology J. Wainwright; 27. The early universe M. Turner; 28. Relativistic astrophysics M. Abramowitz; 29. Astrophysical and observational cosmology B. Carr; 30. Solar system and pulsar tests of gravitation R. Hellings; 31. Earth-based gravitational experiments J. Faller; 32. Resonant bar and microwave gravitational wave
General Relativity and Gravitation, 1989
NASA Astrophysics Data System (ADS)
Ashby, Neil; Bartlett, David F.; Wyss, Walker
1990-11-01
Part I. Classical Relativity and Gravitation Theory: 1. Global properties of exact solutions H. Friedrich; 2. Numerical relativity T. Nakamura; 3. How fast can a pulsar spin? J. L. Friedman; 4. Colliding waves in general relativity V. Ferrari; Part II. Relativistic Astrophysics, Early Universe, and Classical Cosmology: 5. Observations of cosmic microwave radiation R. B. Partridge; 6. Cosmic microwave background radiation (theory) M. Panek; 7. Inflation and quantum cosmology A. D. Linde; 8. Observations of lensing B. Fort; 9. Gravitational lenses: theory and interpretation R. Blandford; Part III. Experimental Gravitation and Gravitational Waves: 10. Solar system tests of GR: recent results and present plans I. Shapiro; 11. Laser interferometer detectors R. Weiss; 12. Resonant bar gravitational wave experiments G. Pizzella; 13. A non-inverse square law test E. Adelberger; Part IV. Quantum Gravity, Superstrings, Quantum Cosmology: 14. Cosmic strings B. Unruh; 15. String theory as a quantum theory of gravity G. Horowitz; 16. Progress in quantum cosmology J. B. Hartle; 17. Self-duality, quantum gravity, Wilson loops and all that A. V. Ashtekar; Part V. Summary Talk: 18. GR-12 Conference summary J. Ehlers II; Part VI. Reports on Workshops/Symposia: 19. Exact solutions and exact properties of Einstein equations V. Moncrieff; 20. Spinors, twistors and complex methods N. Woodhouse; 21. Alternative gravity theories M. Francaviglia; 22. Asymptotia, singularities and global structure B. G. Schmidt; 23. Radiative spacetimes and approximation methods T. Damour; 24. Algebraic computing M. MacCallum; 25. Numerical relativity J. Centrella; 26. Mathematical cosmology J. Wainwright; 27. The early universe M. Turner; 28. Relativistic astrophysics M. Abramowitz; 29. Astrophysical and observational cosmology B. Carr; 30. Solar system and pulsar tests of gravitation R. Hellings; 31. Earth-based gravitational experiments J. Faller; 32. Resonant bar and microwave gravitational wave
ERIC Educational Resources Information Center
Ridgely, Charles T.
2010-01-01
Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…
ERIC Educational Resources Information Center
Ridgely, Charles T.
2010-01-01
Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…
Quantum mechanics, relativity and time
NASA Astrophysics Data System (ADS)
Basini, Giuseppe; Capozziello, Salvatore
2005-01-01
A discussion on quantum mechanics, general relativity and their relations is introduced. The assumption of the absolute validity of conservation laws and the extension to a 5D-space lead to reconsider several shortcomings and paradoxes of modern physics under a new light without the necessity to take into account symmetry breakings. In this picture, starting from first principles, and after a reduction procedure from 5D to 4D, dynamics leads to the natural emergence of two time arrows and ofa scalar-tensor theory of gravity. In this framework, phenomena like entanglement of systems and topology changes can be naturally accounted and, furthermore, several experimental evidences as gamma ray bursts, sizes of astrophysical structures and the observed values of cosmological parameters can be explained. The identification, thanks to conservation laws, of a covariant symplectic structure as a general feature also for gravity can be seen as a deep link common to all the interactions.
Base norms and discrimination of generalized quantum channels
Jenčová, A.
2014-02-15
We introduce and study norms in the space of hermitian matrices, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels, and networks. We further introduce generalized quantum decision problems and show that the maximal average payoffs of decision procedures are again given by these norms. We also study optimality of decision procedures, in particular, we obtain a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum channels exists, such that the input state is maximally entangled.
Quantum networks: General theory and applications
NASA Astrophysics Data System (ADS)
Bisio, A.; Chiribella, G.; D'Ariano, G. M.; Perinotti, P.
2011-06-01
In this work we present a general mathematical framework to deal with
Generalized Open Quantum Walks on Apollonian Networks
Pawela, Łukasz; Gawron, Piotr; Miszczak, Jarosław Adam; Sadowski, Przemysław
2015-01-01
We introduce the model of generalized open quantum walks on networks using the Transition Operation Matrices formalism. We focus our analysis on the mean first passage time and the average return time in Apollonian networks. These results differ significantly from a classical walk on these networks. We show a comparison of the classical and quantum behaviour of walks on these networks. PMID:26177452
Work measurement as a generalized quantum measurement.
Roncaglia, Augusto J; Cerisola, Federico; Paz, Juan Pablo
2014-12-19
We present a new method to measure the work w performed on a driven quantum system and to sample its probability distribution P(w). The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be measured by performing a generalized quantum measurement at a single time. Such measurement, which technically speaking is denoted as a positive operator valued measure reduces to an ordinary projective measurement on an enlarged system. This observation not only demystifies work measurement but also suggests a new quantum algorithm to efficiently sample the distribution P(w). This can be used, in combination with fluctuation theorems, to estimate free energies of quantum states on a quantum computer.
Work Measurement as a Generalized Quantum Measurement
NASA Astrophysics Data System (ADS)
Roncaglia, Augusto J.; Cerisola, Federico; Paz, Juan Pablo
2014-12-01
We present a new method to measure the work w performed on a driven quantum system and to sample its probability distribution P (w ). The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be measured by performing a generalized quantum measurement at a single time. Such measurement, which technically speaking is denoted as a positive operator valued measure reduces to an ordinary projective measurement on an enlarged system. This observation not only demystifies work measurement but also suggests a new quantum algorithm to efficiently sample the distribution P (w ). This can be used, in combination with fluctuation theorems, to estimate free energies of quantum states on a quantum computer.
ERIC Educational Resources Information Center
Jackson, A. T.
1973-01-01
Reviews theoretical and experimental fundamentals of Einstein's theory of general relativity. Indicates that recent development of the theory of the continually expanding universe may lead to revision of the space-time continuum of the finite and unbounded universe. (CC)
ERIC Educational Resources Information Center
Jackson, A. T.
1973-01-01
Reviews theoretical and experimental fundamentals of Einstein's theory of general relativity. Indicates that recent development of the theory of the continually expanding universe may lead to revision of the space-time continuum of the finite and unbounded universe. (CC)
Reformulating the Quantum Uncertainty Relation.
Li, Jun-Li; Qiao, Cong-Feng
2015-08-03
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic quantities. Both these forms are inequalities involving pairwise observables, and are found to be nontrivial to incorporate multiple observables. In this work we introduce a new form of uncertainty relation which may give out complete trade-off relations for variances of observables in pure and mixed quantum systems. Unlike the prevailing uncertainty relations, which are either quantum state dependent or not directly measurable, our bounds for variances of observables are quantum state independent and immune from the "triviality" problem of having zero expectation values. Furthermore, the new uncertainty relation may provide a geometric explanation for the reason why there are limitations on the simultaneous determination of different observables in N-dimensional Hilbert space.
General covariance from the quantum renormalization group
NASA Astrophysics Data System (ADS)
Shyam, Vasudev
2017-03-01
The quantum renormalization group (QRG) is a realization of holography through a coarse-graining prescription that maps the beta functions of a quantum field theory thought to live on the "boundary" of some space to holographic actions in the "bulk" of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the D +1 dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the D dimensional boundary. This will be a particular form of the Wess-Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Poisson bracket algebra. In particular, it will require the metric beta function to be of the gradient form.
Quantum decoherence and interlevel relations
NASA Astrophysics Data System (ADS)
Crull, Elise M.
Quantum decoherence is a dynamical process whereby a system's phase relations become delocalized due to interaction and subsequent entanglement with its environment. This delocalization, or decoherence, forces the quantum system into a state that is apparently classical (or apparently an eigenstate) by prodigiously suppressing features that typically give rise to so-called quantum behavior. Thus it has been frequently proposed by physicists and philosophers alike that decoherence explains the dynamical transition from quantum behavior to classical behavior. Statements like this assume the existence of distinct realms, however, and the present thesis is an exploration of the metaphysical consequences of quantum decoherence motivated by the question of the quantum-to-classical transition and interlevel relations: if there are in-principle "classical" and "quantum" levels, what are the relations between them? And if there are no such levels, what follows? Importantly, the following philosophical investigations are carried out by intentionally leaving aside the measurement problem and concerns about particular interpretations of quantum mechanics. Good philosophical work, it is argued, can be done without adopting a specific interpretational framework and without recourse to the measurement problem. After introducing the physics of decoherence and exploring the four canonical models applied to system-environment interactions, it is argued that, ontologically speaking, there exist no levels. This claim---called the "nontological thesis"---exposes as ill-posed questions regarding the transition from the quantum regime to the classical regime and reveals the inappropriateness of interlevel relations (like reduction, supervenience and emergence) operating within metaphysical frameworks. The nontological thesis has further important consequences regarding intralevel relations: not only are there no meaningful ways to carve the world into levels, but there are no meaningful
Generalized effective description of loop quantum cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Gupt, Brajesh
2015-10-01
The effective description of loop quantum cosmology (LQC) has proved to be a convenient platform to study phenomenological implications of the quantum bounce that resolves the classical big bang singularity. Originally, this description was derived using Gaussian quantum states with small dispersions. In this paper we present a generalization to incorporate states with large dispersions. Specifically, we derive the generalized effective Friedmann and Raychaudhuri equations and propose a generalized effective Hamiltonian which are being used in an ongoing study of the phenomenological consequences of a broad class of quantum geometries. We also discuss an interesting interplay between the physics of states with larger dispersions in standard LQC, and of sharply peaked states in (hypothetical) LQC theories with larger area gap.
Unitary Quantum Relativity - (Work in Progress)
NASA Astrophysics Data System (ADS)
Finkelstein, David Ritz
2016-12-01
A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.
Unitary Quantum Relativity. (Work in Progress)
NASA Astrophysics Data System (ADS)
Finkelstein, David Ritz
2017-01-01
A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.
The complementarity relations of quantum coherence in quantum information processing
Pan, Fei; Qiu, Liang; Liu, Zhi
2017-01-01
We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertainty-like expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given. PMID:28272481
The complementarity relations of quantum coherence in quantum information processing.
Pan, Fei; Qiu, Liang; Liu, Zhi
2017-03-08
We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertainty-like expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given.
The complementarity relations of quantum coherence in quantum information processing
NASA Astrophysics Data System (ADS)
Pan, Fei; Qiu, Liang; Liu, Zhi
2017-03-01
We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertainty-like expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given.
Uncertainty relation for non-Hamiltonian quantum systems
Tarasov, Vasily E.
2013-01-15
General forms of uncertainty relations for quantum observables of non-Hamiltonian quantum systems are considered. Special cases of uncertainty relations are discussed. The uncertainty relations for non-Hamiltonian quantum systems are considered in the Schroedinger-Robertson form since it allows us to take into account Lie-Jordan algebra of quantum observables. In uncertainty relations, the time dependence of quantum observables and the properties of this dependence are discussed. We take into account that a time evolution of observables of a non-Hamiltonian quantum system is not an endomorphism with respect to Lie, Jordan, and associative multiplications.
Relating quantum discord with the quantum dense coding capacity
Wang, Xin; Qiu, Liang Li, Song; Zhang, Chi; Ye, Bin
2015-01-15
We establish the relations between quantum discord and the quantum dense coding capacity in (n + 1)-particle quantum states. A necessary condition for the vanishing discord monogamy score is given. We also find that the loss of quantum dense coding capacity due to decoherence is bounded below by the sum of quantum discord. When these results are restricted to three-particle quantum states, some complementarity relations are obtained.
NASA Technical Reports Server (NTRS)
Ray, J. R.
1982-01-01
Two theories of matter in general relativity, the fluid theory and the kinetic theory, were studied. Results include: (1) a discussion of various methods of completing the fluid equations; (2) a method of constructing charged general relativistic solutions in kinetic theory; and (3) a proof and discussion of the incompatibility of perfect fluid solutions in anisotropic cosmologies. Interpretations of NASA gravitational experiments using the above mentioned results were started. Two papers were prepared for publications based on this work.
NASA Technical Reports Server (NTRS)
Ray, J. R.
1982-01-01
Two theories of matter in general relativity, the fluid theory and the kinetic theory, were studied. Results include: (1) a discussion of various methods of completing the fluid equations; (2) a method of constructing charged general relativistic solutions in kinetic theory; and (3) a proof and discussion of the incompatibility of perfect fluid solutions in anisotropic cosmologies. Interpretations of NASA gravitational experiments using the above mentioned results were started. Two papers were prepared for publications based on this work.
Two basic Uncertainty Relations in Quantum Mechanics
Angelow, Andrey
2011-04-07
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schroedinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
Two basic Uncertainty Relations in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Angelow, Andrey
2011-04-01
In the present article, we discuss two types of uncertainty relations in Quantum Mechanics-multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty relation was discovered by Heisenberg. Few years later (1930) Erwin Schrödinger has generalized and made it more precise than the original. The additive uncertainty relation is based on the three independent statistical moments in Quantum Mechanics-Cov(q,p), Var(q) and Var(p). We discuss the existing symmetry of both types of relations and applicability of the additive form for the estimation of the total error.
Quantum radiation of general nonstationary black holes
NASA Astrophysics Data System (ADS)
Hua, Jia-Chen; Huang, Yong-Chang
2009-02-01
Quantum radiation of general nonstationary black holes is investigated by using the method of generalized tortoise-coordinate transformation (GTT). It is shown in general that the temperature and the shape of the event horizon of this kind of black holes depend on time and angle. Further, we find that the chemical potential in the thermal-radiation spectrum is equal to the highest energy of the negative-energy state of particles in nonthermal radiation for general nonstationary black holes.
Dynamical Correspondence in a Generalized Quantum Theory
NASA Astrophysics Data System (ADS)
Niestegge, Gerd
2015-05-01
In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and JBW-algebras). One particularly important distinguishing property was identified by Alfsen and Shultz and is the existence of a dynamical correspondence. It reproduces the dual role of the selfadjoint operators as observables and generators of dynamical groups in quantum mechanics. In the paper, this concept is extended to another class of nonassociative algebras, arising from recent studies of the quantum logics with a conditional probability calculus and particularly of those that rule out third-order interference. The conditional probability calculus is a mathematical model of the Lüders-von Neumann quantum measurement process, and third-order interference is a property of the conditional probabilities which was discovered by Sorkin (Mod Phys Lett A 9:3119-3127, 1994) and which is ruled out by quantum mechanics. It is shown then that the postulates that a dynamical correspondence exists and that the square of any algebra element is positive still characterize, in the class considered, those algebras that emerge from the selfadjoint parts of C*-algebras equipped with the Jordan product. Within this class, the two postulates thus result in ordinary quantum mechanics using the complex Hilbert space or, vice versa, a genuine generalization of quantum theory must omit at least one of them.
Generalized Hofmann quantum process fidelity bounds for quantum filters
NASA Astrophysics Data System (ADS)
Sedlák, Michal; Fiurášek, Jaromír
2016-04-01
We propose and investigate bounds on the quantum process fidelity of quantum filters, i.e., probabilistic quantum operations represented by a single Kraus operator K . These bounds generalize the Hofmann bounds on the quantum process fidelity of unitary operations [H. F. Hofmann, Phys. Rev. Lett. 94, 160504 (2005), 10.1103/PhysRevLett.94.160504] and are based on probing the quantum filter with pure states forming two mutually unbiased bases. Determination of these bounds therefore requires far fewer measurements than full quantum process tomography. We find that it is particularly suitable to construct one of the probe bases from the right eigenstates of K , because in this case the bounds are tight in the sense that if the actual filter coincides with the ideal one, then both the lower and the upper bounds are equal to 1. We theoretically investigate the application of these bounds to a two-qubit optical quantum filter formed by the interference of two photons on a partially polarizing beam splitter. For an experimentally convenient choice of factorized input states and measurements we study the tightness of the bounds. We show that more stringent bounds can be obtained by more sophisticated processing of the data using convex optimization and we compare our methods for different choices of the input probe states.
The Generalized Quantum Episodic Memory Model.
Trueblood, Jennifer S; Hemmer, Pernille
2016-12-21
Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over-distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over-distribution effect and subadditivity have been widely observed in item and source-memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal-detection theory. A dual-trace model called the over-distribution (OD) model (Brainerd & Reyna, 2008) can explain the episodic over-distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory (GQEM) model, which extends the Quantum Episodic Memory (QEM) model developed by Brainerd, Wang, and Reyna (2013). We test GQEM by comparing it to the OD model using data from a novel item-memory experiment and a previously published source-memory experiment (Kellen, Singmann, & Klauer, 2014) examining the over-distribution effect. Using the best-fit parameters from the over-distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory.
Introducing Relativity into Quantum Chemistry
ERIC Educational Resources Information Center
Li, Wai-Kee; Blinder, S. M.
2011-01-01
It is not often realized by chemists that the special theory of relativity is behind several aspects of quantum chemistry. The Schrdinger equation itself is based on relations between space-time and energy-momentum four vectors. Electron spin is, of course, the most obvious manifestation of relativity. The chemistry of some heavy elements is…
Introducing Relativity into Quantum Chemistry
ERIC Educational Resources Information Center
Li, Wai-Kee; Blinder, S. M.
2011-01-01
It is not often realized by chemists that the special theory of relativity is behind several aspects of quantum chemistry. The Schrdinger equation itself is based on relations between space-time and energy-momentum four vectors. Electron spin is, of course, the most obvious manifestation of relativity. The chemistry of some heavy elements is…
Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
General relativistic effects in quantum interference of photons
NASA Astrophysics Data System (ADS)
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Ralph, Timothy C.; Brukner, Časlav
2012-11-01
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon’s coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.
Teaching General Relativity to the Layperson
ERIC Educational Resources Information Center
Egdall, Mark
2009-01-01
This paper describes a lay course on general relativity (GR) given at the Osher Lifelong Learning Institute at Florida International University. It is presented in six hour-and-a-half weekly sessions. Other courses offered by the author include special relativity (which precedes the course described here), quantum theory, and cosmology. Students…
Teaching General Relativity to the Layperson
ERIC Educational Resources Information Center
Egdall, Mark
2009-01-01
This paper describes a lay course on general relativity (GR) given at the Osher Lifelong Learning Institute at Florida International University. It is presented in six hour-and-a-half weekly sessions. Other courses offered by the author include special relativity (which precedes the course described here), quantum theory, and cosmology. Students…
General relativistic effects in quantum interference of “clocks”
NASA Astrophysics Data System (ADS)
Zych, M.; Pikovski, I.; Costa, F.; Brukner, Č.
2016-06-01
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of “clocks”, which aim to test novel quantum effects that arise from time dilation. “Clock” interference experiments could be realised with atoms or photons in near future laboratory experiments.
Geometric uncertainty relation for mixed quantum states
Andersson, Ole Heydari, Hoshang
2014-04-15
In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in a canonical way rise to a Riemannian metric and a symplectic structure on the base space. With these we derive a geometric uncertainty relation for observables acting on quantum systems in mixed states. We also give a geometric proof of the classical Robertson-Schrödinger uncertainty relation, and we compare the two. They turn out not to be equivalent, because of the multiple dimensions of the gauge group for general mixed states. We give examples of observables for which the geometric relation provides a stronger estimate than that of Robertson and Schrödinger, and vice versa.
Endomorphisms of Quantum Generalized Weyl Algebras
NASA Astrophysics Data System (ADS)
Kitchin, Andrew P.; Launois, Stéphane
2014-07-01
We prove that every endomorphism of a simple quantum generalized Weyl algebra A over a commutative Laurent polynomial ring in one variable is an automorphism. This is achieved by obtaining an explicit classification of all endomorphisms of A. Our main result applies to minimal primitive factors of the quantized enveloping algebra and certain minimal primitive quotients of the positive part of.
Tachyons in general relativity
Schwartz, Charles
2011-05-15
We consider the motion of tachyons (faster-than-light particles) in the framework of general relativity. An important feature is the large contribution of low energy tachyons to the energy-momentum tensor. We also calculate the gravitational field produced by tachyons in particular geometric arrangements; and it appears that there could be self-cohering bundles of such matter. This leads us to suggest that such theoretical ideas might be relevant to major problems (dark matter and dark energy) in current cosmological models.
Generalized Weyl-Wigner map and Vey quantum mechanics
NASA Astrophysics Data System (ADS)
Dias, Nuno Costa; Prata, João Nuno
2001-12-01
The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, clarifying the relation between the two formulations, is still missing. In this article we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantum mechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.
Generalized coherent and intelligent states for exact solvable quantum systems
NASA Astrophysics Data System (ADS)
El Kinani, A. H.; Daoud, M.
2002-02-01
The so-called Gazeau-Klauder and Perelomov coherent states are introduced for an arbitrary quantum system. We give also the general framework to construct the generalized intelligent states which minimize the Robertson-Schrödinger uncertainty relation. As illustration, the Pöschl-Teller potentials of trigonometric type will be chosen. We show the advantage of the analytical representations of Gazeau-Klauder and Perelomov coherent states in obtaining the generalized intelligent states in analytical way.
Quantum corrections to newtonian potential and generalized uncertainty principle
NASA Astrophysics Data System (ADS)
Scardigli, Fabio; Lambiase, Gaetano; Vagenas, Elias
2017-08-01
We use the leading quantum corrections to the newtonian potential to compute the deformation parameter of the generalized uncertainty principle. By assuming just only General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum, our calculation gives, to first order, a specific numerical result. We briefly discuss the physical meaning of this value, and compare it with the previously obtained bounds on the generalized uncertainty principle deformation parameter.
Generalized quantum statistics and Lie (super)algebras
Stoilova, N. I.
2016-03-25
Generalized quantum statistics, such as paraboson and parafermion statistics, are characterized by triple relations which are related to Lie (super)algebras of type B. The correspondence of the Fock spaces of parabosons, parafermions as well as the Fock space of a system of parafermions and parabosons to irreducible representations of (super)algebras of type B will be pointed out. Example of generalized quantum statistics connected to the basic classical Lie superalgebra B(1|1) ≡ osp(3|2) with interesting physical properties, such as noncommutative coordinates, will be given. Therefore the article focuses on the question, addressed already in 1950 by Wigner: do the equation of motion determine the quantum mechanical commutation relation?.
Beyond Einstein's General Relativity
NASA Astrophysics Data System (ADS)
Lobo, Francisco S. N.
2015-04-01
Modern astrophysical and cosmological models are plagued with two severe theoretical difficulties, namely, the dark energy and the dark matter problems. Relative to the former, high-precision observational data have confirmed with startling evidence that the Universe is undergoing a phase of accelerated expansion. This phase, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing gravitational equations. Several candidates, responsible for this expansion, have been proposed in the literature, in particular, dark energy models and modified gravity, amongst others. Outstanding questions are related to the nature of this so-called “dark energy” that is driving the acceleration of the universe, and whether it is due to the vacuum energy or a dynamical field. On the other hand, the late-time cosmic acceleration may be due to modifications of General Relativity, which introduce new degrees of freedom to the gravitational sector itself. We analyze some of the modified theories of gravity that address these intriguing and exciting problems facing modern physics, and explore the foundations of gravitation theory, essential for the construction of modified theories of gravity.
On variational expressions for quantum relative entropies
NASA Astrophysics Data System (ADS)
Berta, Mario; Fawzi, Omar; Tomamichel, Marco
2017-09-01
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback-Leibler divergence over projective measurement statistics, is strictly smaller than Umegaki's quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petz' conclusion remains true if we allow general positive operator-valued measures. Second, we extend the result to Rényi relative entropies and show that for non-commuting states the sandwiched Rényi relative entropy is strictly larger than the measured Rényi relative entropy for α \\in (1/2, ∞) and strictly smaller for α \\in [0,1/2) . The latter statement provides counterexamples for the data processing inequality of the sandwiched Rényi relative entropy for α < 1/2 . Our main tool is a new variational expression for the measured Rényi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive.
Uncertainty relations based on skew information with quantum memory
NASA Astrophysics Data System (ADS)
Ma, ZhiHao; Chen, ZhiHua; Fei, Shao-Ming
2017-01-01
We present a new uncertainty relation by defining a measure of uncertainty based on skew information. For bipartite systems, we establish uncertainty relations with the existence of a quantum memory. A general relation between quantum correlations and tight bounds of uncertainty has been presented.
General quantum constraints on detector noise in continuous linear measurements
NASA Astrophysics Data System (ADS)
Miao, Haixing
2017-01-01
In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum noise of the detector, arising from quantum fluctuations in the detector input and output. It determines how fast we acquire information about the system and also influences the system evolution in terms of measurement backaction. We therefore often categorize it as the so-called imprecision noise and quantum backaction noise. There is a general Heisenberg-like uncertainty relation that constrains the magnitude of and the correlation between these two types of quantum noise. The main result of this paper is to show that, when the detector becomes ideal, i.e., at the quantum limit with minimum uncertainty, not only does the uncertainty relation takes the equal sign as expected, but also there are two new equalities. This general result is illustrated by using the typical cavity QED setup with the system being either a qubit or a mechanical oscillator. Particularly, the dispersive readout of a qubit state, and the measurement of mechanical motional sideband asymmetry are considered.
Relational quadrilateralland II: The Quantum Theory
NASA Astrophysics Data System (ADS)
Anderson, Edward; Kneller, Sophie
2014-04-01
We provide the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are ℂℙ2 and the cone over this. We consider exact free and isotropic HO potential cases and perturbations about these. Moreover, our purely relational kinematical quantization is distinct from the usual one for ℂℙ2, which turns out to carry absolutist connotations instead. Thus, this paper is the first to note absolute-versus-relational motion distinctions at the kinematical rather than dynamical level. It is also an example of value to the discussion of kinematical quantization along the lines of Isham, 1984. The relational quadrilateral is the simplest RPM whose mathematics is not standard in atomic physics (the triangle and four particles on a line are both based on 𝕊2 and ℝ3 mathematics). It is far more typical of the general quantum relational N-a-gon than the previously studied case of the relational triangle. We consider useful integrals as regards perturbation theory and the peaking interpretation of quantum cosmology. We subsequently consider problem of time (PoT) applications of this: quantum Kuchař beables, the Machian version of the semiclassical approach and the timeless naïve Schrödinger interpretation. These go toward extending the combined Machian semiclassical-Histories-Timeless Approach of [Int. J. Mod. Phys. D23 (2014) 1450014] to the case of the quadrilateral, which will be treated in subsequent papers.
NASA Astrophysics Data System (ADS)
Zhou, Nanrun; Hu, Yiqun; Gong, Lihua; Li, Guangyong
2017-06-01
A new quantum image encryption scheme is suggested by using the iterative generalized Arnold transforms and the quantum image cycle shift operations. The times of the quantum image cycle shift operations are controlled by a hyper-chaotic sequence generated by a new 4D hyper-chaotic system. The image pixels are scrambled by the iterative generalized Arnold transform, and the values of the pixels are altered by the quantum image cycle shift operations. The four initial conditions of the new 4D hyper-chaotic system are exploited to control the two parameters, the iterative rounds of the generalized Arnold transform and the times of the quantum image cycle shift operations, respectively. Thus, the main keys of the proposed quantum image encryption scheme are the four initial conditions of the new 4D hyper-chaotic system and the key space is relatively large enough. Simulation results and theoretical analyses demonstrate that the proposed quantum image encryption scheme outperforms its classical counterparts apparently.
Relativistic quantum metrology: exploiting relativity to improve quantum measurement technologies.
Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette
2014-05-22
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.
Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies
Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette
2014-01-01
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects. PMID:24851858
Generalized mutual information of quantum critical chains
NASA Astrophysics Data System (ADS)
Alcaraz, F. C.; Rajabpour, M. A.
2015-04-01
We study the generalized mutual information I˜n of the ground state of different critical quantum chains. The generalized mutual information definition that we use is based on the well established concept of the Rényi divergence. We calculate this quantity numerically for several distinct quantum chains having either discrete Z (Q ) symmetries (Q -state Potts model with Q =2 ,3 ,4 and Z (Q ) parafermionic models with Q =5 ,6 ,7 ,8 and also Ashkin-Teller model with different anisotropies) or the U (1 ) continuous symmetries (Klein-Gordon field theory, X X Z and spin-1 Fateev-Zamolodchikov quantum chains with different anisotropies). For the spin chains these calculations were done by expressing the ground-state wave functions in two special bases. Our results indicate some general behavior for particular ranges of values of the parameter n that defines I˜n. For a system, with total size L and subsystem sizes ℓ and L -ℓ , the I˜n has a logarithmic leading behavior given by c/˜n4 log[L/π sin(π/ℓ L ) ] where the coefficient c˜n is linearly dependent on the central charge c of the underlying conformal field theory describing the system's critical properties.
Duality relation for quantum ratchets.
Peguiron, J; Grifoni, M
2005-01-01
A duality relation between the long-time dynamics of a quantum Brownian particle in a tilted ratchet potential and a driven dissipative tight-binding model is reported. It relates a situation of weak dissipation in one model to strong dissipation in the other one, and vice versa. We apply this duality relation to investigate transport and rectification in ratchet potentials: From the linear mobility we infer ground-state delocalization for weak dissipation. We report reversals induced by adiabatic driving and temperature in the ratchet current and its dependence on the potential shape.
Generalized quantum interference of correlated photon pairs
Kim, Heonoh; Lee, Sang Min; Moon, Han Seb
2015-01-01
Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source. PMID:25951143
Quantum physics reimagined for the general public
NASA Astrophysics Data System (ADS)
Bobroff, Julien
2015-03-01
Quantum Physics has always been a challenging issue for outreach. It is invisible, non-intuitive and written in sophisticated mathematics. In our ``Physics Reimagined'' research group, we explore new ways to present that field to the general public. Our approach is to develop close collaborations between physicists and designers or graphic artists. By developing this new kind of dialogue, we seek to find new ways to present complex phenomena and recent research topics to the public at large. For example, we created with web-illustrators a series of 3D animations about basic quantum laws and research topics (graphene, Bose-Einstein condensation, decoherence, pump-probe techniques, ARPES...). We collaborated with designers to develop original setups, from quantum wave animated models or foldings to a superconducting circus with levitating animals. With illustrators, we produced exhibits, comic strips or postcards displaying the physicists in their labs, either famous ones or even our own colleagues in their daily life as researchers. With artists, we recently made a stop-motion picture to explain in an esthetic way the process of discovery and scientific publication. We will discuss how these new types of outreach projects allowed us to engage the public with modern physics both on a scientific and cultural level and how the concepts and process can easily be replicated and expanded by other physicists. We are at the precise time when creative tools, interfaces, and ways of sharing and learning are rapidly evolving (wikipedia, MOOCs, smartphones...). If scientists don't step forward to employ these tools and develop new resources, other people will, and the integrity of the science and underlying character of research risks being compromised. All our productions are free to use and can be downloaded at www.PhysicsReimagined.com (for 3D quantum videos, specific link: www.QuantumMadeSimple.com) This work benefited from the support of the Chair ``Physics Reimagined
Tests of General Theory of Relativity
NASA Astrophysics Data System (ADS)
Brynjolfsson, Ari
2002-04-01
Einstein’s theory of general relativity and experiments proving it are all in the domain of classical physics. These include experiments by Pound, Rebka, and Snider of the gravitational redshift of 14.4 keV photons; the rocket experiments by Vessot et al.; the Galileo redshift experiments by Krisher et al.; the gravitational deflection of light experiments by Riveros and Vucetich; and delay of echoes of radar signals passing close to Sun as observed by Shapiro et al. Bohr’s correspondence principle assures that the quantum mechanical theory of general relativity agrees with Einstein’s classical theory when frequency and gravitational field gradient approach zero, or when photons cannot interact with the gravitational field. Quantum theory invalidates some of the assumption made by Einstein. His argument that equally many crests of waves must arrive on Earth as leave Sun is correct in classical physics, but impermissible in quantum mechanics. We will show that solar redshift experiments contradict the classical theory and support a quantum mechanically modified theory of general relativity. This changes drastically the entire theory, including the equivalence principle.
Strongly magnetized rotating dipole in general relativity
NASA Astrophysics Data System (ADS)
Pétri, J.
2016-10-01
Context. Electromagnetic waves arise in many areas of physics. Solutions are difficult to find in the general case. Aims: We numerically integrate Maxwell equations in a 3D spherical polar coordinate system. Methods: Straightforward finite difference methods would lead to a coordinate singularity along the polar axis. Spectral methods are better suited for such artificial singularities that are related to the choice of a coordinate system. When the radiating object rotates like a star, for example, special classes of solutions to Maxwell equations are worthwhile to study, such as quasi-stationary regimes. Moreover, in high-energy astrophysics, strong gravitational and magnetic fields are present especially around rotating neutron stars. Results: To study such systems, we designed an algorithm to solve the time-dependent Maxwell equations in spherical polar coordinates including general relativity and quantum electrodynamical corrections to leading order. As a diagnostic, we computed the spin-down luminosity expected for these stars and compared it to the classical or non-relativistic and non-quantum mechanical results. Conclusions: Quantum electrodynamics leads to an irrelevant change in the spin-down luminosity even for a magnetic field of about the critical value of 4.4 × 109 T. Therefore the braking index remains close to its value for a point dipole in vacuum, namely n = 3. The same conclusion holds for a general-relativistic quantum electrodynamically corrected force-free magnetosphere.
The Confrontation between General Relativity and Experiment.
Will, Clifford M
2006-01-01
The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.
The Confrontation between General Relativity and Experiment.
Will, Clifford M
2001-01-01
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light defl ection the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to half a percent using the Hulse-Taylor binary pulsar, and new binary pulsar systems may yield further improvements. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.
A Generalized Information Theoretical Model for Quantum Secret Sharing
NASA Astrophysics Data System (ADS)
Bai, Chen-Ming; Li, Zhi-Hui; Xu, Ting-Ting; Li, Yong-Ming
2016-11-01
An information theoretical model for quantum secret sharing was introduced by H. Imai et al. (Quantum Inf. Comput. 5(1), 69-80 2005), which was analyzed by quantum information theory. In this paper, we analyze this information theoretical model using the properties of the quantum access structure. By the analysis we propose a generalized model definition for the quantum secret sharing schemes. In our model, there are more quantum access structures which can be realized by our generalized quantum secret sharing schemes than those of the previous one. In addition, we also analyse two kinds of important quantum access structures to illustrate the existence and rationality for the generalized quantum secret sharing schemes and consider the security of the scheme by simple examples.
NASA Astrophysics Data System (ADS)
Mashhoon, Bahram
2014-12-01
A brief account of the present status of the recent nonlocal generalization of Einstein's theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenbock's torsion and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline-Kuhn approach to modified gravity. To account for the observational data regarding dark matter, nonlocality is associated with a characteristic length scale of order 1 kpc. The confrontation of nonlocal gravity with observation is briefly discussed.
ERIC Educational Resources Information Center
Stauffer, Frederic R.
1984-01-01
Proposes novel methods of solving mechanics and dynamics problems by changing frames of reference. Uses these ideas to pursue Einstein's notions of inertial and uniformly rotating reference frames, gravitational and inertial mass, and the gravitational bending of light in relation to the simple original problem. (JM)
A General Method of Selecting Quantum Channel for Bidirectional Quantum Teleportation
NASA Astrophysics Data System (ADS)
Fu, Hong-Zi; Tian, Xiu-Lao; Hu, Yang
2014-06-01
Based on tensor representation and Bell basis measurement in bidirectional quantum teleportation, a criterion that can be used to judge whether a four-qubit quantum state can be regarded as quantum channel or not in bidirectional teleportation is suggested and a theoretical scheme of bidirectional teleportation via four-qubit state as the quantum channel is proposed. In accordance with this criterion we give a general method of selecting quantum channel in bidirectional teleportation, which is determined by the channel parameter matrix R in the Bell basis measurement. This general method provide a theoretical basis for quantum channel selection in bidirectional quantum teleportation experiments.
Quantum groups and functional relations for lower rank
NASA Astrophysics Data System (ADS)
Nirov, Kh. S.; Razumov, A. V.
2017-02-01
A detailed construction of the universal integrability objects related to the integrable systems associated with the quantum loop algebra Uq(L(sl2)) is given. The full proof of the functional relations in the form independent of the representation of the quantum loop algebra on the quantum space is presented. The case of the general gradation and general twisting is treated. The specialization of the universal functional relations to the case when the quantum space is the state space of a discrete spin chain is described. This is a digression of the corresponding consideration for the case of the quantum loop algebra Uq(L(sl3)) with an extension to the higher spin case.
Relativity of quantum states and observables
NASA Astrophysics Data System (ADS)
Loveridge, L.; Busch, P.; Miyadera, T.
2017-02-01
Under the principle that quantum-mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as the incorporation of a quantum reference frame, we show that the usual quantum description approximates the relative one precisely when the reference system admits an appropriate localisable quantity and a localised state. From this follows a new perspective on the nature and reality of quantum superpositions and optical coherence.
Hamiltonian formulation of general relativity.
NASA Astrophysics Data System (ADS)
Teitelboim, Claudio
The following sections are included: * INTRODUCTION * HAMILTONIAN FORMULATION OF GAUGE THEORIES (PRE-BRST) * BRST HAMILTONIAN FORMULATION OF GAUGE THEORIES * DYNAMICS OF GRAVITATIONAL FIELD * DOES THE HAMILTONIAN VANISH? GENERAL COVARIANCE AS AN "ORDINARY" GAUGE INVARIANCE * GENERALLY COVARIANT SYSTEMS * TIME AS A CANONICAL VARIABLE. ZERO HAMILTONIAN * Parametrized Systems * Zero Hamiltonian * Parametrization and Explicit Time Dependence * TIME REPARAMETRIZATION INVARIANCE * Form of Gauge Transformations * Must the Hamiltonian be Zero for a Generally Covariant System? * Simple Example of a Generally Covariant System with a Nonzero Hamiltonian * "TRUE DYNAMICS" VERSUS GAUGE TRANSFORMATIONS * Interpretation of the Formalism * Reduced Phase Space * MUST TIME FLOW? * GAUGE INDEPENDENCE OF PATH INTEGRAL FOR A PARAMETRIZED SYSTEM ILLUSTRATED. EQUIVALENCE OF THE GAUGES t = τ AND t = 0 * Reduced Phase Space Transition Amplitude as a Reduced Phase Space Path Integral * Canonical Gauge Conditions * Gauge
A family of generalized quantum entropies: definition and properties
NASA Astrophysics Data System (ADS)
Bosyk, G. M.; Zozor, S.; Holik, F.; Portesi, M.; Lamberti, P. W.
2016-08-01
We present a quantum version of the generalized (h,φ )-entropies, introduced by Salicrú et al. for the study of classical probability distributions. We establish their basic properties and show that already known quantum entropies such as von Neumann, and quantum versions of Rényi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicrú form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum (h,φ )-entropies under the action of quantum operations and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement and introduce a discussion on possible generalized conditional entropies as well.
General conditions for quantum adiabatic evolution
Comparat, Daniel
2009-07-15
Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution [H({epsilon}t),{epsilon}{yields}0], are insufficient to describe an evolution driven by the Hamiltonian H(t) itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian H(t). As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions)
Generalized Entropic Uncertainty Relations with Tsallis' Entropy
NASA Technical Reports Server (NTRS)
Portesi, M.; Plastino, A.
1996-01-01
A generalization of the entropic formulation of the Uncertainty Principle of Quantum Mechanics is considered with the introduction of the q-entropies recently proposed by Tsallis. The concomitant generalized measure is illustrated for the case of phase and number operators in quantum optics. Interesting results are obtained when making use of q-entropies as the basis for constructing generalized entropic uncertainty measures.
The Confrontation between General Relativity and Experiment.
Will, Clifford M
2014-01-01
The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.
Properties and relative measure for quantifying quantum synchronization
NASA Astrophysics Data System (ADS)
Li, Wenlin; Zhang, Wenzhao; Li, Chong; Song, Heshan
2017-07-01
Although quantum synchronization phenomena and corresponding measures have been widely discussed recently, it is still an open question how to characterize directly the influence of nonlocal correlation, which is the key distinction for identifying classical and quantum synchronizations. In this paper, we present basic postulates for quantifying quantum synchronization based on the related theory in Mari's work [Phys. Rev. Lett. 111, 103605 (2013), 10.1103/PhysRevLett.111.103605], and we give a general formula of a quantum synchronization measure with clear physical interpretations. By introducing Pearson's parameter, we show that the obvious characteristics of our measure are the relativity and monotonicity. As an example, the measure is applied to describe synchronization among quantum optomechanical systems under a Markovian bath. We also show the potential by quantifying generalized synchronization and discrete variable synchronization with this measure.
Generalized Weyl quantization on the cylinder and the quantum phase
Przanowski, Maciej Brzykcy, Przemysław
2013-10-15
Generalized Weyl quantization formalism for the cylindrical phase space S{sup 1}×R{sup 1} is developed. It is shown that the quantum observables relevant to the phase of the linear harmonic oscillator or electromagnetic field can be represented within this formalism by the self-adjoint operators on the Hilbert space L{sup 2}(S{sup 1}). -- Highlights: •The generalized Weyl quantization on the cylindrical phase space is formulated. •A self-adjoint phase operator on the Hilbert space of the square integrable functions on the circle is given. •A new uncertainty relation between the quantum phase and the number operator is found.
Hybrid quantum computing: semicloning for general database retrieval
NASA Astrophysics Data System (ADS)
Lanzagorta, Marco; Uhlmann, Jeffrey K.
2005-05-01
Quantum computing (QC) has become an important area of research in computer science because of its potential to provide more efficient algorithmic solutions to certain problems than are possible with classical computing (CC). In particular, QC is able to exploit the special properties of quantum superposition to achieve computational parallelism beyond what can be achieved with parallel CC computers. However, these special properties are not applicable for general computation. Therefore, we propose the use of "hybrid quantum computers" (HQCs) that combine both classical and quantum computing architectures in order to leverage the benefits of both. We demonstrate how an HQC can exploit quantum search to support general database operations more efficiently than is possible with CC. Our solution is based on new quantum results that are of independent significance to the field of quantum computing. More specifically, we demonstrate that the most restrictive implications of the quantum No-Cloning Theorem can be avoided through the use of semiclones.
Quantum affine algebras and universal functional relations
NASA Astrophysics Data System (ADS)
Nirov, Kh S.; Razumov, A. V.
2016-01-01
By the universal integrability objects we mean certain monodromy-type and transfer- type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is actually determined by the structure of the universal R-matrix. We call functional relations between such universal integrability objects, and so, being independent of the representation in the quantum space, the universal functional relations. We present a short review of the universal functional relations for the quantum integrable systems associated with the quantum groups of loop Lie algebras.
Improved uncertainty relation in the presence of quantum memory
NASA Astrophysics Data System (ADS)
Xiao, Yunlong; Jing, Naihuan; Fei, Shao-Ming; Li-Jost, Xianqing
2016-12-01
Berta et al’s uncertainty principle in the presence of quantum memory (Berta et al 2010 Nat. Phys. 6 659) reveals uncertainties with quantum side information between the observables. In the recent important work of Coles and Piani (2014 Phys. Rev. A 89 022112), the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty relation in the presence of quantum memory and find the exact dependence on all d largest overlaps between two measurements on any d-dimensional Hilbert space. Our bound is rigorously shown to be strictly tighter than previous entropic bounds in the presence of quantum memory, which have potential applications to quantum cryptography with entanglement witnesses and quantum key distributions.
Quantum-coherent mixtures of causal relations
MacLean, Jean-Philippe W.; Ried, Katja; Spekkens, Robert W.; Resch, Kevin J.
2017-01-01
Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common-cause acting on both. Here we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's effect, whereby two independent causes can become correlated on observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell's theorem and the search for quantum gravity. PMID:28485394
Teaching General Relativity to the Layperson
NASA Astrophysics Data System (ADS)
Egdall, Mark
2009-11-01
This paper describes a lay course on general relativity (GR) given at the Osher Lifelong Learning Institute at Florida International University. It is presented in six hour-and-a-half weekly sessions. Other courses offered by the author include special relativity (which precedes the course described here), quantum theory, and cosmology. Students are people 50 and older, mostly retired or semi-retired like me. They come from all walks of life, including medical doctors, ballet directors, educators, cruise line executives, and poets. Most are college educated, but with little or no formal physics education. A few have technical backgrounds, e.g., chemistry or physics.
Geometric Phase for Adiabatic Evolutions of General Quantum States
Wu, Biao; Liu, Jie; Niu, Qian; Singh, David J
2005-01-01
The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.
Quantum mechanical generalization of the balistic electron wind theory
NASA Astrophysics Data System (ADS)
Lacina, A.
1980-06-01
The Fiks' quasiclassical theory of the electron wind force is quantum mechanically generalized. Within the framework of this generalization the space dependence of the electron wind force is calculated in the vicinity of an interface between two media. It is found that quantum corrections may be comparable with or even greater than corresponding quasiclassical values.
Super quantum discord for general two qubit X states
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Yu, Bing
2017-04-01
The exact solutions of the super quantum discord are derived for general two qubit X states in terms of a one-variable function. Several exact solutions of the super quantum discord are given for the general X state over nontrivial regions of a seven-dimensional manifold.
The generalized second law implies a quantum singularity theorem
NASA Astrophysics Data System (ADS)
Wall, Aron C.
2013-08-01
The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose’s original singularity theorem, it implies that spacetime is null-geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann-Robertson-Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. The introduction describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.)
Rényi generalizations of the conditional quantum mutual information
Berta, Mario; Seshadreesan, Kaushik P.; Wilde, Mark M.
2015-02-15
The conditional quantum mutual information I(A; B|C) of a tripartite state ρ{sub ABC} is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is non-negative for any tripartite state, that it decreases under local operations applied to systems A and B, and that it obeys the duality relation I(A; B|C) = I(A; B|D) for a four-party pure state on systems ABCD. The conditional mutual information also underlies the squashed entanglement, an entanglement measure that satisfies all of the axioms desired for an entanglement measure. As such, it has been an open question to find Rényi generalizations of the conditional mutual information, that would allow for a deeper understanding of the original quantity and find applications beyond the traditional memoryless setting of quantum information theory. The present paper addresses this question, by defining different α-Rényi generalizations I{sub α}(A; B|C) of the conditional mutual information, some of which we can prove converge to the conditional mutual information in the limit α → 1. Furthermore, we prove that many of these generalizations satisfy non-negativity, duality, and monotonicity with respect to local operations on one of the systems A or B (with it being left as an open question to prove that monotonicity holds with respect to local operations on both systems). The quantities defined here should find applications in quantum information theory and perhaps even in other areas of physics, but we leave this for future work. We also state a conjecture regarding the monotonicity of the Rényi conditional mutual informations defined here with respect to the Rényi parameter α. We prove that this conjecture is true in some special cases and when α is in a neighborhood of one.
Von Neumann's quantization of general relativity
NASA Astrophysics Data System (ADS)
Arbuzov, A. B.; Cherny, A. Yu.; Cirilo-Lombardo, D. J.; Nazmitdinov, R. G.; Han, Nguyen Suan; Pavlov, A. E.; Pervushin, V. N.; Zakharov, A. F.
2017-05-01
Von Neumann's procedure is applied to quantizing general relativity. Initial data for dynamical variables in the Planck epoch, where the Hubble parameter value coincided with the Planck mass are quantized. These initial data are defined in terms of the Fock orthogonal simplex in the tangent Minkowski spacetime and the Dirac conformal interval. The Einstein cosmological principle is used to average the logarithm of the determinant of the spatial metric over the spatial volume of the visible Universe. The splitting of general coordinate transformations into diffeomorphisms and transformations of the initial data is introduced. In accordance with von Neumann's procedure, the vacuum state is treated is a quantum ensemble that is degenerate in quantum numbers of nonvacuum states. The distribution of the vacuum state leads to the Casimir effect in gravidynamics in just the same way as in electrodynamics. The generating functional for perturbation theory in gravidynamics is found by solving the quantum energy constraint. The applicability range of gravidynamics is discussed along with the possibility of employing this theory to interpret modern observational data.
Quantum integrable systems related to lie algebras
NASA Astrophysics Data System (ADS)
Olshanetsky, M. A.; Perelomov, A. M.
1983-03-01
Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors [83] devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g2v( q) of the following 5 types: vI( q) = q-2, vII( q) = sinh-2q, vIII( q) = sin-2q, v IV(q) = P(q) , vV( q) = q-2 + ω2q2. Here P(q) is the Weierstrass function, so that the first three cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbour potential exp( qjqj+ 1 ) is moreover considered. This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest.
Quaternionic quantization principle in general relativity and supergravity
NASA Astrophysics Data System (ADS)
Kober, Martin
2016-01-01
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space-time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to 𝒩 = 1 supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.
Jack polynomial fractional quantum Hall states and their generalizations
NASA Astrophysics Data System (ADS)
Baratta, Wendy; Forrester, Peter J.
2011-02-01
In the study of fractional quantum Hall states, a certain clustering condition involving up to four integers has been identified. We give a simple proof that particular Jack polynomials with α=-(r-1)/(k+1), (r-1) and (k+1) relatively prime, and with partition given in terms of its frequencies by [n0k0k0k⋯0m] satisfy this clustering condition. Our proof makes essential use of the fact that these Jack polynomials are translationally invariant. We also consider nonsymmetric Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre polynomials, and Macdonald polynomials from the viewpoint of the clustering.
Spinning fluids in general relativity
NASA Technical Reports Server (NTRS)
Ray, J. R.; Smalley, L. L.
1982-01-01
General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.
Spinning fluids in general relativity
NASA Technical Reports Server (NTRS)
Ray, J. R.; Smalley, L. L.
1982-01-01
General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.
Relational observables in 2D quantum gravity
Gary, Michael; Giddings, Steven B.
2007-05-15
Local observation is an important problem both for the foundations of a quantum theory of gravity and for applications to quantum-cosmological problems such as eternal inflation. While gauge-invariant local observables cannot be defined, it has been argued that appropriate relational observables approximately reduce to local observables in certain states. However, quantum mechanics and gravity together imply limitations on the precision of their localization. Such a relational framework is studied in the context of two-dimensional gravity, where there is a high degree of analytic control. This example furnishes a concrete example of some of the essential features of relational observables.
Colloquium: Quantum fluctuation relations: Foundations and applications
NASA Astrophysics Data System (ADS)
Campisi, Michele; Hänggi, Peter; Talkner, Peter
2011-07-01
Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars the reader is guided through a self-contained exposition of the theory and applications of quantum fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between quantum fluctuation relations and (non)linear response theory. A number of fundamental issues are clarified which were not completely settled in the prior literature. The main focus is on (i) work fluctuation relations for transiently driven closed or open quantum systems, and (ii) on fluctuation relations for heat and matter exchange in quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.
Directions in General Relativity, Vol. 2
NASA Astrophysics Data System (ADS)
Hu, B. L.; Jacobson, T. A.
2005-10-01
Preface; Dieter Brill: a spacetime perspective; 1. Thawing the frozen formalism: the difference between observables and what we observe A. Anderson; 2. Jacobi's action and the density of states J. D. Brown and J. W. York; 3. Decoherence of correlation histories E. Calzetta and B. L. Hu; 4. The initial value problem in light of Ashtekar's variables R. Capovilla, J. Dell and T. Jacobson; 5. Status report on an axiomatic basis for functional integration P. Cartier and C. DeWitt-Morette; 6. Solution of the coupled Einstein constraints on asymptotically Euclidean manifolds Y. Choquet-Bruhat; 7. Compact Cauchy horizons and Cauchy surfaces P. Chrusciel and J. Isenberg; 8. The classical electron J. M. Cohen and E. Mustafa; 9. Gauge (in)variance, mass and parity in D=3 revisited S. Deser; 10. Triality, exceptional Lie groups and Dirac operators F. Flaherty; 11. The reduction of the state vector and limitations on measurement in the quantum mechanics of closed systems J. B. Hartle; 12 Quantum linearization instabilities of de Sitter spacetime A. Higuchi; 13. What is the true description of charged black holes? G. T. Horowitz; 14. Limits on the adiabatic index in static stellar models L. Lindblom and A. K. M. Masood-ul-Alam; 15. On the relativity of rotation B. Mashhoon; 16. Recent progress and open problems in linearization stability V. E. Moncrief; 17. Brill waves N. Murchadha; 18. You can't get there from here: constraints on topology change K. Schleich and D. M. Witt; 19. Time, measurement and information loss in quantum cosmology L. Smolin; 20. Impossible measurements on quantum fields R. Sorkin; 21. A new condition implying the existence of a constant mean curvature foliation F. J. Tipler; 22. Maximal slices in stationary spacetimes with ergoregions R. M. Wald; 23. (1 + 1) - Dimensional methods for general relativity J. H. Yoon; 24. Coalescence of primal gravity waves to make cosmological mass without matter D. E. Holz, W. A. Miller, M. Wakano and J. A. Wheeler
Uncertainty relations for general unitary operators
NASA Astrophysics Data System (ADS)
Bagchi, Shrobona; Pati, Arun Kumar
2016-10-01
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the uncertainty relation for the unitary operators, we obtain the tight state-independent lower bound for the uncertainty of two Pauli observables and anticommuting observables in higher dimensions. With regard to the minimum-uncertainty states, we derive the minimum-uncertainty state equation by the analytic method and relate this to the ground-state problem of the Harper Hamiltonian. Furthermore, the higher-dimensional limit of the uncertainty relations and minimum-uncertainty states are explored. From an operational point of view, we show that the uncertainty in the unitary operator is directly related to the visibility of quantum interference in an interferometer where one arm of the interferometer is affected by a unitary operator. This shows a principle of preparation uncertainty, i.e., for any quantum system, the amount of visibility for two general noncommuting unitary operators is nontrivially upper bounded.
Quasilocal Hamiltonians in general relativity
Anderson, Michael T.
2010-10-15
We analyze the definition of quasilocal energy in general relativity based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular, the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consistent definition of quasilocal energy in general relativity requires, at a minimum, a framework based on the (currently unknown) geometric well-posedness of the initial boundary value problem for the Einstein equations.
The Concept of General Relativity is not Related to Reality
NASA Astrophysics Data System (ADS)
Kotas, Ronald
2015-04-01
The concept of general relativity is not related to reality. It is not real or factual Science. GR cannot account for objects falling to earth or for the weight of objects sitting on the earth. The Cavendish demonstration showing the attraction between two masses at right angles to earth's gravity, is not explained by GR. No one can prove the existence of ``space fabric.'' The concept of ``space time'' effects causing gravitational attraction between masses is wrong. Conservation law of energy - momentum does not exist in GR. LIGO fails in detecting ``gravity waves'' because there is no ``space fabric'' to transmit them. The Gravity B Probe data manipulated to show some effects, is not proof of ``space fabric.'' It is Nuclear Quantum Gravitation that provides clear definitive explanation of Gravity and Gravitation. It is harmonious with Newtonian and Quantum Mechanics, and Scientific Logic. Nuclear Quantum Gravitation has 10 clear, Scientific proofs and 21 more good indications. With this theory the Physical Forces are Unified. See: OBSCURANTISM ON EINSTEIN GRAVITATION? http://www.santilli-foundation.org/inconsistencies-gravitation.php and Einstein's Theory of Relativity versus Classical Mechanics, by Paul Marmet http://www.newtonphysics.on.ca/einstein/
Extending quantum mechanics entails extending special relativity
NASA Astrophysics Data System (ADS)
Aravinda, S.; Srikanth, R.
2016-05-01
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QMs) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum non-locality, and implies that special relativity has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime at the ontological level has Minkowski causal structure.
Quantum enigma cipher as a generalization of the quantum stream cipher
NASA Astrophysics Data System (ADS)
Kato, Kentaro
2016-09-01
Various types of randomizations for the quantum stream cipher by Y00 protocol have been developed so far. In particular, it must be noted that the analysis of immunity against correlation attacks with a new type of randomization by Hirota and Kurosawa prompted a new look at the quantum stream cipher by Y00 protocol (Quant. Inform. Process. 6(2) 2007). From the preceding study on the quantum stream cipher, we recognized that the quantum stream cipher by Y00 protocol would be able to be generalized to a new type of physical cipher that has potential to exceed the Shannon limit by installing additional randomization mechanisms, in accordance with the law of quantum mechanics. We call this new type of physical random cipher the quantum enigma cipher. In this article, we introduce the recent developments for the quantum stream cipher by Y00 protocol and future plans toward the quantum enigma cipher.
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
Generalizing Prototype Theory: A Formal Quantum Framework.
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Quantum Random Walks with General Particle States
NASA Astrophysics Data System (ADS)
Belton, Alexander C. R.
2014-06-01
A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This unifies and extends previous work on repeated-interactions models, including that of Attal and Pautrat (Ann Henri Poincaré 7:59-104 2006) and Belton (J Lond Math Soc 81:412-434, 2010; Commun Math Phys 300:317-329, 2010). When the random-walk generator acts by ampliation and either multiplication or conjugation by a unitary operator, it is shown that the quantum stochastic cocycle which arises in the limit is driven by a unitary process.
Dimensional Analysis and General Relativity
ERIC Educational Resources Information Center
Lovatt, Ian
2009-01-01
Newton's law of gravitation is a central topic in the first-year physics curriculum. A lecturer can go beyond the physical details and use the history of gravitation to discuss the development of scientific ideas; unfortunately, the most recent chapter in this history, general relativity, is not covered in first-year courses. This paper discusses…
Dimensional Analysis and General Relativity
ERIC Educational Resources Information Center
Lovatt, Ian
2009-01-01
Newton's law of gravitation is a central topic in the first-year physics curriculum. A lecturer can go beyond the physical details and use the history of gravitation to discuss the development of scientific ideas; unfortunately, the most recent chapter in this history, general relativity, is not covered in first-year courses. This paper discusses…
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Special Relativity at the Quantum Scale
Lam, Pui K.
2014-01-01
It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's “checker-board” trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum “coordinates”. This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point. PMID:25531675
Special relativity at the quantum scale.
Lam, Pui K
2014-01-01
It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's "checker-board" trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum "coordinates". This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point.
Possible universal quantum algorithms for generalized Turaev-Viro invariants
NASA Astrophysics Data System (ADS)
Vélez, Mario; Ospina, Juan
2011-05-01
An emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological invariants for knots and links (Jones polynomials, HOMFLY polynomials, Khovanov polynomials); topological invariants for graphs (Tutte polynomial and Bollobás-Riordan polynomial); topological invariants for 3-manifolds (Reshetiskin-Turaev, Turaev-Viro and Turaer-Viro-Ocneanu invariants) and topological invariants for 4-manifolds( Crane-Yetter invariants). In a few words, TQC is concerned with the formulation of quantum algorithms for the computation of these topological invariants in quantum topology. Given that one of the fundamental achievements of quantum topology was the discovery of strong connections between monoidal categories and 3-dimensional manifolds, in TQC is possible and necessary to exploit such connections with the purpose to formulate universal quantum algorithms for topological invariants of 3-manifolds. In the present work we make an exploration of such possibilities. Specifically we search for universal quantum algorithms for generalized Turaev-Viro invariants of 3-manifolds such as the Turaev-Viro-Ocneanu invariants, the Kashaev-Baseilhac-Benedetti invariants of 3-manifolds with links and the Geer-Kashaev-Turaev invariants of 3-manifolds with a link and a principal bundle. We also look for physical systems (three dimensional topological insulators and three-dimensional gravity) over which implement the resulting universal topological quantum algorithms.
Multipartite entanglement accumulation in quantum states: Localizable generalized geometric measure
NASA Astrophysics Data System (ADS)
Sadhukhan, Debasis; Roy, Sudipto Singha; Pal, Amit Kumar; Rakshit, Debraj; SenDe, Aditi; Sen, Ujjwal
2017-02-01
Multiparty quantum states are useful for a variety of quantum information and computation protocols. We define a multiparty entanglement measure based on local measurements on a multiparty quantum state and an entanglement measure averaged on the postmeasurement ensemble. Using the generalized geometric measure as the measure of multipartite entanglement for the ensemble, we demonstrate, in the case of several well-known classes of multipartite pure states, that the localized multipartite entanglement can exceed the entanglement present in the original state. We also show that measurement over multiple parties may be beneficial in enhancing localizable multipartite entanglement. We point out that localizable generalized geometric measure faithfully signals quantum critical phenomena in well-known quantum spin models even when considerable finite-size effect is present in the system.
Generalized energy measurements and modified transient quantum fluctuation theorems.
Watanabe, Gentaro; Venkatesh, B Prasanna; Talkner, Peter
2014-05-01
Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions.
Generalized cluster decomposition principle illustrated in waveguide quantum electrodynamics
NASA Astrophysics Data System (ADS)
Xu, Shanshan; Fan, Shanhui
2017-06-01
We show that the form of the cluster decomposition principle, commonly used in quantum field theory, needs to be significantly generalized. As an illustration, we consider the general structure of two-photon S matrix for a waveguide coupled to a local quantum system that supports multiple ground states. The presence of the multiple ground states results in a noncommutative aspect of the system with respect to the exchange of the orders of photons. Consequently, the two-photon S matrix significantly differs from the standard form in quantum field theory.
Generalized uncertainty principle in Bianchi type I quantum cosmology
NASA Astrophysics Data System (ADS)
Vakili, B.; Sepangi, H. R.
2007-07-01
We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.
Quantum Fluctuation Relations for the Lindblad Master Equation
NASA Astrophysics Data System (ADS)
Chetrite, R.; Mallick, K.
2012-08-01
An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.
Testing general relativity on accelerators
Kalaydzhyan, Tigran
2015-09-07
Within the general theory of relativity, the curvature of spacetime is related to the energy and momentum of the present matter and radiation. One of the more specific predictions of general relativity is the deflection of light and particle trajectories in the gravitational field of massive objects. Bending angles for electromagnetic waves and light in particular were measured with a high precision. However, the effect of gravity on relativistic massive particles was never studied experimentally. Here we propose and analyze experiments devoted to that purpose. We demonstrate a high sensitivity of the laser Compton scattering at high energy accelerators tomore » the effects of gravity. The main observable – maximal energy of the scattered photons – would experience a significant shift in the ambient gravitational field even for otherwise negligible violation of the equivalence principle. In conclusion, we confirm predictions of general relativity for ultrarelativistic electrons of energy of tens of GeV at a current level of resolution and expect our work to be a starting point of further high-precision studies on current and future accelerators, such as PETRA, European XFEL and ILC.« less
On quantum Rényi entropies: A new generalization and some properties
Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco
2013-12-15
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.
"imprinting" in General Relativity Tests?
NASA Astrophysics Data System (ADS)
Iorio, Lorenzo
We investigate possible a priori "imprinting" of general relativity itself on spaceraft-based tests of it. We deal with some performed or proposed time-delay ranging experiments in the Sun's gravitational field. The "imprint" of general relativity on the Astronomical Unit and the solar gravitational constant GM⊙, not solved for in the spacecraft-based time-delay test performed so far, may induce an a priori bias of the order of 10-6 in typical solar system ranging experiments aimed to measuring the space curvature PPN parameter γ. It is too small by one order of magnitude to be of concern for the performed Cassini experiment, but it would affect future planned or proposed tests aiming to reach a 10-7-10-9 accuracy in determining γ.
General Relativity and Spacetime Relationism.
NASA Astrophysics Data System (ADS)
Hoefer, Carl
1992-01-01
This dissertation takes up the project of showing that, in the context of the general theory of relativity (GTR), spacetime relationism is not a refuted or hopeless view, as many in the recent literature have maintained (John Earman, Michael Friedman, and others). Most of the challenges to the relationist view in General Relativity can be satisfactorily answered; in addition, the opposing absolutist and substantivalist views of spacetime can be shown to be problematic. The crucial burden for relationists concerned with GTR is to show that the realistic cosmological models, i.e. those that may be roughly accurate representations of our universe, satisfy Mach's ideas about the origin of inertia. This dissertation clears the way for and begins such a demonstration. After a brief discussion of the problem of the nature of spacetime and its history in the Introduction, chapters 2 and 3 provide conceptual analysis and criticism of contemporary philosophical arguments about relationism, absolutism, and particularly substantivalism. The current best arguments in favor of substantivalism are shown to be flawed, with the exception of the argument from inertial and metrical structure; and on this issue, it is shown that both relationism and substantivalism need to argue for modifications of GTR (restriction of its models to those with certain features) in order to have a non-trivial explanation of inertial and metrical structure. For relationists, a Machian account of the origin of inertia in some models of GTR is required. Chapter 4 demonstrates that such a Machian account is equivalent to the demand for a truly general relativity of motion. Chapter 5 explores the history of Einstein's commitment to Mach's ideas in his work on GTR. Through an examination of the history of Einstein's attempts to impose Machian constraints on the models of General Relativity, further insight into the nature of this problem is obtained, as are reasons to believe that the project is by no means
Bubble collisions in general relativity
NASA Astrophysics Data System (ADS)
Sikos, S. T. C.; Wu, Z. C.
The collision of two bubbles of true vacuum in a background of false vacuum is considered in the context of General Relativity. It is found that in the thin wall approximation, the problem can be solved exactly. The region to the future of the collision is described by the pseudo-Schwarzschild de Sitter metric. The parameters in this metric are found by solving the junction conditions at each collision.
NASA Astrophysics Data System (ADS)
Johannsen, Tim
2016-06-01
General relativity has been widely tested in weak gravitational fields but still stands largely untested in the strong-field regime. According to the no-hair theorem, black holes in general relativity depend only on their masses and spins and are described by the Kerr metric. Mass and spin are the first two multipole moments of the Kerr spacetime and completely determine all higher-order moments. The no-hair theorem and, hence, general relativity can be tested by measuring potential deviations from the Kerr metric affecting such higher-order moments. Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, is a prime target for precision tests of general relativity with several experiments across the electromagnetic spectrum. First, near-infrared (NIR) monitoring of stars orbiting around Sgr A* with current and new instruments is expected to resolve their orbital precessions. Second, timing observations of radio pulsars near the Galactic center may detect characteristic residuals induced by the spin and quadrupole moment of Sgr A*. Third, the event horizon telescope, a global network of mm and sub-mm telescopes, aims to study Sgr A* on horizon scales and to image the silhouette of its shadow cast against the surrounding accretion flow using very-long baseline interferometric (VLBI) techniques. Both NIR and VLBI observations may also detect quasiperiodic variability of the emission from the accretion flow of Sgr A*. In this review, I discuss our current understanding of the spacetime of Sgr A* and the prospects of NIR, timing, and VLBI observations to test its Kerr nature in the near future.
General Relativity in the Undergraduate Physics Curriculum
NASA Astrophysics Data System (ADS)
Hartle, James
2005-04-01
Einstein's theory of gravitation --- general relativity--- will shortly be a century old. At is core is one of the most beautiful and revolutionary conceptions of modern science --- the idea that gravity is the geometry of four-dimensional curved spacetime. Together with quantum theory, general relativity is one of the two most profound developments of twentieth century physics. General relativity underlies our understanding of the universe on the largest distance scales, and is central to the the explanation of such frontier astrophysical phenomena gravitational collapse,black holes, X-ray sources, neutron stars, active galactic nuclei, gravitational waves, and the big bang. General relativity is the intellectual origin of many ideas in contemporary elementary particle physics such as string theory. This talk will make the case that an introduction to general relativity is naturally a part education of every undergraduate physics major, and describe a `physics first' approach to teaching at that level. The simplest physically relevant solutions of the Einstein equation, such as those representing black holes, simple cosmologies, and gravitational waves, are presented first without derivation. Their observational consequences are explored by the study of the motion of test particles and light rays in them.This brings the student to the physical phenomena as quickly aspossible. It is the part of the subject most directly connectedto classical mechanics, and requires the minimum of new mathematical ideas. The Einstein equation is introduced later to show where these geometries originate. A course for junior or senior level physics students based on theseprinciples has been part of the undergraduate curriculum at the University of California, Santa Barbara for several decades. It works.
Results from Numerical General Relativity
NASA Technical Reports Server (NTRS)
Baker, John G.
2011-01-01
For several years numerical simulations have been revealing the details of general relativity's predictions for the dynamical interactions of merging black holes. I will review what has been learned of the rich phenomenology of these mergers and the resulting gravitational wave signatures. These wave forms provide a potentially observable record of the powerful astronomical events, a central target of gravitational wave astronomy. Asymmetric radiation can produce a thrust on the system which may accelerate the single black hole resulting from the merger to high relative velocity.
Gravitation. [Book on general relativity
NASA Technical Reports Server (NTRS)
Misner, C. W.; Thorne, K. S.; Wheeler, J. A.
1973-01-01
This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.
Gravitation. [Book on general relativity
NASA Technical Reports Server (NTRS)
Misner, C. W.; Thorne, K. S.; Wheeler, J. A.
1973-01-01
This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.
Rorick, Amber; Michael, Matthew A.; Yang, Liu; Zhang, Yong
2015-01-01
Oxygen is an important element in most biologically significant molecules and experimental solid-state 17O NMR studies have provided numerous useful structural probes to study these systems. However, computational predictions of solid-state 17O NMR chemical shift tensor properties are still challenging in many cases and in particular each of the prior computational work is basically limited to one type of oxygen-containing systems. This work provides the first systematic study of the effects of geometry refinement, method and basis sets for metal and non-metal elements in both geometry optimization and NMR property calculations of some biologically relevant oxygen-containing compounds with a good variety of XO bonding groups, X= H, C, N, P, and metal. The experimental range studied is of 1455 ppm, a major part of the reported 17O NMR chemical shifts in organic and organometallic compounds. A number of computational factors towards relatively general and accurate predictions of 17O NMR chemical shifts were studied to provide helpful and detailed suggestions for future work. For the studied various kinds of oxygen-containing compounds, the best computational approach results in a theory-versus-experiment correlation coefficient R2 of 0.9880 and mean absolute deviation of 13 ppm (1.9% of the experimental range) for isotropic NMR shifts and R2 of 0.9926 for all shift tensor properties. These results shall facilitate future computational studies of 17O NMR chemical shifts in many biologically relevant systems, and the high accuracy may also help refinement and determination of active-site structures of some oxygen-containing substrate bound proteins. PMID:26274812
Rorick, Amber; Michael, Matthew A; Yang, Liu; Zhang, Yong
2015-09-03
Oxygen is an important element in most biologically significant molecules, and experimental solid-state (17)O NMR studies have provided numerous useful structural probes to study these systems. However, computational predictions of solid-state (17)O NMR chemical shift tensor properties are still challenging in many cases, and in particular, each of the prior computational works is basically limited to one type of oxygen-containing system. This work provides the first systematic study of the effects of geometry refinement, method, and basis sets for metal and nonmetal elements in both geometry optimization and NMR property calculations of some biologically relevant oxygen-containing compounds with a good variety of XO bonding groups (X = H, C, N, P, and metal). The experimental range studied is of 1455 ppm, a major part of the reported (17)O NMR chemical shifts in organic and organometallic compounds. A number of computational factors toward relatively general and accurate predictions of (17)O NMR chemical shifts were studied to provide helpful and detailed suggestions for future work. For the studied kinds of oxygen-containing compounds, the best computational approach results in a theory-versus-experiment correlation coefficient (R(2)) value of 0.9880 and a mean absolute deviation of 13 ppm (1.9% of the experimental range) for isotropic NMR shifts and an R(2) value of 0.9926 for all shift-tensor properties. These results shall facilitate future computational studies of (17)O NMR chemical shifts in many biologically relevant systems, and the high accuracy may also help the refinement and determination of active-site structures of some oxygen-containing substrate-bound proteins.
On Entropy Production of Repeated Quantum Measurements I. General Theory
NASA Astrophysics Data System (ADS)
Benoist, T.; Jakšić, V.; Pautrat, Y.; Pillet, C.-A.
2017-07-01
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility related to the hypothesis testing of the arrow of time. Under a suitable chaoticity assumption, we establish a Large Deviation Principle and a Fluctuation Theorem for the EP.
Uncertainty relations and approximate quantum error correction
NASA Astrophysics Data System (ADS)
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.
Limiting values and general relativity
NASA Astrophysics Data System (ADS)
Pyrohova, U. V.; Golubov, O. A.
2015-10-01
From the general theory of relativity it is known that the force of gravitational interaction never exceeds the value Fmax=c2/4G. In this paper we try to make the notion of the force limit intuitively understandable, and illustrate it with thought experiments with such exotic objects as black holes. It was found that maximum limits of force, power, and flow of mass exist in nature. These limits are physically equivalent. All the maximum values could be seen only on a black hole surface. Moreover, maximum limits of force, power, and mass flow are inevitable consequences of properties of the event horizon of a black hole. And vice versa, the existence of black holes could be deduced from the principle of the maximum force. So, these three principles also could be considered as features of a black hole. The role played by the maximum force in general relativity is similar to the role played by speed of light in special relativity.
Conservation laws, uncertainty relations, and quantum limits of measurements.
Ozawa, Masanao
2002-02-04
The uncertainty relation between the noise operator and the conserved quantity leads to a bound on the accuracy of general measurements. The bound extends the assertion by Wigner, Araki, and Yanase that conservation laws limit the accuracy of "repeatable," or "nondisturbing," measurements to general measurements, and improves the one previously obtained by Yanase for spin measurements. The bound represents an obstacle to making a small quantum computer.
Positive spaces, generalized semi-densities, and quantum interactions
NASA Astrophysics Data System (ADS)
Canarutto, Daniel
2012-03-01
The basics of quantum particle physics on a curved Lorentzian background are expressed in a formulation which has original aspects and exploits some non-standard mathematical notions. In particular, positive spaces and generalized semi-densities (in a distributional sense) are shown to link, in a natural way, discrete multi-particle spaces to distributional bundles of quantum states. The treatment of spinor and boson fields is partly original also from an algebraic point of view and suggests a non-standard approach to quantum interactions. The case of electroweak interactions provides examples.
Generalization of continuous-variable quantum cloning with linear optics
Zhai Zehui; Guo Juan; Gao Jiangrui
2006-05-15
We propose an asymmetric quantum cloning scheme. Based on the proposal and experiment by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)], we generalize it to two asymmetric cases: quantum cloning with asymmetry between output clones and between quadrature variables. These optical implementations also employ linear elements and homodyne detection only. Finally, we also compare the utility of symmetric and asymmetric cloning in an analysis of a squeezed-state quantum key distribution protocol and find that the asymmetric one is more advantageous.
Relating quantum coherence and correlations with entropy-based measures.
Wang, Xiao-Li; Yue, Qiu-Ling; Yu, Chao-Hua; Gao, Fei; Qin, Su-Juan
2017-09-21
Quantum coherence and quantum correlations are important quantum resources for quantum computation and quantum information. In this paper, using entropy-based measures, we investigate the relationships between quantum correlated coherence, which is the coherence between subsystems, and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement measure formulated by quantum correlated coherence is lower and upper bounded by the relative entropy of entanglement and the entanglement of formation, respectively, and equal to the relative entropy of entanglement for all the maximally correlated states.
Reasonable fermionic quantum information theories require relativity
NASA Astrophysics Data System (ADS)
Friis, Nicolai
2016-03-01
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: the marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.
A Generalized Detailed Balance Relation
NASA Astrophysics Data System (ADS)
Ruelle, David
2016-08-01
Given a system M in a thermal bath we obtain a generalized detailed balance relation for the ratio r=π _τ (K→ J)/π _τ (J→ K) of the transition probabilities M:J→ K and M:K→ J in time τ . We assume an active bath, containing solute molecules in metastable states. These molecules may react with M and the transition J→ K occurs through different channels α involving different reactions with the bath. We find that r=sum p^α r^α , where p^α is the probability that channel α occurs, and r^α depends on the amount of heat (more precisely enthalpy) released to the bath in channel α.
Spacecraft Tests of General Relativity
NASA Technical Reports Server (NTRS)
Anderson, John D.
1997-01-01
Current spacecraft tests of general relativity depend on coherent radio tracking referred to atomic frequency standards at the ground stations. This paper addresses the possibility of improved tests using essentially the current system, but with the added possibility of a space-borne atomic clock. Outside of the obvious measurement of the gravitational frequency shift of the spacecraft clock, a successor to the suborbital flight of a Scout D rocket in 1976 (GP-A Project), other metric tests would benefit most directly by a possible improved sensitivity for the reduced coherent data. For purposes of illustration, two possible missions are discussed. The first is a highly eccentric Earth orbiter, and the second a solar-conjunction experiment to measure the Shapiro time delay using coherent Doppler data instead of the conventional ranging modulation.
Spacecraft Tests of General Relativity
NASA Technical Reports Server (NTRS)
Anderson, John D.
1997-01-01
Current spacecraft tests of general relativity depend on coherent radio tracking referred to atomic frequency standards at the ground stations. This paper addresses the possibility of improved tests using essentially the current system, but with the added possibility of a space-borne atomic clock. Outside of the obvious measurement of the gravitational frequency shift of the spacecraft clock, a successor to the suborbital flight of a Scout D rocket in 1976 (GP-A Project), other metric tests would benefit most directly by a possible improved sensitivity for the reduced coherent data. For purposes of illustration, two possible missions are discussed. The first is a highly eccentric Earth orbiter, and the second a solar-conjunction experiment to measure the Shapiro time delay using coherent Doppler data instead of the conventional ranging modulation.
Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments
NASA Astrophysics Data System (ADS)
Pagel, D.; Nalbach, P.; Alvermann, A.; Fehske, H.; Thorwart, M.
2013-10-01
We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal) state. Starting from the exact solution for the oscillator dynamics we study fluctuations of the oscillator position as well as of the energy current through the oscillator under general nonequilibrium conditions. In particular, we formulate a fluctuation-dissipation relation for the oscillator position autocorrelation function that generalizes the standard result for the case of a single bath at thermal equilibrium. Moreover, we show that the generating function for the position operator fulfils a generalized Gallavotti-Cohen-like relation. For the energy transfer through the oscillator, we determine the average energy current together with the current fluctuations. Finally, we discuss the generalization of the cumulant generating function for the energy transfer to nonthermal bath preparations.
Path integral quantization of generalized quantum electrodynamics
Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.
2011-02-15
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green's functions and a discussion about the obtained results are presented.
Path integral quantization of generalized quantum electrodynamics
NASA Astrophysics Data System (ADS)
Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.
2011-02-01
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac’s methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green’s functions and a discussion about the obtained results are presented.
Generalized uncertainty principle and analogue of quantum gravity in optics
NASA Astrophysics Data System (ADS)
Braidotti, Maria Chiara; Musslimani, Ziad H.; Conti, Claudio
2017-01-01
The design of optical systems capable of processing and manipulating ultra-short pulses and ultra-focused beams is highly challenging with far reaching fundamental technological applications. One key obstacle routinely encountered while implementing sub-wavelength optical schemes is how to overcome the limitations set by standard Fourier optics. A strategy to overcome these difficulties is to utilize the concept of a generalized uncertainty principle (G-UP) which has been originally developed to study quantum gravity. In this paper we propose to use the concept of G-UP within the framework of optics to show that the generalized Schrödinger equation describing short pulses and ultra-focused beams predicts the existence of a minimal spatial or temporal scale which in turn implies the existence of maximally localized states. Using a Gaussian wavepacket with complex phase, we derive the corresponding generalized uncertainty relation and its maximally localized states. Furthermore, we numerically show that the presence of nonlinearity helps the system to reach its maximal localization. Our results may trigger further theoretical and experimental tests for practical applications and analogues of fundamental physical theories.
Quantum indistinguishability from general representations of SU(2n)
NASA Astrophysics Data System (ADS)
Harrison, J. M.; Robbins, J. M.
2004-04-01
A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. London Ser. A 453, 1771-1790 (1997)] is generalized within a group-theoretical framework. The construction of Berry and Robbins is reformulated in terms of certain locally flat vector bundles over n-particle configuration space. It is shown how families of such bundles can be constructed from irreducible representations of the group SU(2n). The construction of Berry and Robbins, which leads to a definite connection between spin and statistics (the physically correct connection), is shown to correspond to the completely symmetric representations. The spin-statistics connection is typically broken for general SU(2n) representations, which may admit, for a given value of spin, both Bose and Fermi statistics, as well as parastatistics. The determination of the allowed values of the spin and statistics reduces to the decomposition of certain zero-weight representations of a (generalized) Weyl group of SU(2n). A formula for this decomposition is obtained using the Littlewood-Richardson theorem for the decomposition of representations of U(m+n) into representations of U(m)×U(n).
Certifying the quantumness of a generalized coherent control scenario
Scholak, Torsten Brumer, Paul
2014-11-28
We consider the role of quantum mechanics in a specific coherent control scenario, designing a “coherent control interferometer” as the essential tool that links coherent control to quantum fundamentals. Building upon this allows us to rigorously display the genuinely quantum nature of a generalized weak-field coherent control scenario (utilizing 1 vs. 2 photon excitation) via a Bell-CHSH test. Specifically, we propose an implementation of “quantum delayed-choice” in a bichromatic alkali atom photoionization experiment. The experimenter can choose between two complementary situations, which are characterized by a random photoelectron spin polarization with particle-like behavior on the one hand, and by spin controllability and wave-like nature on the other. Because these two choices are conditioned coherently on states of the driving fields, it becomes physically unknowable, prior to measurement, whether there is control over the spin or not.
Generalized quantum gravity condensates for homogeneous geometries and cosmology
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Pranzetti, Daniele; Ryan, James P.; Sindoni, Lorenzo
2015-12-01
We construct a generalized class of quantum gravity condensate states that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective cosmological dynamics from the group field theory formalism, and thus also from loop quantum gravity. However, they represent an improvement over the simplest condensates used in the literature, in that they are defined by an infinite superposition of graph-based states encoding in a precise way the topology of the spatial manifold. The construction is based on the definition of refinement operators on spin network states, written in a second quantized language. The construction also lends itself easily to application to the case of spherically symmetric quantum geometries.
Quantum gauge freedom in very special relativity
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker; Panigrahi, Prasanta K.
2017-02-01
We demonstrate Yokoyama gaugeon formalism for the Abelian one-form gauge (Maxwell) as well as for Abelian two-form gauge theory in the very special relativity (VSR) framework. In VSR scenario, the extended action due to introduction of gaugeon fields also possesses form invariance under quantum gauge transformations. It is observed that the gaugeon field together with gauge field naturally acquire mass, which is different from the conventional Higgs mechanism. The quantum gauge transformation implements a shift in gauge parameter. Further, we analyze the BRST symmetric gaugeon formalism in VSR which embeds only one subsidiary condition rather than two.
Macrostate equivalence of two general ensembles and specific relative entropies
NASA Astrophysics Data System (ADS)
Mori, Takashi
2016-08-01
The two criteria of ensemble equivalence, i.e., macrostate equivalence and measure equivalence, are investigated for a general pair of states. Macrostate equivalence implies the two ensembles are indistinguishable by the measurement of macroscopic quantities obeying the large-deviation principle, and measure equivalence means that the specific relative entropy of these two states vanishes in the thermodynamic limit. It is shown that measure equivalence implies a macrostate equivalence for a general pair of states by deriving an inequality connecting the large-deviation rate functions to the specific relative Renyi entropies. The result is applicable to both quantum and classical systems. As applications, a sufficient condition for thermalization, the time scale of quantum dynamics of macrovariables, and the second law with strict irreversibility in a quantum quench are discussed.
On solar system dynamics in general relativity
NASA Astrophysics Data System (ADS)
Battista, Emmanuele; Esposito, Giampiero; di Fiore, Luciano; Dell'Agnello, Simone; Simo, Jules; Grado, Aniello
Recent work in the literature has advocated using the Earth-Moon-planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body problem of classical celestial mechanics is just an approximation of a much more complicated setting, where all celestial bodies in the solar system are subject to their mutual gravitational interactions, while solar radiation pressure and other sources of nongravitational perturbations also affect the dynamics, it is conceptually desirable to improve the current understanding of solar system dynamics in general relativity, as a first step towards a more accurate theoretical study of orbital motion in the weak-gravity regime. For this purpose, starting from the Einstein equations in the de Donder-Lanczos gauge, this paper arrives first at the Levi-Civita Lagrangian for the geodesic motion of planets, showing in detail under which conditions the effects of internal structure and finite extension get canceled in general relativity to first post-Newtonian order. The resulting nonlinear ordinary differential equations for the motion of planets and satellites are solved for the Earth’s orbit about the Sun, written down in detail for the Sun-Earth-Moon system, and investigated for the case of planar motion of a body immersed in the gravitational field produced by the other bodies (e.g. planets with their satellites). At this stage, we prove an exact property, according to which the fourth-order time derivative of the original system leads to a linear system of ordinary differential equations. This opens an interesting perspective on forthcoming research on planetary motions in general relativity within the solar system, although the resulting equations remain a challenge for numerical and qualitative studies. Last, the evaluation of quantum corrections to location of collinear and noncollinear Lagrangian points for the planar restricted
Ideal stars and General Relativity
NASA Astrophysics Data System (ADS)
Frønsdal, Christian
2007-12-01
We study a system of differential equations that governs the distribution of matter in the theory of General Relativity. The new element in this paper is the use of a dynamical action principle that includes all the degrees of freedom, matter as well as metric. The matter lagrangian defines a relativistic version of non-viscous, isentropic hydrodynamics. The matter fields are a scalar density and a velocity potential; the conventional, four-vector velocity field is replaced by the gradient of the potential and its scale is fixed by one of the Eulerian equations of motion, an innovation that significantly affects the imposition of boundary conditions. If the density is integrable at infinity, then the metric approaches the Schwarzschild metric at large distances. There are stars without boundary and with finite total mass; the metric shows rapid variation in the neighbourhood of the Schwarzschild radius and there is a very small core where a singularity indicates that the gas laws break down. For stars with boundary there emerges a new, critical relation between the radius and the gravitational mass, a consequence of the stronger boundary conditions. Tentative applications are suggested, to certain Red Giants, and to neutron stars, but the investigation reported here was limited to homogeneous polytropes. Comparison with the results of Oppenheimer and Volkoff on neutron cores shows a close agreement of numerical results. However, in the model the boundary of the star is fixed uniquely by the required matching of the interior metric to the external Schwarzschild metric, which is not the case in the traditional approach. There are solutions for which the metric is very close to the Schwarzshild metric everywhere outside the horizon, where the source is concentrated. The Schwarzschild metric is interpreted as the metric of an ideal, limiting configuration of matter, not as the metric of empty space.
Generalized Kahler Geometry in View of Supersymmetric Quantum Mechanics
NASA Astrophysics Data System (ADS)
Wang, Yicao
2011-04-01
This paper contains a detailed study of generalized Kahler geometry from the viewpoint of quantum 0+1-dimensional supersymmetric σ-model. Peierls brackets rather than canonical quantization are used to quantize the superclassical system. Supercharges (or relevant differential operators) are expressed explicitly and covariantly. Index theorems in this context are also discussed briefly.
Are Einstein's Laws of Relativity a Quantum Effect?
NASA Astrophysics Data System (ADS)
Brändas, Erkki J.
The problem of unifying quantum mechanics with special and general relativity is reconsidered from a relativistically invariant first principles theory. The ingredients are: (i) analytic extension of quantum mechanics into the complex plane via a complex symmetric ansatz, involving (ii) particle- antiparticle states interacting through a kinematical law including (iii) dynamical features such as time- and length-scale contractions and examining (iv) the likelihood of the so-called general Jordan block formations. The extended formulation has a wider set of solutions compared to standard mechanics, with general gauge invariance appropriately embedded. In the present development we establish connections with the Klein-Gordon-Dirac relativistic theories and confirm dynamical features like space and time contractions, Einstein's law of light deflection in a gravitational field, and the appearance of the Schwarzschild-gravitational radius associated with every mass-matter object.
Generalized quantum counting algorithm for non-uniform amplitude distribution
NASA Astrophysics Data System (ADS)
Tan, Jianing; Ruan, Yue; Li, Xi; Chen, Hanwu
2017-03-01
We give generalized quantum counting algorithm to increase universality of quantum counting algorithm. Non-uniform initial amplitude distribution is possible due to the diversity of situations on counting problems or external noise in the amplitude initialization procedure. We give the reason why quantum counting algorithm is invalid on this situation. By modeling in three-dimensional space spanned by unmarked state, marked state and free state to the entire Hilbert space of n qubits, we find Grover iteration can be regarded as improper rotation in the space. This allows us to give formula to solve counting problem. Furthermore, we express initial amplitude distribution in the eigenvector basis of improper rotation matrix. This is necessary to obtain mathematical analysis of counting problem on various situations. Finally, we design four simulation experiments, the results of which show that compared with original quantum counting algorithm, generalized quantum counting algorithm wins great satisfaction from three aspects: (1) Whether initial amplitude distribution is uniform; (2) the diversity of situations on counting problems; and (3) whether phase estimation technique can get phase exactly.
Generalized contexts and consistent histories in quantum mechanics
Losada, Marcelo; Laura, Roberto
2014-05-15
We analyze a restriction of the theory of consistent histories by imposing that a valid description of a physical system must include quantum histories which satisfy the consistency conditions for all states. We prove that these conditions are equivalent to imposing the compatibility conditions of our formalism of generalized contexts. Moreover, we show that the theory of consistent histories with the consistency conditions for all states and the formalism of generalized context are equally useful representing expressions which involve properties at different times.
General Method for Constructing Local Hidden Variable Models for Entangled Quantum States
NASA Astrophysics Data System (ADS)
Cavalcanti, D.; Guerini, L.; Rabelo, R.; Skrzypczyk, P.
2016-11-01
Entanglement allows for the nonlocality of quantum theory, which is the resource behind device-independent quantum information protocols. However, not all entangled quantum states display nonlocality. A central question is to determine the precise relation between entanglement and nonlocality. Here we present the first general test to decide whether a quantum state is local, and show that the test can be implemented by semidefinite programing. This method can be applied to any given state and for the construction of new examples of states with local hidden variable models for both projective and general measurements. As applications, we provide a lower-bound estimate of the fraction of two-qubit local entangled states and present new explicit examples of such states, including those that arise from physical noise models, Bell-diagonal states, and noisy Greenberger-Horne-Zeilinger and W states.
Generalized Jaynes-Cummings model as a quantum search algorithm
Romanelli, A.
2009-07-15
We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states. This algorithm behaves like Grover's algorithm; the optimal search time is proportional to the square root of the size of the search set and the probability to find the searched state oscillates periodically in time. In this frame, it is possible to reinterpret the usual Jaynes-Cummings model as a trivial case of the quantum search algorithm.
Special relativity in a discrete quantum universe
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-10-01
The hypothesis of a discrete fabric of the universe, the "Planck scale," is always on stage since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for the continuum. Here, we show how the clash can be overcome within a discrete quantum theory where the evolution of fields is described by a quantum cellular automaton. The reconciliation is achieved by defining the change of observer as a change of representation of the dynamics, without any reference to space-time. We use the relativity principle, i.e., the invariance of dynamics under change of inertial observer, to identify a change of inertial frame with a symmetry of the dynamics. We consider the full group of such symmetries, and recover the usual Lorentz group in the relativistic regime of low energies, while at the Planck scale the covariance is nonlinearly distorted.
On superpotentials in general relativity
NASA Astrophysics Data System (ADS)
Stolín, Oldřich; Novotný, Jan
2001-10-01
It is shown that the Einstein—Freud, Landau—Lifshitz and Møller tetrad super-potentials represent special cases of a more general construction. The tetrad version of the Landau—Lifshitz superpotential is derived.
Action principle for the generalized harmonic formulation of general relativity
Brown, J. David
2011-10-15
An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona-Casas, and Palenzuela. The relationship between the generalized harmonic action and the Bona, Bona-Casas, and Palenzuela action is discussed in detail.
Quantum dice rolling: a multi-outcome generalization of quantum coin flipping
NASA Astrophysics Data System (ADS)
Aharon, N.; Silman, J.
2010-03-01
The problem of quantum dice rolling (DR)—a generalization of the problem of quantum coin flipping (CF) to more than two outcomes and parties—is studied in both its weak and strong variants. We prove by construction that quantum mechanics allows for (i) weak N-sided DR admitting arbitrarily small bias for any N and (ii) two-party strong N-sided DR saturating Kitaev's bound for any N. To derive (ii) we also prove by construction that quantum mechanics allows for (iii) strong imbalanced CF saturating Kitaev's bound for any degree of imbalance. Furthermore, as a corollary of (ii) we introduce a family of optimal 2m-party strong nm-sided DR protocols for any pair m and n.
Uniform acceleration in general relativity
NASA Astrophysics Data System (ADS)
Friedman, Yaakov; Scarr, Tzvi
2015-10-01
We extend de la Fuente and Romero's (Gen Relativ Gravit 47:33, 2015) defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit solutions. We use generalized Fermi-Walker transport to parallel transport the Frenet basis along the trajectory. In flat spacetime, we obtain velocity and acceleration transformations from a uniformly accelerated system to an inertial system. We obtain the time dilation between accelerated clocks. We apply our acceleration transformations to the motion of a charged particle in a constant electromagnetic field and recover the Lorentz-Abraham-Dirac equation.
c -number quantum generalized Langevin equation for an open system
NASA Astrophysics Data System (ADS)
Kantorovich, L.; Ness, H.; Stella, L.; Lorenz, C. D.
2016-11-01
We derive a c -number generalized Langevin equation (GLE) describing the evolution of the expectation values xixit of the atomic position operators xi of an open system. The latter is coupled linearly to a harmonic bath kept at a fixed temperature. The equations of motion contain a non-Markovian friction term with the classical kernel [L. Kantorovich, Phys. Rev. B 78, 094304 (2008), 10.1103/PhysRevB.78.094304] and a zero mean non-Gaussian random force with correlation functions that depend on the initial preparation of the open system. We used a density operator formalism without assuming that initially the combined system was decoupled. The only approximation made in deriving quantum GLE consists of assuming that the Hamiltonian of the open system at time t can be expanded up to the second order with respect to operators of atomic displacements ui=xi-
Quantum entanglement and a metaphysics of relations
NASA Astrophysics Data System (ADS)
Esfeld, Michael
This paper argues for a metaphysics of relations based on a characterization of quantum entanglement in terms of non-separability, thereby regarding entanglement as a sort of holism. By contrast to a radical metaphysics of relations, the position set out in this paper recognizes things that stand in the relations, but claims that, as far as the relations are concerned, there is no need for these things to have qualitative intrinsic properties underlying the relations. This position thus opposes a metaphysics of individual things that are characterized by intrinsic properties. A principal problem of the latter position is that it seems that we cannot gain any knowledge of these properties insofar as they are intrinsic. Against this background, the rationale behind a metaphysics of relations is to avoid a gap between epistemology and metaphysics.
Casimir effect, quantum fluctuations and related topics
NASA Astrophysics Data System (ADS)
Hushwater, Velvel Shaia
Casimir forces are the very long-range (retarded) forces between electrically neutral systems. Such forces may be thought of as arising from the quantum fluctuations of the electromagnetic field. Contrary to popular opinion such forces need not be attractive. After giving a foundation of the method of the change in the 'zero-point energy' we show how other methods to compute Casimir forces follow from it. We consider the repulsion between electric and magnetic dipoles induced by vacuum fluctuations of electromagnetic field. The calculation are made by the use of the Heisenberg picture operators and by the stochastic electrodynamics approach. We present a purely geometrical proof of the image method, and use it to discuss the Casimir interaction between an atom and a plate. We study the Casimir repulsion between a perfectly conducting and an infinitely permeable plate with the radiation pressure approach. This example illustrates how a repulsive force arises as a consequence of the redistribution of vacuum-field modes corresponding to specific boundary conditions. We show that result is independent of a cutoff function. Discussing the connection with perturbation theory, we prove the negativity of the leading order shift in the ground state. The Casimir effect supports the reality of the 'zero- point energy.' To clarify this we present a novel approach to quantum theory, based on the principle of the quantization of the ensemble-averaged action variable. This quantization leads to the probabilistic description of coordinates and momentum as random variables, which satisfy the uncertainty relation. Using such variables we show that the 'quantum momentum function' must satisfy the Riccati differential equation, which can be converted to the Schrodinger equation for the Ψ function. We derive also the form of basic operators and the rule for probabilities in quantum mechanics. We show that the approach leads to a simple interpretation of gauge invariance, and discuss
Numerical Hydrodynamics in General Relativity.
Font, José A
2000-01-01
The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented.
Renyi generalizations of the conditional quantum mutual information
2015-02-23
cocycles. Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences, 83A(2):251–263, December 1983. [2] Gerardo Adesso... Mathematical and General, 37(5):L55, 2004. [4] Tsuyoshi Ando. Convexity of certain maps on positive definite matrices and applications to Hadamard...of Mathematical Physics, 56(2):022202, February 2015. arXiv:1310.7178. [6] Pascal Basler. Characterization of correlations in classical and quantum
On the general constraints in single qubit quantum process tomography
Bhandari, Ramesh; Peters, Nicholas A.
2016-05-18
In this study, we briefly review single-qubit quantum process tomography for trace-preserving and nontrace-preserving processes, and derive explicit forms of the general constraints for fitting experimental data. These forms provide additional insight into the structure of the process matrix. We illustrate this with several examples, including a discussion of qubit leakage error models and the intuition which can be gained from their process matrices.
General relativity and satellite orbits
NASA Technical Reports Server (NTRS)
Rubincam, D. P.
1975-01-01
The general relativistic correction to the position of a satellite is found by retaining Newtonian physics for an observer on the satellite and introducing a potential. The potential is expanded in terms of the Keplerian elements of the orbit and substituted in Lagrange's equations. Integration of the equations shows that a typical earth satellite with small orbital eccentricity is displaced by about 17 cm. from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. The moon is displaced by about the same amounts. Application of the equations to Mercury gives a total displacement of about 58 km. after one orbit and a maximum periodic displacement of about 12 km.
Autonomous quantum to classical transitions and the generalized imaging theorem
Briggs, John S.; Feagin, James M.
2016-03-16
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.
Holonomy groups in general relativity
Hall, G.S.; Kay, W.
1988-02-01
The infinitesimal holonomy group structure of space-time is discussed and related to the Petrov type of the Weyl tensor and the algebraic (Segre) type of the energy-momentum tensor. The number of covariant derivatives of the curvature tensor required to determine the infinitesimal holonomy group is determined in each case and the complete classification scheme is tabulated. Some special cases of physical interest are investigated in more detail. A geometrical approach is followed throughout.
Role of information theoretic uncertainty relations in quantum theory
Jizba, Petr; Dunningham, Jacob A.; Joo, Jaewoo
2015-04-15
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.
Canonical quantization of general relativity in discrete space-times.
Gambini, Rodolfo; Pullin, Jorge
2003-01-17
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.
Fluctuation-dissipation relation in a resonantly driven quantum medium.
Erukhimova, Maria; Tokman, Mikhail
2015-06-15
Noise associated with the spontaneous emission in a coherently driven medium is calculated. The significant field-induced modification of relation between the noise power and damping constant in a thermal reservoir is obtained. The nonlinear noise exchange between different atomic frequencies leads to violation of standard relations dictated by the fluctuation-dissipation theorem. The developed general method is applied to the EIT system, attractive for realization of different quantum-information processing devices. It is shown that there is a significant factor defining the thermal noise at operating frequency in the EIT system. It is the averaged number of thermal photons at low frequency of ground state splitting.
"Spring theory of relativity" originating from quantum mechanics
NASA Astrophysics Data System (ADS)
Yefremov, Alexander P.
Compact derivation of mathematical equations similar to those of quantum and classical mechanics is given on the base of fractal decomposition of a three-dimensional space. In physical units the equations become Shrödinger and Hamilton-Jacobi equations, the wave function of a free particle associated with a virtual ring. Locally uniform motion of the ring in the physical space provides an original helix (or regular cylindrical spring) model of a relativistic theory equivalent in results with special relativity, the free particle's relativistic Lagrangian emerging automatically. Irregular spring model generates theory similar to general relativity.
Pulsar timing and general relativity
NASA Technical Reports Server (NTRS)
Backer, D. C.; Hellings, R. W.
1986-01-01
Techniques are described for accounting for relativistic effects in the analysis of pulsar signals. Design features of instrumentation used to achieve millisecond accuracy in the signal measurements are discussed. The accuracy of the data permits modeling the pulsar physical characteristics from the natural glitches in the emissions. Relativistic corrections are defined for adjusting for differences between the pulsar motion in its spacetime coordinate system relative to the terrestrial coordinate system, the earth's motion, and the gravitational potentials of solar system bodies. Modifications of the model to allow for a binary pulsar system are outlined, including treatment of the system as a point mass. Finally, a quadrupole model is presented for gravitational radiation and techniques are defined for using pulsars in the search for gravitational waves.
Pulsar timing and general relativity
NASA Technical Reports Server (NTRS)
Backer, D. C.; Hellings, R. W.
1986-01-01
Techniques are described for accounting for relativistic effects in the analysis of pulsar signals. Design features of instrumentation used to achieve millisecond accuracy in the signal measurements are discussed. The accuracy of the data permits modeling the pulsar physical characteristics from the natural glitches in the emissions. Relativistic corrections are defined for adjusting for differences between the pulsar motion in its spacetime coordinate system relative to the terrestrial coordinate system, the earth's motion, and the gravitational potentials of solar system bodies. Modifications of the model to allow for a binary pulsar system are outlined, including treatment of the system as a point mass. Finally, a quadrupole model is presented for gravitational radiation and techniques are defined for using pulsars in the search for gravitational waves.
Separate universes beyond general relativity
NASA Astrophysics Data System (ADS)
Hu, Wayne; Joyce, Austin
2017-02-01
We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate Friedmann-Robertson-Walker cosmology in their angle average. In order to be able to identify the local volume expansion and curvature in a long-wavelength perturbation with those of the separate universe, we show that the lapse perturbation must be much smaller in amplitude than the curvature potential on a time slicing that comoves with the Einstein tensor. Interpreting the Einstein tensor as an effective stress-energy tensor, the condition is that the effective stress energy comoves with freely falling synchronous observers who establish the local expansion, so that the local curvature is conserved. By matching the expansion history of these synchronous observers in cosmological simulations, one can establish and test consistency relations even in the nonlinear regime of modified gravity theories.
Pfalzgraff, William C; Kelly, Aaron; Markland, Thomas E
2015-12-03
The development of methods that can efficiently and accurately treat nonadiabatic dynamics in quantum systems coupled to arbitrary atomistic environments remains a significant challenge in problems ranging from exciton transport in photovoltaic materials to electron and proton transfer in catalysis. Here we show that our recently introduced MF-GQME approach, which combines Ehrenfest mean field theory with the generalized quantum master equation framework, is able to yield quantitative accuracy over a wide range of charge-transfer regimes in fully atomistic environments. This is accompanied by computational speed-ups of up to 3 orders of magnitude over a direct application of Ehrenfest theory. This development offers the opportunity to efficiently investigate the atomistic details of nonadiabatic quantum relaxation processes in regimes where obtaining accurate results has previously been elusive.
Quantum Bayesianism as the basis of general theory of decision-making.
Khrennikov, Andrei
2016-05-28
We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability-one the basic laws of classical probability theory. © 2016 The Author(s).
Quantum Bayesianism as the basis of general theory of decision-making
2016-01-01
We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability—one the basic laws of classical probability theory. PMID:27091160
The role of relative entropy in quantum information theory
NASA Astrophysics Data System (ADS)
Vedral, V.
2002-01-01
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates this review from the usual presentation in that they are shown to follow logically from one crucial property of relative entropy. Within the review, optimal bounds on the enhanced speed that quantum computers can achieve over their classical counterparts are outlined using information-theoretic arguments. In addition, important implications of quantum information theory for thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations, including quantum superdense coding, quantum teleportation, and Deutsch's and Grover's algorithms, are also included.
A New Generalization of von Neumann Relative Entropy
NASA Astrophysics Data System (ADS)
Li, Jing; Cao, Huaixin
2017-08-01
In quantum information, von Neumann relative entropy has a great applications and operational interpretations in diverse fields, and von Neumann entropy is an important tool for describing the uncertainty of a quantum state. In this paper, we generalize the classical von Neumann relative entropy S(ρ||σ) and von Neumann entropy S(ρ) to f-von Neumann relative entropy \\widetilde {S}f(ρ ||σ ) and f-von Neumann entropy \\widetilde {S}f(ρ ) induced by a logarithm-like function f, respectively, and explore their properties. We prove that \\widetilde {S}f(ρ ||σ ) is nonnegative and then prove that \\widetilde {S}f(ρ ) has nonnegativity, boundedness, concavity, subadditivity and so on. Later, we show the stability and continuity of the \\widetilde {S}f(ρ ) with respect to the trace distance. In the case that f(x) = -log x, the resulted entropies reduce the classical von Neumann relative entropy and von Neumann entropy, respectively. This means that our results extend the usual results to a more general setting and then have some potential applications in quantum information.
Quantum discord for the general two-qubit case
NASA Astrophysics Data System (ADS)
Wu, Xiaohua; Zhou, Tao
2015-06-01
Recently, Girolami and Adesso (Phys Rev A 83: 052108, 2011) have demonstrated that the calculation of quantum discord for two-qubit case can be viewed as to solve a pair of transcendental equation. In the present work, we introduce the generalized Choi-Jamiolkowski isomorphism and apply it as a convenient tool for constructing transcendental equations. For the general two-qubit case, we show that the transcendental equations always have a finite set of universal solutions; this result can be viewed as a generalization of the one obtained by Ali et al. (Phys Rev A 81: 042105, 2010). For a subclass of state, we find the analytical solutions by solving the transcendental equations.
Position-dependent mass quantum Hamiltonians: general approach and duality
NASA Astrophysics Data System (ADS)
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.
Autonomous quantum to classical transitions and the generalized imaging theorem
Briggs, John S.; Feagin, James M.
2016-03-16
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantummore » to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.« less
Generalized Wilson chain for solving multichannel quantum impurity problems
NASA Astrophysics Data System (ADS)
Mitchell, Andrew K.; Galpin, Martin R.; Wilson-Fletcher, Samuel; Logan, David E.; Bulla, Ralf
2014-03-01
The numerical renormalization group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within dynamical mean field theory. Here we present a simple generalization of the Wilson chain, which improves the scaling of computational cost with the number of conduction bands, bringing more complex problems within reach. The method is applied to calculate the t matrix of the three-channel Kondo model at T =0, which shows universal crossovers near non-Fermi-liquid critical points. A nonintegrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening and overscreening mechanisms.
Non-Markovian quantum jump with generalized Lindblad master equation.
Huang, X L; Sun, H Y; Yi, X X
2008-10-01
The Monte Carlo wave function method or the quantum-trajectory-jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. We extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Markovian jump approach and the computational efficiency of this method is also discussed.
The quantum chaos conjecture and generalized continued fractions
NASA Astrophysics Data System (ADS)
Pustyl'nikov, L. D.
2003-04-01
The proof of the quantum chaos conjecture is given for a class of systems including as a special case the model of a rotating particle under the action of periodic impulse perturbations. (The distribution of the distances between adjacent energy levels is close to the Poisson distribution and differs from it by terms of the third order of smallness.) The proof reduces to a result in number theory on the distribution of the distances between adjacent fractional parts of values of a polynomial, while the estimate of the remainder term is based on the new theory of generalized continued fractions for vectors.
Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes
Houshmand, Monireh; Hosseini-Khayat, Saied
2011-02-15
Quantum convolutional codes, like their classical counterparts, promise to offer higher error correction performance than block codes of equivalent encoding complexity, and are expected to find important applications in reliable quantum communication where a continuous stream of qubits is transmitted. Grassl and Roetteler devised an algorithm to encode a quantum convolutional code with a ''pearl-necklace'' encoder. Despite their algorithm's theoretical significance as a neat way of representing quantum convolutional codes, it is not well suited to practical realization. In fact, there is no straightforward way to implement any given pearl-necklace structure. This paper closes the gap between theoretical representation and practical implementation. In our previous work, we presented an efficient algorithm to find a minimal-memory realization of a pearl-necklace encoder for Calderbank-Shor-Steane (CSS) convolutional codes. This work is an extension of our previous work and presents an algorithm for turning a pearl-necklace encoder for a general (non-CSS) quantum convolutional code into a realizable quantum convolutional encoder. We show that a minimal-memory realization depends on the commutativity relations between the gate strings in the pearl-necklace encoder. We find a realization by means of a weighted graph which details the noncommutative paths through the pearl necklace. The weight of the longest path in this graph is equal to the minimal amount of memory needed to implement the encoder. The algorithm has a polynomial-time complexity in the number of gate strings in the pearl-necklace encoder.
Plimak, L.I.; Fleischhauer, M.; Olsen, M.K.; Collett, M.J.
2003-01-01
We present an introduction to phase-space techniques (PST) based on a quantum-field-theoretical (QFT) approach. In addition to bridging the gap between PST and QFT, our approach results in a number of generalizations of the PST. First, for problems where the usual PST do not result in a genuine Fokker-Planck equation (even after phase-space doubling) and hence fail to produce a stochastic differential equation (SDE), we show how the system in question may be approximated via stochastic difference equations (S{delta}E). Second, we show that introducing sources into the SDE's (or S{delta}E's) generalizes them to a full quantum nonlinear stochastic response problem (thus generalizing Kubo's linear reaction theory to a quantum nonlinear stochastic response theory). Third, we establish general relations linking quantum response properties of the system in question to averages of operator products ordered in a way different from time normal. This extends PST to a much wider assemblage of operator products than are usually considered in phase-space approaches. In all cases, our approach yields a very simple and straightforward way of deriving stochastic equations in phase space.
Quantum interferometric visibility as a witness of general relativistic proper time
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Brukner, Časlav
2011-01-01
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter–wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov–Bohm effect, where a particle in a flat space–time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'—a particle with evolving internal degrees of freedom—that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space–time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. PMID:22009037
NASA Astrophysics Data System (ADS)
Thapliyal, Kishore; Verma, Amit; Pathak, Anirban
2015-12-01
Recently, a large number of protocols for bidirectional controlled state teleportation (BCST) have been proposed using n-qubit entangled states (nin {5,6,7}) as quantum channel. Here, we propose a general method of selecting multiqubit (n>4) quantum channels suitable for BCST and show that all the channels used in the existing protocols of BCST can be obtained using the proposed method. Further, it is shown that the quantum channels used in the existing protocols of BCST form only a negligibly small subset of the set of all the quantum channels that can be constructed using the proposed method to implement BCST. It is also noted that all these quantum channels are also suitable for controlled bidirectional remote state preparation. Following the same logic, methods for selecting quantum channels for other controlled quantum communication tasks, such as controlled bidirectional joint remote state preparation and controlled quantum dialogue, are also provided.
General Relativity in (1 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2008-01-01
We describe a theory of gravity in (1 + 1) dimensions that can be thought of as a toy model of general relativity. The theory should be a useful pedagogical tool, because it is mathematically much simpler than general relativity but shares much of the same conceptual structure; in particular, it gives a simple illustration of how gravity arises…
General Relativity in (1 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2008-01-01
We describe a theory of gravity in (1 + 1) dimensions that can be thought of as a toy model of general relativity. The theory should be a useful pedagogical tool, because it is mathematically much simpler than general relativity but shares much of the same conceptual structure; in particular, it gives a simple illustration of how gravity arises…
Directions in General Relativity, Vol. 1
NASA Astrophysics Data System (ADS)
Hu, B. L.; Ryan, M. P., Jr.; Vishveshwara, C. V.
2005-10-01
1. Remarks concerning the geometrics of gravity, gauge fields and quantum theory J. S. Anandan; 2. Gravity and the unification of fundamental interactions R. L. Arnowitt and P. Nath; 3. Minisuperspaces: symmetrics and quantization A. Ashtekar, R. S. Tate and C. Uggla; 4. Quantum cosmology B. K. Berger; 5. A pictorial history of some gravitational instanton D. Brill and K.- T. Pirk; 6. No time machines from lightlike sources in 2+1 gravity S. Deser and A. R. Steif; 7. Inhomogeneity and anisotropy genertation in FRW cosmologies G. F. R. Ellis and D. R. Matravers; 8. Misner, kinks and Black Holes D. Finkelstein; 9. The quantum mechanics of closed systems J. B. Hartle; 10. Cosmological vacuum open system W. A. Hiscock and D. A. Samuel; 11. Minisuperspace as a quantum open system B. L. Hu, J. P. Paz and S. Sinha; 12. Ricci flow on minisuperspaces and the geometry-topology problem J. Isenberg and M. Jackson; 13. Classical and quantum dynamics of Black Hole interiors W. Israel; 14. Matter time in canonical quantum gravity K. V. Kuchar; 15. The isotropy and homogeneity of the universe R. A. Matzner; 16. Recent advances in ADM reduction V. Moncrief; 17. Some progress in classical canonical gravity J. M. Nester; 18. Harmonic map formulation of colliding electrovac place waves Y. Nutku; 19. Geometry, the renormalization groups and gravity D. J. O'Connor and C. R. Stephens; 20. An example of the indeterminacy of the already-unified theory R. Penrose; 21. Nonstatic metric of Hiscock-Gott type A. K. Raychaudhuri; 22. Non-standard phase space variables, quantization and path-integrals, or little ado about much M. P. Ryan, Jr. and Sergio Hojmann; 23. The present status of the decaying neutrino theory D. W. Sciama; 24. Exploiting the computer to investigate Black Holes and cosmic censorship S. L. Shapiro and S. A. Teukolsky; 25. Misner space as a prototype for almost any pathology K. S. Thorne; 26. Relativity and rotation C. V. Vishveshwara; 27. The first law of Black Hole
Some Properties of Generalized Connections in Quantum Gravity
NASA Astrophysics Data System (ADS)
Velhinho, J. M.
2002-12-01
Theories of connections play an important role in fundamental interactions, including Yang-Mills theories and gravity in the Ashtekar formulation. Typically in such cases, the classical configuration space {A}/ {G} of connections modulo gauge transformations is an infinite dimensional non-linear space of great complexity. Having in mind a rigorous quantization procedure, methods of functional calculus in an extension of {A}/ {G} have been developed. For a compact gauge group G, the compact space /line { {A}{ {/}} {G}} ( ⊃ {A}/ {G}) introduced by Ashtekar and Isham using C*-algebraic methods is a natural candidate to replace {A}/ {G} in the quantum context, 1 allowing the construction of diffeomorphism invariant measures. 2,3,4 Equally important is the space of generalized connections bar {A} introduced in a similar way by Baez. 5 bar {A} is particularly useful for the definition of vector fields in /line { {A}{ {/}} {G}} , fundamental in the construction of quantum observables. 6 These works crucially depend on the use of (generalized) Wilson variables associated to certain types of curves. We will consider the case of piecewise analytic curves, 1,2,5 althought most of the arguments apply equally to the piecewise smooth case. 7,8...
Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect
NASA Astrophysics Data System (ADS)
Yang, Bo; Hu, Zi-Xiang; Lee, Ching Hua; Papić, Z.
2017-04-01
We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems that are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to expand any translation-invariant interaction over a complete basis, and directly reveals the intrinsic metric of incompressible FQH fluids. We show that purely anisotropic pseudopotentials give rise to new types of bound states for small particle clusters in the infinite plane, and can be used as a diagnostic of FQH nematic order. We also demonstrate that generalized pseudopotentials quantify the anisotropic contribution to the effective interaction potential, which can be particularly large in models of fractional Chern insulators.
Tsallis entropy and general polygamy of multiparty quantum entanglement in arbitrary dimensions
NASA Astrophysics Data System (ADS)
Kim, Jeong San
2016-12-01
We establish a unified view of the polygamy of multiparty quantum entanglement in arbitrary dimensions. Using quantum Tsallis-q entropy, we provide a one-parameter class of polygamy inequalities of multiparty quantum entanglement. This class of polygamy inequalities reduces to the known polygamy inequalities based on tangle and entanglement of assistance for a selective choice of the parameter q . We further provide one-parameter generalizations of various quantum correlations based on Tsallis-q entropy. By investigating the properties of the generalized quantum correlations, we provide a sufficient condition on which the Tsallis-q polygamy inequalities hold in multiparty quantum systems of arbitrary dimensions.
Testing general relativity with current cosmological data
Daniel, Scott F.; Linder, Eric V.; Smith, Tristan L.; Caldwell, Robert R.; Cooray, Asantha; Leauthaud, Alexie; Lombriser, Lucas
2010-06-15
Deviations from general relativity, such as could be responsible for the cosmic acceleration, would influence the growth of large-scale structure and the deflection of light by that structure. We clarify the relations between several different model-independent approaches to deviations from general relativity appearing in the literature, devising a translation table. We examine current constraints on such deviations, using weak gravitational lensing data of the CFHTLS and COSMOS surveys, cosmic microwave background radiation data of WMAP5, and supernova distance data of Union2. A Markov chain Monte Carlo likelihood analysis of the parameters over various redshift ranges yields consistency with general relativity at the 95% confidence level.
Universality in uncertainty relations for a quantum particle
NASA Astrophysics Data System (ADS)
Kechrimparis, Spiros; Weigert, Stefan
2016-09-01
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle’s variances and its covariance is bounded from below. Whenever a global minimum exists, an uncertainty relation has been obtained. The squeezed number states of a harmonic oscillator are found to be universal: no other pure or mixed states will saturate any such relation. Geometrically, we identify a convex uncertainty region in the space of second moments which is bounded by the inequality derived by Robertson and Schrödinger. Our approach provides a unified perspective on existing uncertainty relations for a single continuous variable, and it leads to new inequalities for second moments which can be checked experimentally.
Quantum dynamics in continuum for proton transport--generalized correlation.
Chen, Duan; Wei, Guo-Wei
2012-04-07
As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and
Quantum dynamics in continuum for proton transport—Generalized correlation
Chen, Duan; Wei, Guo-Wei
2012-01-01
As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and
Quantum dynamics in continuum for proton transport—Generalized correlation
NASA Astrophysics Data System (ADS)
Chen, Duan; Wei, Guo-Wei
2012-04-01
As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and
NASA Astrophysics Data System (ADS)
Erol, V.
2016-04-01
Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.
Erol, V.
2016-04-21
Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.
Hoang, Andre H.; Ruiz-Femenia, Pedro
2006-12-01
We discuss the form and construction of general color singlet heavy particle-antiparticle pair production currents for arbitrary quantum numbers, and issues related to evanescent spin operators and scheme dependences in nonrelativistic QCD in n=3-2{epsilon} dimensions. The anomalous dimensions of the leading interpolating currents for heavy quark and colored scalar pairs in arbitrary {sup 2S+1}L{sub J} angular-spin states are determined at next-to-leading order in the nonrelativistic power counting.
A General Framework for Relative Impact Indicators.
ERIC Educational Resources Information Center
Egghe, Leo; Rousseau, Ronald
2003-01-01
Discussion of the assessment and comparison of scientific journals, bibliometrics, and types of impact factors focuses on a general framework for the relative comparison of journal impact. Highlights include the relative impact of a journal within a set of journals, or meta-journal; and mathematical explorations of relative indicators. (Author/LRW)
Uncertainty relations for general phase spaces
NASA Astrophysics Data System (ADS)
Werner, Reinhard F.
2016-04-01
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the equality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.
Fang Baolong; Yang Zhen; Ye Liu
2009-05-15
We propose a scheme for implementing a partial general quantum cloning machine with superconducting quantum-interference devices coupled to a nonresonant cavity. By regulating the time parameters, our system can perform optimal symmetric (asymmetric) universal quantum cloning, optimal symmetric (asymmetric) phase-covariant cloning, and optimal symmetric economical phase-covariant cloning. In the scheme the cavity is only virtually excited, thus, the cavity decay is suppressed during the cloning operations.
Einstein and General Relativity: Historical Perspectives.
ERIC Educational Resources Information Center
Chandrasekhar, S.
1979-01-01
This paper presented in the 1978 Oppenheimer Memorial Lecture at Los Alamos Scientific Laboratories on August 17, 1978, discusses Einstein's contributions to physics, in particular, his discovery of the general theory of relativity. (HM)
Einstein and General Relativity: Historical Perspectives.
ERIC Educational Resources Information Center
Chandrasekhar, S.
1979-01-01
This paper presented in the 1978 Oppenheimer Memorial Lecture at Los Alamos Scientific Laboratories on August 17, 1978, discusses Einstein's contributions to physics, in particular, his discovery of the general theory of relativity. (HM)
Particle Pair Production in Cosmological General Relativity
NASA Astrophysics Data System (ADS)
Oliveira, Firmin J.
2012-12-01
The Cosmological General Relativity (CGR) of Carmeli, a 5-dimensional (5-D) theory of time, space and velocity, predicts the existence of an acceleration a 0= c/ τ due to the expansion of the universe, where c is the speed of light in vacuum, τ=1/ h is the Hubble-Carmeli time constant, where h is the Hubble constant at zero distance and no gravity. The Carmeli force on a particle of mass m is F c = ma 0, a fifth force in nature. In CGR, the effective mass density ρ eff = ρ- ρ c , where ρ is the matter density and ρ c is the critical mass density which we identify with the vacuum mass density ρ vac =- ρ c . The fields resulting from the weak field solution of the Einstein field equations in 5-D CGR and the Carmeli force are used to hypothesize the production of a pair of particles. The mass of each particle is found to be m= τc 3/4 G, where G is Newton's constant. The vacuum mass density derived from the physics is ρ vac =- ρ c =-3/8 πGτ 2. We make a connection between the cosmological constant of the Friedmann-Robertson-Walker model and the vacuum mass density of CGR by the relation Λ=-8 πGρ vac =3/ τ 2. Each black hole particle defines its own volume of space enclosed by the event horizon, forming a sub-universe. The cosmic microwave background (CMB) black body radiation at the temperature T o =2.72548 K which fills that volume is found to have a relationship to the ionization energy of the Hydrogen atom. Define the radiation energy ɛ γ =(1- g) mc 2/ N γ , where (1- g) is the fraction of the initial energy mc 2 which converts to photons, g is a function of the baryon density parameter Ω b and N γ is the total number of photons in the CMB radiation field. We make the connection with the ionization energy of the first quantum level of the Hydrogen atom by the hypothesis ɛ_{γ} = ( 1 - g ) m c^2 / N_{γ } = α^2 μ c^2/2, where α is the fine-structure constant and μ= m p f/(1+ f), where f= m e / m p with m e the electron mass and m p the
Detecting the relative localisation of quantum particles
NASA Astrophysics Data System (ADS)
Knott, P. A.; Sindt, J.; Dunningham, J. A.
2013-06-01
One interpretation of how the classical world emerges from quantum physics involves the build-up of certain robust entangled states between particles due to scattering events [1]. This is intriguing because it links classical behaviour with the uniquely quantum effect of entanglement and differs from other interpretations that say classicality arises when quantum correlations are lost or neglected in measurements. However, the problem with this new interpretation has been finding an experimental way of verifying it. Here we outline a straightforward scheme that enables just that and should, in principle, allow experiments to confirm the theory to any desired degree of accuracy.
On homogeneous second order linear general quantum difference equations.
Faried, Nashat; Shehata, Enas M; El Zafarani, Rasha M
2017-01-01
In this paper, we prove the existence and uniqueness of solutions of the β-Cauchy problem of second order β-difference equations [Formula: see text] [Formula: see text], in a neighborhood of the unique fixed point [Formula: see text] of the strictly increasing continuous function β, defined on an interval [Formula: see text]. These equations are based on the general quantum difference operator [Formula: see text], which is defined by [Formula: see text], [Formula: see text]. We also construct a fundamental set of solutions for the second order linear homogeneous β-difference equations when the coefficients are constants and study the different cases of the roots of their characteristic equations. Finally, we drive the Euler-Cauchy β-difference equation.
The Unruh Effect in General Boundary Quantum Field Theory
NASA Astrophysics Data System (ADS)
Colosi, Daniele; Rätzel, Dennis
2013-03-01
In the framework of the general boundary formulation (GBF) of scalar quantum field theory we obtain a coincidence of expectation values of local observables in the Minkowski vacuum and in a particular state in Rindler space. This coincidence could be seen as a consequence of the identification of the Minkowski vacuum as a thermal state in Rindler space usually associated with the Unruh effect. However, we underline the difficulty in making this identification in the GBF. Beside the Feynman quantization prescription for observables that we use to derive the coincidence of expectation values, we investigate an alternative quantization prescription called Berezin-Toeplitz quantization prescription, and we find that the coincidence of expectation values does not exist for the latter.
The General Fishbone Like Dispersion Relation
NASA Astrophysics Data System (ADS)
Zonca, Fulvio
2015-12-01
The following sections are included: * Introduction * Motivation and outline * Fundamental equations * The collisionless gyrokinetic equation * Vorticity equation * Quasi-neutrality condition * Perpendicular Ampère's law * Studying collective modes in burning plasmas * Ideal plasma equilibrium in the low-β limit * Approximations for the energetic population * Characteristic frequencies of particle motions * Alfvén wave frequency and wavelength orderings * Applications of the general theoretical framework * The general fishbone like dispersion relation * Properties of the fishbone like dispersion relation * Derivation of the fishbone like dispersion relation * Special cases of the fishbone like dispersion relation * Toroidal Alfvén Eigenmodes (TAE) * Alfvén Cascades * Summary and discussions * Acknowledgments * References
A golden age of general relativity? Some remarks on the history of general relativity
NASA Astrophysics Data System (ADS)
Goenner, Hubert
2017-03-01
This article deals with the concepts "renaissance" and "low water mark between 1925 and 1955" of general relativity suggested in the literature. By empirical data, it is shown that no such period did exist. Research on general relativity continued continuously since the 1920s interrupted only by the second world war. On a broad scale, research on general relativity started only after 1945.
Misra, Avijit; Biswas, Anindya; Pati, Arun K; Sen De, Aditi; Sen, Ujjwal
2015-05-01
Quantum discord is a measure of quantum correlations beyond the entanglement-separability paradigm. It is conceptualized by using the von Neumann entropy as a measure of disorder. We introduce a class of quantum correlation measures as differences between total and classical correlations, in a shared quantum state, in terms of the sandwiched relative Rényi and Tsallis entropies. We compare our results with those obtained by using the traditional relative entropies. We find that the measures satisfy all the plausible axioms for quantum correlations. We evaluate the measures for shared pure as well as paradigmatic classes of mixed states. We show that the measures can faithfully detect the quantum critical point in the transverse quantum Ising model and find that they can be used to remove an unquieting feature of nearest-neighbor quantum discord in this respect. Furthermore, the measures provide better finite-size scaling exponents of the quantum critical point than the ones for other known order parameters, including entanglement and information-theoretic measures of quantum correlations.
NASA Astrophysics Data System (ADS)
Misra, Avijit; Biswas, Anindya; Pati, Arun K.; SenDe, Aditi; Sen, Ujjwal
2015-05-01
Quantum discord is a measure of quantum correlations beyond the entanglement-separability paradigm. It is conceptualized by using the von Neumann entropy as a measure of disorder. We introduce a class of quantum correlation measures as differences between total and classical correlations, in a shared quantum state, in terms of the sandwiched relative Rényi and Tsallis entropies. We compare our results with those obtained by using the traditional relative entropies. We find that the measures satisfy all the plausible axioms for quantum correlations. We evaluate the measures for shared pure as well as paradigmatic classes of mixed states. We show that the measures can faithfully detect the quantum critical point in the transverse quantum Ising model and find that they can be used to remove an unquieting feature of nearest-neighbor quantum discord in this respect. Furthermore, the measures provide better finite-size scaling exponents of the quantum critical point than the ones for other known order parameters, including entanglement and information-theoretic measures of quantum correlations.
General covariance in quantum gravity at a Lifshitz point
NASA Astrophysics Data System (ADS)
Hořava, Petr; Melby-Thompson, Charles M.
2010-09-01
In the minimal formulation of gravity with Lifshitz-type anisotropic scaling, the gauge symmetries of the system are foliation-preserving diffeomorphisms of spacetime. Consequently, compared to general relativity, the spectrum contains an extra scalar graviton polarization. Here we investigate the possibility of extending the gauge group by a local U(1) symmetry to “nonrelativistic general covariance.” This extended gauge symmetry eliminates the scalar graviton, and forces the coupling constant λ in the kinetic term of the minimal formulation to take its relativistic value, λ=1. The resulting theory exhibits anisotropic scaling at short distances, and reproduces many features of general relativity at long distances.
Anisotropic Generalized Ghost Pilgrim Dark Energy Model in General Relativity
NASA Astrophysics Data System (ADS)
Santhi, M. Vijaya; Rao, V. U. M.; Aditya, Y.
2017-02-01
A spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type- I Universe filled with matter and generalized ghost pilgrim dark energy (GGPDE) has been studied in general theory of relativity. To obtain determinate solution of the field equations we have used scalar expansion proportional to the shear scalar which leads to a relation between the metric potentials. Some well-known cosmological parameters (equation of state (EoS) parameter ( ω Λ), deceleration parameter ( q) and squared speed of sound {vs2}) and planes (ω _{Λ }-dot {ω }_{Λ } and statefinder) are constructed for obtained model. The discussion and significance of these parameters is totally done through pilgrim dark energy parameter ( β) and cosmic time ( t).
NASA Astrophysics Data System (ADS)
Wu, Zhu Lian; Gao, Ming Xuan; Wang, Ting Ting; Wan, Xiao Yan; Zheng, Lin Ling; Huang, Cheng Zhi
2014-03-01
A general quantitative pH sensor for environmental and intracellular applications was developed by the facile hydrothermal preparation of dicyandiamide (DCD) N-doped high quantum yield (QY) graphene quantum dots (GQDs) using citric acid (CA) as the carbon source. The obtained N-doped GQDs have excellent photoluminesence (PL) properties with a relatively high QY of 36.5%, suggesting that N-doped chemistry could promote the QY of carbon nanomaterials. The possible mechanism for the formation of the GQDs involves the CA self-assembling into a nanosheet structure through intermolecular H-bonding at the initial stage of the reaction, and then the pure graphene core with many function groups formed through the dehydration between the carboxyl and hydroxyl of the intermolecules under hydrothermal conditions. These N-doped GQDs have low toxicity, and are photostable and pH-sensitive between 1.81 to 8.96, giving a general pH sensor with a wide range of applications from real water to intracellular contents.A general quantitative pH sensor for environmental and intracellular applications was developed by the facile hydrothermal preparation of dicyandiamide (DCD) N-doped high quantum yield (QY) graphene quantum dots (GQDs) using citric acid (CA) as the carbon source. The obtained N-doped GQDs have excellent photoluminesence (PL) properties with a relatively high QY of 36.5%, suggesting that N-doped chemistry could promote the QY of carbon nanomaterials. The possible mechanism for the formation of the GQDs involves the CA self-assembling into a nanosheet structure through intermolecular H-bonding at the initial stage of the reaction, and then the pure graphene core with many function groups formed through the dehydration between the carboxyl and hydroxyl of the intermolecules under hydrothermal conditions. These N-doped GQDs have low toxicity, and are photostable and pH-sensitive between 1.81 to 8.96, giving a general pH sensor with a wide range of applications from real water
Three-wave interaction and Manley-Rowe relations in quantum hydrodynamics
NASA Astrophysics Data System (ADS)
Wallin, Erik; Zamanian, Jens; Brodin, Gert; Brodin
2014-08-01
The theory for nonlinear three-wave interaction in magnetized plasmas is reconsidered using quantum hydrodynamics. The general coupling coefficients are calculated for the generalized Bohm de Broglie term. It is found that the Manley-Rowe relations are fulfilled only if the form of the particle dispersive term coincides with the standard expression. The implications of our results are discussed.
Entanglement Entropy from Surface Terms in General Relativity
NASA Astrophysics Data System (ADS)
Bhattacharyya, Arpan; Sinha, Aninda
2013-10-01
Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1 + 1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados-Teitelboim-Zanelli (BTZ) black hole, the Gibbons-Hawking-York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.
General relativity as a two-dimensional CFT
NASA Astrophysics Data System (ADS)
Adamo, Tim
2015-11-01
The tree-level scattering amplitudes of general relativity (GR) encode the full nonlinearity of the Einstein field equations. Yet remarkably compact expressions for these amplitudes have been found which seem unrelated to a perturbative expansion of the Einstein-Hilbert action. This suggests an entirely different description of GR which makes this on-shell simplicity manifest. Taking our cue from the tree-level amplitudes, we discuss how such a description can be found. The result is a formulation of GR in terms of a solvable two-dimensional conformal field theory (CFT), with the Einstein equations emerging as quantum consistency conditions.
Black hole based tests of general relativity
NASA Astrophysics Data System (ADS)
Yagi, Kent; Stein, Leo C.
2016-03-01
General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is in systems that contain one or more black holes. Black holes are the most compact objects in the Universe, providing probes of the strongest-possible gravitational fields. We are motivated to study strong-field gravity since many theories give large deviations from general relativity only at large field strengths, while recovering the weak-field behavior. In this article, we review how one can probe general relativity and various alternative theories of gravity by using electromagnetic waves from a black hole with an accretion disk, and gravitational waves from black hole binaries. We first review model-independent ways of testing gravity with electromagnetic/gravitational waves from a black hole system. We then focus on selected examples of theories that extend general relativity in rather simple ways. Some important characteristics of general relativity include (but are not limited to) (i) only tensor gravitational degrees of freedom, (ii) the graviton is massless, (iii) no quadratic or higher curvatures in the action, and (iv) the theory is four-dimensional. Altering a characteristic leads to a different extension of general relativity: (i) scalar-tensor theories, (ii) massive gravity theories, (iii) quadratic gravity, and (iv) theories with large extra dimensions. Within each theory, we describe black hole solutions, their properties, and current and projected constraints on each theory using black hole based tests of gravity. We close this review by listing some of the open problems in model-independent tests and within each specific theory.
General very special relativity in Finsler cosmology
Kouretsis, A. P.; Stathakopoulos, M.; Stavrinos, P. C.
2009-05-15
General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation.
General very special relativity in Finsler cosmology
NASA Astrophysics Data System (ADS)
Kouretsis, A. P.; Stathakopoulos, M.; Stavrinos, P. C.
2009-05-01
General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation.
Correlated electrons in coupled quantum dots and related phenomena
NASA Astrophysics Data System (ADS)
Ugajin, Ryuichi
1998-01-01
Three topics related to correlated electrons in coupled quantum dots are discussed. The first is quasi-resonance between multi-electron states, which causes hitherto unremarked types of resonant absorption in coupled quantum dots. The second is electron tunneling through a Hubbard gap, which is induced by an increase in the density of electrons in a quantum-dot chain under an overall confining potential. The third is Mott transition in a two-dimensional quantum-dot array induced by an external electric field. In this system, the metal-insulator transition goes through a heavy electron phase in which the density of correlated electrons fluctuates.
Quantum analysis and thermodynamic operator relations in stochastic energetics
NASA Astrophysics Data System (ADS)
Koide, Tomoi
2017-08-01
We introduce a model of the quantum Brownian motion coupled to a classical neat bath by using the operator differential proposed in the quantum analysis. We then define the heat operator by adapting the idea of the stochastic energetics. The introduced operator satisfies the relations which are analogous to the first and second laws of thermodynamics.
Relative submajorization and its use in quantum resource theories
NASA Astrophysics Data System (ADS)
Renes, Joseph M.
2016-12-01
We introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics, bipartite entanglement, and quantum coherence. Relative majorization is an ordering on pairs of vectors induced by stochastic transformations: One pair of vectors relatively majorizes another when there exists a stochastic transformation taking the former to the latter. Relative submajorization is a weakened version in which a substochastic matrix need only generate a vector pair obeying certain positivity conditions relative to the input pair. In the context of resource theories, we show that the relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another, also when assisted by additional standard resources such as useful work or maximally entangled states. These characterizations have a geometric formulation as the ratios or differences, respectively, between the Lorenz curves associated with the input and output resources, making them efficient to compute. We also find several interesting bounds on the reversibility of a given transformation in terms of the properties of the forward transformation. The main technical tool used to establish these results is the linear programming duality, which is used to show that any instance of relative submajorization can be "dilated" to an instance of strict relative majorization.
Takeoka, Masahiro; Fujiwara, Mikio; Mizuno, Jun; Sasaki, Masahide
2004-05-01
Quantum-information theory predicts that when the transmission resource is doubled in quantum channels, the amount of information transmitted can be increased more than twice by quantum-channel coding technique, whereas the increase is at most twice in classical information theory. This remarkable feature, the superadditive quantum-coding gain, can be implemented by appropriate choices of code words and corresponding quantum decoding which requires a collective quantum measurement. Recently, an experimental demonstration was reported [M. Fujiwara et al., Phys. Rev. Lett. 90, 167906 (2003)]. The purpose of this paper is to describe our experiment in detail. Particularly, a design strategy of quantum-collective decoding in physical quantum circuits is emphasized. We also address the practical implication of the gain on communication performance by introducing the quantum-classical hybrid coding scheme. We show how the superadditive quantum-coding gain, even in a small code length, can boost the communication performance of conventional coding techniques.
Erol, Volkan; Ozaydin, Fatih; Altintas, Azmi Ali
2014-06-24
Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.
Erol, Volkan; Ozaydin, Fatih; Altintas, Azmi Ali
2014-01-01
Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa. PMID:24957694
NASA Astrophysics Data System (ADS)
Hayden, Patrick; Myers, Robert
2017-01-01
Patrick Hayden and Robert Myers describe how the study of “qubits”, quantum bits of information, may hold the key to uniting quantum theory and general relativity into a unified theory of quantum gravity
Castelnovo, Claudio . E-mail: castel@buphy.bu.edu; Chamon, Claudio; Mudry, Christopher; Pujol, Pierre
2005-08-01
Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar-Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave functions are intimately related to the partition functions of combinatorial problems of classical statistical physics. We show that all the known examples of quantum Hamiltonians, when fine-tuned to their RK points, belong to a larger class of real, symmetric, and irreducible matrices that admit what we dub a Stochastic Matrix Form (SMF) decomposition. Matrices that are SMF decomposable are shown to be in one-to-one correspondence with stochastic classical systems described by a Master equation of the matrix type, hence their name. It then follows that the equilibrium partition function of the stochastic classical system partly controls the zero-temperature quantum phase diagram, while the relaxation rates of the stochastic classical system coincide with the excitation spectrum of the quantum problem. Given a generic quantum Hamiltonian construed as an abstract operator defined on some Hilbert space, we prove that there exists a continuous manifold of bases in which the representation of the quantum Hamiltonian is SMF decomposable, i.e., there is a (continuous) manifold of distinct stochastic classical systems related to the same quantum problem. Finally, we illustrate with three examples of Hamiltonians fine-tuned to their RK points, the triangular quantum dimer model, the quantum eight-vertex model, and the quantum three-coloring model on the honeycomb lattice, how they can be understood within our framework, and how this allows for immediate generalizations, e.g., by adding non-trivial interactions to these models.
Affine generalization of the Komar complex of general relativity
NASA Astrophysics Data System (ADS)
Mielke, Eckehard W.
2001-02-01
On the basis of the ``on shell'' Noether identities of the metric-affine gauge approach of gravity, an affine superpotential is derived which comprises the energy- and angular-momentum content of exact solutions. In the special case of general relativity (GR) or its teleparallel equivalent, the Komar or Freud complex, respectively, are recovered. Applying this to the spontaneously broken anti-de Sitter gauge model of McDowell and Mansouri with an induced Euler term automatically yields the correct mass and spin of the Kerr-AdS solution of GR with a (induced) cosmological constant without the factor two discrepancy of the Komar formula.
Fractional angular momentum in noncommutative generalized Chern-Simons quantum mechanics
NASA Astrophysics Data System (ADS)
Zhang, Xi-Lun; Sun, Yong-Li; Wang, Qing; Long, Zheng-Wen; Jing, Jian
2016-07-01
The noncommutative generalized Chern-Simons quantum mechanics, i.e., the Chern-Simons quantum mechanics on the noncommutative plane in the presence of Aharonov-Bohm magnetic vector potentials, is studied in this paper. We focus our attention on the canonical orbital angular momentum and show that there are two different approaches to produce the fractional angular momentum in the noncommutative generalized Chern-Simons quantum mechanics.
Wu, Zhu Lian; Gao, Ming Xuan; Wang, Ting Ting; Wan, Xiao Yan; Zheng, Lin Ling; Huang, Cheng Zhi
2014-04-07
A general quantitative pH sensor for environmental and intracellular applications was developed by the facile hydrothermal preparation of dicyandiamide (DCD) N-doped high quantum yield (QY) graphene quantum dots (GQDs) using citric acid (CA) as the carbon source. The obtained N-doped GQDs have excellent photoluminesence (PL) properties with a relatively high QY of 36.5%, suggesting that N-doped chemistry could promote the QY of carbon nanomaterials. The possible mechanism for the formation of the GQDs involves the CA self-assembling into a nanosheet structure through intermolecular H-bonding at the initial stage of the reaction, and then the pure graphene core with many function groups formed through the dehydration between the carboxyl and hydroxyl of the intermolecules under hydrothermal conditions. These N-doped GQDs have low toxicity, and are photostable and pH-sensitive between 1.81 to 8.96, giving a general pH sensor with a wide range of applications from real water to intracellular contents.
Projective structure and holonomy in general relativity
NASA Astrophysics Data System (ADS)
Hall, G. S.; Lonie, D. P.
2011-04-01
This review presents a study of the situation when two spacetimes admit the same (unparametrized) geodesics, that is, when they are projectively related. The solution is based on the curvature class and the holonomy type of a spacetime and it transpires that all holonomy possibilities can be solved except the most general one and that the consequence of two spacetimes being projectively related leads, in many cases, to their associated Levi-Civita connections being identical. Some results are also given regarding the general case. It is also shown that the holonomy types of projectively related spacetimes are very closely related. The theory is then applied, with Einstein's principle of equivalence in mind, to 'generic' spacetimes.
Tests of general relativity using pulsars
NASA Technical Reports Server (NTRS)
Reichley, P. E.
1971-01-01
The arrival times of the pulses from each pulsar are measured by a cesium clock. The observations are all made at a frequency of 2388 MHz (12.5 cm wavelength) on a 26 m dish antenna. The effect of interstellar charged particles is a random one that increases the noise level on the arrival time measurements. The variation in clock rate is shown consisting of two effects: the time dilation effect of special relativity and the red shift effect of general relativity.
Tests of General Relativity with GW150914
NASA Astrophysics Data System (ADS)
Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Bacon, P.; Bader, M. K. M.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Behnke, B.; Bejger, M.; Bell, A. S.; Bell, C. J.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bogan, C.; Bohe, A.; Bojtos, P.; Bond, C.; Bondu, F.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, H. Y.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Cominsky, L.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dattilo, V.; Dave, I.; Daveloza, H. P.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Virgilio, A.; Dojcinoski, G.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Engels, W.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gatto, A.; Gaur, G.; Gehrels, N.; Gemme, G.; Gendre, B.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Hofman, D.; Hollitt, S. E.; Holt, K.; Holz, D. E.; Hopkins, P.; Hosken, D. J.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Idrisy, A.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Islas, G.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jang, H.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Johnson-McDaniel, N. K.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Haris, M. K.; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kennedy, R.; Key, J. S.; Khalaidovski, A.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, C.; Kim, J.; Kim, K.; Kim, Nam-Gyu; Kim, Namjun; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Koehlenbeck, S. M.; Kokeyama, K.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Krishnan, B.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, P.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lange, J.; Lantz, B.; Lasky, P. D.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B. M.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Lockerbie, N. A.; Logue, J.; Lombardi, A. L.; London, L. T.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lousto, C. O.; Lovelace, G.; Lück, H.; Lundgren, A. P.; Luo, J.; Lynch, R.; Ma, Y.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña-Sandoval, F.; Magee, R. M.; Mageswaran, M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandel, I.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mendoza-Gandara, D.; Mercer, R. A.; Merilh, E.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nedkova, K.; Nelemans, G.; Neri, M.; Neunzert, A.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. 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S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Tomlinson, C.; Tonelli, M.; Torres, C. V.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Trozzo, L.; Tse, M.; Turconi, M.; Tuyenbayev, D.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; Vallisneri, M.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; Van Den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Voss, D.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; White, D. J.; Whiting, B. F.; Williams, D.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Worden, J.; Wright, J. L.; Wu, G.; Yablon, J.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, H.; Yvert, M.; ZadroŻny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, F.; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; Boyle, M.; Campanelli, M.; Hemberger, D. A.; Kidder, L. E.; Ossokine, S.; Scheel, M. A.; Szilagyi, B.; Teukolsky, S.; Zlochower, Y.; LIGO Scientific; Virgo Collaborations
2016-06-01
The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasinormal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parametrized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a 90%-confidence lower bound of 1013 km . In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.
Cooperative Education General Related Instructional Units.
ERIC Educational Resources Information Center
Arizona State Dept. of Vocational Education, Phoenix.
Resulting from the efforts of teacher-coordinators in a 3-week workshop, this study guide was designed to help student-trainees adjust to the many factors of the world of work. Including material useful in a general related class, the study guide is arranged in the following 10 units: (1) Introduction To Cooperative Education, (2) Youth Clubs and…
Does Physics Need Special and General Relativity?
NASA Astrophysics Data System (ADS)
Dunning-Davies, Jeremy
Here it is intended to reconsider briefly some of the objections which have arisen over the years to both the Special and General Theories of Relativity before raising the question of whether or not either of these two theories is actually required by modern physics.
General Relativity theory: tests through time
NASA Astrophysics Data System (ADS)
Yatskiv, Ya. S.; Alexandrov, A. N.; Vavilova, I. B.; Zhdanov, V. I.; Kudrya, Yu. N.; Parnovsky, S. L.; Fedorova, O. V.; Khmil, S. V.
2005-09-01
Theoretical basis of General relativity Theory, its experimental tests as well as GRT applications are briefly summarized taking into account the results of the last decade. The monograph addresses scientists, post-graduated students, and students specialized in the natural sciences as well as everyone who takes a great interest in GRT.
Tests of General Relativity with GW150914.
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Downes, T P; Drago, M; Drever, R W P; Driggers, J C; Du, Z; Ducrot, M; Dwyer, S E; Edo, T B; Edwards, M C; Effler, A; Eggenstein, H-B; Ehrens, P; Eichholz, J; Eikenberry, S S; Engels, W; Essick, R C; Etzel, T; Evans, M; Evans, T M; Everett, R; Factourovich, M; Fafone, V; Fair, H; Fairhurst, S; Fan, X; Fang, Q; Farinon, S; Farr, B; Farr, W M; Favata, M; Fays, M; Fehrmann, H; Fejer, M M; Ferrante, I; Ferreira, E C; Ferrini, F; Fidecaro, F; Fiori, I; Fiorucci, D; Fisher, R P; Flaminio, R; Fletcher, M; Fournier, J-D; Franco, S; Frasca, S; Frasconi, F; Frei, Z; Freise, A; Frey, R; Frey, V; Fricke, T T; Fritschel, P; Frolov, V V; Fulda, P; Fyffe, M; Gabbard, H A G; Gair, J R; Gammaitoni, L; Gaonkar, S G; Garufi, F; Gatto, A; Gaur, G; Gehrels, N; Gemme, G; Gendre, B; Genin, E; Gennai, A; George, J; Gergely, L; Germain, V; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S; Giaime, J A; Giardina, K D; Giazotto, A; Gill, K; Glaefke, A; Goetz, E; Goetz, R; Gondan, L; González, G; Gonzalez Castro, J M; Gopakumar, A; Gordon, N A; Gorodetsky, M L; Gossan, S E; Gosselin, M; Gouaty, R; Graef, C; Graff, P B; Granata, M; Grant, A; Gras, S; Gray, C; Greco, G; Green, A C; Groot, P; Grote, H; Grunewald, S; Guidi, G M; Guo, X; Gupta, A; Gupta, M K; Gushwa, K E; Gustafson, E K; Gustafson, R; Hacker, J J; Hall, B R; Hall, E D; Hammond, G; Haney, M; Hanke, M M; Hanks, J; Hanna, C; Hannam, M D; Hanson, J; Hardwick, T; Harms, J; Harry, G M; Harry, I W; Hart, M J; Hartman, M T; Haster, C-J; Haughian, K; Healy, J; Heidmann, A; Heintze, M C; Heitmann, H; Hello, P; Hemming, G; Hendry, M; Heng, I S; Hennig, J; Heptonstall, A W; Heurs, M; Hild, S; Hoak, D; Hodge, K A; Hofman, D; Hollitt, S E; Holt, K; Holz, D E; Hopkins, P; Hosken, D J; Hough, J; Houston, E A; Howell, E J; Hu, Y M; Huang, S; Huerta, E A; Huet, D; Hughey, B; Husa, S; Huttner, S H; Huynh-Dinh, T; Idrisy, A; Indik, N; Ingram, D R; Inta, R; Isa, H N; Isac, J-M; Isi, M; Islas, G; Isogai, T; Iyer, B R; Izumi, K; Jacqmin, T; Jang, H; Jani, K; Jaranowski, P; Jawahar, S; Jiménez-Forteza, F; Johnson, W W; Johnson-McDaniel, N K; Jones, D I; Jones, R; Jonker, R J G; Ju, L; Haris, M K; Kalaghatgi, C V; Kalogera, V; Kandhasamy, S; Kang, G; Kanner, J B; Karki, S; Kasprzack, M; Katsavounidis, E; Katzman, W; Kaufer, S; Kaur, T; Kawabe, K; Kawazoe, F; Kéfélian, F; Kehl, M S; Keitel, D; Kelley, D B; Kells, W; Kennedy, R; Key, J S; Khalaidovski, A; Khalili, F Y; Khan, I; Khan, S; Khan, Z; Khazanov, E A; Kijbunchoo, N; Kim, C; Kim, J; Kim, K; Kim, Nam-Gyu; Kim, Namjun; Kim, Y-M; King, E J; King, P J; Kinzel, D L; Kissel, J S; Kleybolte, L; Klimenko, S; Koehlenbeck, S M; Kokeyama, K; Koley, S; Kondrashov, V; Kontos, A; Korobko, M; Korth, W Z; Kowalska, I; Kozak, D B; Kringel, V; Krishnan, B; Królak, A; Krueger, C; Kuehn, G; Kumar, P; Kuo, L; Kutynia, A; Lackey, B D; Landry, M; Lange, J; Lantz, B; Lasky, P D; Lazzarini, A; Lazzaro, C; Leaci, P; Leavey, S; Lebigot, E O; Lee, C H; Lee, H K; Lee, H M; Lee, K; Lenon, A; Leonardi, M; Leong, J R; Leroy, N; Letendre, N; Levin, Y; Levine, B M; Li, T G F; Libson, A; Littenberg, T B; Lockerbie, N A; Logue, J; Lombardi, A L; London, L T; Lord, J E; Lorenzini, M; Loriette, V; Lormand, M; Losurdo, G; Lough, J D; Lousto, C O; Lovelace, G; Lück, H; Lundgren, A P; Luo, J; Lynch, R; Ma, Y; MacDonald, T; Machenschalk, B; MacInnis, M; Macleod, D M; Magaña-Sandoval, F; Magee, R M; Mageswaran, M; Majorana, E; Maksimovic, I; Malvezzi, V; Man, N; Mandel, I; Mandic, V; Mangano, V; Mansell, G L; Manske, M; Mantovani, M; Marchesoni, F; Marion, F; Márka, S; Márka, Z; Markosyan, A S; Maros, E; Martelli, F; Martellini, L; Martin, I W; Martin, R M; Martynov, D V; Marx, J N; Mason, K; Masserot, A; Massinger, T J; Masso-Reid, M; Matichard, F; Matone, L; Mavalvala, N; Mazumder, N; Mazzolo, G; McCarthy, R; McClelland, D E; McCormick, S; McGuire, S C; McIntyre, G; McIver, J; McManus, D J; McWilliams, S T; Meacher, D; Meadors, G D; Meidam, J; Melatos, A; Mendell, G; Mendoza-Gandara, D; Mercer, R A; Merilh, E; Merzougui, M; Meshkov, S; Messenger, C; Messick, C; Meyers, P M; Mezzani, F; Miao, H; Michel, C; Middleton, H; Mikhailov, E E; Milano, L; Miller, J; Millhouse, M; Minenkov, Y; Ming, J; Mirshekari, S; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moggi, A; Mohan, M; Mohapatra, S R P; Montani, M; Moore, B C; Moore, C J; Moraru, D; Moreno, G; Morriss, S R; Mossavi, K; Mours, B; Mow-Lowry, C M; Mueller, C L; Mueller, G; Muir, A W; Mukherjee, Arunava; Mukherjee, D; Mukherjee, S; Mukund, N; Mullavey, A; Munch, J; Murphy, D J; Murray, P G; Mytidis, A; Nardecchia, I; Naticchioni, L; Nayak, R K; Necula, V; Nedkova, K; Nelemans, G; Neri, M; Neunzert, A; Newton, G; Nguyen, T T; Nielsen, A B; Nissanke, S; Nitz, A; Nocera, F; Nolting, D; Normandin, M E; Nuttall, L K; Oberling, J; Ochsner, E; O'Dell, J; Oelker, E; Ogin, G H; Oh, J J; Oh, S H; Ohme, F; Oliver, M; Oppermann, P; Oram, Richard J; O'Reilly, B; O'Shaughnessy, R; Ottaway, D J; Ottens, R S; Overmier, H; Owen, B J; Pai, A; Pai, S A; Palamos, J R; Palashov, O; Palomba, C; Pal-Singh, A; Pan, H; Pan, Y; Pankow, C; Pannarale, F; Pant, B C; Paoletti, F; Paoli, A; Papa, M A; Paris, H R; Parker, W; Pascucci, D; Pasqualetti, A; Passaquieti, R; Passuello, D; Patricelli, B; Patrick, Z; Pearlstone, B L; Pedraza, M; Pedurand, R; Pekowsky, L; Pele, A; Penn, S; Perreca, A; Pfeiffer, H P; Phelps, M; Piccinni, O; Pichot, M; Piergiovanni, F; Pierro, V; Pillant, G; Pinard, L; Pinto, I M; Pitkin, M; Poggiani, R; Popolizio, P; Post, A; Powell, J; Prasad, J; Predoi, V; Premachandra, S S; Prestegard, T; Price, L R; Prijatelj, M; Principe, M; Privitera, S; Prix, R; Prodi, G A; Prokhorov, L; Puncken, O; Punturo, M; Puppo, P; Pürrer, M; Qi, H; Qin, J; Quetschke, V; Quintero, E A; Quitzow-James, R; Raab, F J; Rabeling, D S; Radkins, H; Raffai, P; Raja, S; Rakhmanov, M; Rapagnani, P; Raymond, V; Razzano, M; Re, V; Read, J; Reed, C M; Regimbau, T; Rei, L; Reid, S; Reitze, D H; Rew, H; Reyes, S D; Ricci, F; Riles, K; Robertson, N A; Robie, R; Robinet, F; Rocchi, A; Rolland, L; Rollins, J G; Roma, V J; Romano, R; Romanov, G; Romie, J H; Rosińska, D; Rowan, S; Rüdiger, A; Ruggi, P; Ryan, K; Sachdev, S; Sadecki, T; Sadeghian, L; Salconi, L; Saleem, M; Salemi, F; Samajdar, A; Sammut, L; Sanchez, E J; Sandberg, V; Sandeen, B; Sanders, J R; Sassolas, B; Sathyaprakash, B S; Saulson, P R; Sauter, O; Savage, R L; Sawadsky, A; Schale, P; Schilling, R; Schmidt, J; Schmidt, P; Schnabel, R; Schofield, R M S; Schönbeck, A; Schreiber, E; Schuette, D; Schutz, B F; Scott, J; Scott, S M; Sellers, D; Sengupta, A S; Sentenac, D; Sequino, V; Sergeev, A; Serna, G; Setyawati, Y; Sevigny, A; Shaddock, D A; Shah, S; Shahriar, M S; Shaltev, M; Shao, Z; Shapiro, B; Shawhan, P; Sheperd, A; Shoemaker, D H; Shoemaker, D M; Siellez, K; Siemens, X; Sigg, D; Silva, A D; Simakov, D; Singer, A; Singer, L P; Singh, A; Singh, R; Singhal, A; Sintes, A M; Slagmolen, B J J; Smith, J R; Smith, N D; Smith, R J E; Son, E J; Sorazu, B; Sorrentino, F; Souradeep, T; Srivastava, A K; Staley, A; Steinke, M; Steinlechner, J; Steinlechner, S; Steinmeyer, D; Stephens, B C; Stone, R; Strain, K A; Straniero, N; Stratta, G; Strauss, N A; Strigin, S; Sturani, R; Stuver, A L; Summerscales, T Z; Sun, L; Sutton, P J; Swinkels, B L; Szczepańczyk, M J; Tacca, M; Talukder, D; Tanner, D B; Tápai, M; Tarabrin, S P; Taracchini, A; Taylor, R; Theeg, T; Thirugnanasambandam, M P; Thomas, E G; Thomas, M; Thomas, P; Thorne, K A; Thorne, K S; Thrane, E; Tiwari, S; Tiwari, V; Tokmakov, K V; Tomlinson, C; Tonelli, M; Torres, C V; Torrie, C I; Töyrä, D; Travasso, F; Traylor, G; Trifirò, D; Tringali, M C; Trozzo, L; Tse, M; Turconi, M; Tuyenbayev, D; Ugolini, D; Unnikrishnan, C S; Urban, A L; Usman, S A; Vahlbruch, H; Vajente, G; Valdes, G; Vallisneri, M; van Bakel, N; van Beuzekom, M; van den Brand, J F J; Van Den Broeck, C; Vander-Hyde, D C; van der Schaaf, L; van Heijningen, J V; van Veggel, A A; Vardaro, M; Vass, S; Vasúth, M; Vaulin, R; Vecchio, A; Vedovato, G; Veitch, J; Veitch, P J; Venkateswara, K; Verkindt, D; Vetrano, F; Viceré, A; Vinciguerra, S; Vine, D J; Vinet, J-Y; Vitale, S; Vo, T; Vocca, H; Vorvick, C; Voss, D; Vousden, W D; Vyatchanin, S P; Wade, A R; Wade, L E; Wade, M; Walker, M; Wallace, L; Walsh, S; Wang, G; Wang, H; Wang, M; Wang, X; Wang, Y; Ward, R L; Warner, J; Was, M; Weaver, B; Wei, L-W; Weinert, M; Weinstein, A J; Weiss, R; Welborn, T; Wen, L; Weßels, P; Westphal, T; Wette, K; Whelan, J T; White, D J; Whiting, B F; Williams, D; Williams, R D; Williamson, A R; Willis, J L; Willke, B; Wimmer, M H; Winkler, W; Wipf, C C; Wittel, H; Woan, G; Worden, J; Wright, J L; Wu, G; Yablon, J; Yam, W; Yamamoto, H; Yancey, C C; Yap, M J; Yu, H; Yvert, M; Zadrożny, A; Zangrando, L; Zanolin, M; Zendri, J-P; Zevin, M; Zhang, F; Zhang, L; Zhang, M; Zhang, Y; Zhao, C; Zhou, M; Zhou, Z; Zhu, X J; Zucker, M E; Zuraw, S E; Zweizig, J; Boyle, M; Campanelli, M; Hemberger, D A; Kidder, L E; Ossokine, S; Scheel, M A; Szilagyi, B; Teukolsky, S; Zlochower, Y
2016-06-03
The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasinormal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parametrized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a 90%-confidence lower bound of 10^{13} km. In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.
General Relativity Without General Relativity: Self-Gravitating Systems and Effective Geometries
NASA Astrophysics Data System (ADS)
Bini, Donato; Cherubini, Christian; Filippi, Simonetta; Geralico, Andrea
Perturbations of Newtonian self-gravitating barotropic perfect fluid systems can be studied via an extension of the "effective geometry" formalism. The case of polytropic spherical stars described by the Lane-Emden equation has been studied in the past in the known cases of existing explicit solutions relevant for both stellar and galactic dynamics. Applications of the formalism in the case of rotating configurations found via William's "matching method" and possible generalizations are here discussed. The present formulation represents another natural scenario, in addition with the usual one of quantum condensates in laboratories, in which the acoustic analogy has physical relevance.
Boundary and corner terms in the action for general relativity
NASA Astrophysics Data System (ADS)
Jubb, Ian; Samuel, Joseph; Sorkin, Rafael D.; Surya, Sumati
2017-03-01
We revisit the action principle for general relativity, motivated by the path integral approach to quantum gravity. We consider a spacetime region whose boundary has piecewise C 2 components, each of which can be spacelike, timelike or null and consider metric variations in which only the pullback of the metric to the boundary is held fixed. Allowing all such metric variations we present a unified treatment of the spacelike, timelike and null boundary components using Cartan’s tetrad formalism. Apart from its computational simplicity, this formalism gives us a simple way of identifying corner terms. We also discuss ‘creases’ which occur when the boundary is the event horizon of a black hole. Our treatment is geometric and intrinsic and we present our results both in the computationally simpler tetrad formalism as well as the more familiar metric formalism. We recover known results from a simpler and more general point of view and find some new ones.
Leibnizian relationalism for general relativistic physics
NASA Astrophysics Data System (ADS)
Vassallo, Antonio; Esfeld, Michael
2016-08-01
An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple and being informative.
Probe light-shift elimination in generalized hyper-Ramsey quantum clocks
NASA Astrophysics Data System (ADS)
Zanon-Willette, T.; de Clercq, E.; Arimondo, E.
2016-04-01
We present an interrogation scheme for the next generation of quantum clocks to suppress frequency shifts induced by laser probing fields that are themselves based on generalized hyper-Ramsey resonances. Sequences of composite laser pulses with a specific selection of phases, frequency detunings, and durations are combined to generate a very efficient and robust frequency locking signal with an almost perfect elimination of the light shift from off-resonant states and to decouple the unperturbed frequency measurement from the laser's intensity. The frequency lock point generated from synthesized error signals using either π /4 or 3 π /4 laser phase steps during the intermediate pulse is tightly protected against large laser-pulse area variations and errors in potentially applied frequency shift compensations. Quantum clocks based on weakly allowed or completely forbidden optical transitions in atoms, ions, molecules, and nuclei will benefit from these hyperstable laser frequency stabilization schemes to reach relative accuracies below the 10-18 level.
Action scales for quantum decoherence and their relation to structures in phase space
Alonso, Daniel; Brouard, S.; Palao, Jose P.; Mayato, R. Sala
2004-05-01
A characteristic action {delta}S is defined whose magnitude determines some properties of the expectation value of a general quantum displacement operator. These properties are related to the capability of a given environmental ''monitoring'' system to induce decoherence in quantum systems coupled to it. We show that the scale for effective decoherence is given by {delta}S{approx_equal}({Dirac_h}/2{pi}). We relate this characteristic action with a complementary quantity, {delta}Z, and analyze their connection with the main features of the pattern of structures developed by the environmental state in different phase space representations. The relevance of the {delta}S-action scale is illustrated using both a model quantum system solved numerically and a set of model quantum systems for which analytical expressions for the time-averaged expectation value of the displacement operator are obtained explicitly.
Quantum image encryption based on generalized affine transform and logistic map
NASA Astrophysics Data System (ADS)
Liang, Hao-Ran; Tao, Xiang-Yang; Zhou, Nan-Run
2016-07-01
Quantum circuits of the generalized affine transform are devised based on the novel enhanced quantum representation of digital images. A novel quantum image encryption algorithm combining the generalized affine transform with logistic map is suggested. The gray-level information of the quantum image is encrypted by the XOR operation with a key generator controlled by the logistic map, while the position information of the quantum image is encoded by the generalized affine transform. The encryption keys include the independent control parameters used in the generalized affine transform and the logistic map. Thus, the key space is large enough to frustrate the possible brute-force attack. Numerical simulations and analyses indicate that the proposed algorithm is realizable, robust and has a better performance than its classical counterpart in terms of computational complexity.
Universality of affine formulation in general relativity
NASA Astrophysics Data System (ADS)
Kijowski, Jerzy; Werpachowski, Roman
2007-02-01
The affine variational principle for general relativity, proposed in 1978 by one of us, is a good remedy for the nonuniversal properties of the standard, metric formulation, arising when the matter Lagrangian depends upon the metric derivatives. The affine version of the theory cures the standard drawback of the metric version, where the leading (second-order) term of the field equations depends upon the matter fields and its causal structure violates the light cone structure of the metric. Choosing the affine connection (and not the metric one) as the gravitational configuration, simplifies considerably the canonical structure of the theory and is more suitable for the purposes of its quantization along the lines of Ashtekar and Lewandowski. We show how the affine formulation provides a simple method to handle boundary integrals in general relativity theory.
Generalized Tests for Eight GRB Luminosity Relations
NASA Astrophysics Data System (ADS)
Schaefer, Bradley E.; Collazzi, Andrew C.
2007-02-01
Long-duration gamma-ray bursts (GRBs) have eight luminosity relations where observable burst properties can yield the burst luminosity and hence distance. This turns GRBs into useful tools of cosmology. Recently, two tests have been proposed (by Nakar & Piran and by Li) for which one of the eight relations is claimed to have significant problems. In this Letter, we generalize these tests and apply them to all eight GRB luminosity relations. (1) All eight relations pass the Nakar & Piran test after accounting for the uncertainties on the data and the dispersions of the correlations. (2) All eight relations are good when the GRB redshifts are known, for example, for calibration of the relations and for GRB Hubble diagram purposes. (3) We confirm the earlier results that the Eγ,iso-Epeak Amati relation must produce very large error bars whenever an unknown redshift being sought is >~1.4. (4) The Eγ-Epeak relation of Ghirlanda et al. must produce very large error bars whenever an unknown redshift being sought is >~3.4. (55) The other six relations have no problem at all from the ambiguity test of Li.
Correlated quadratures of resonance fluorescence and the generalized uncertainty relation
NASA Technical Reports Server (NTRS)
Arnoldus, Henk F.; George, Thomas F.; Gross, Rolf W. F.
1994-01-01
Resonance fluorescence from a two-state atom has been predicted to exhibit quadrature squeezing below the Heisenberg uncertainty limit, provided that the optical parameters (Rabi frequency, detuning, laser linewidth, etc.) are chosen carefully. When the correlation between two quadratures of the radiation field does not vanish, however, the Heisenberg limit for quantum fluctuations might be an unrealistic lower bound. A generalized uncertainty relation, due to Schroedinger, takes into account the possible correlation between the quadrature components of the radiation, and it suggests a modified definition of squeezing. We show that the coherence between the two levels of a laser-driven atom is responsible for the correlation between the quadrature components of the emitted fluorescence, and that the Schrodinger uncertainty limit increases monotonically with the coherence. On the other hand, the fluctuations in the quadrature field diminish with an increasing coherence, and can disappear completely when the coherence reaches 1/2, provided that certain phase relations hold.
Generalization of the Time-Energy Uncertainty Relation of Anandan-Aharonov Type
NASA Technical Reports Server (NTRS)
Hirayama, Minoru; Hamada, Takeshi; Chen, Jin
1996-01-01
A new type of time-energy uncertainty relation was proposed recently by Anandan and Aharonov. Their formula, to estimate the lower bound of time-integral of the energy-fluctuation in a quantum state is generalized to the one involving a set of quantum states. This is achieved by obtaining an explicit formula for the distance between two finitely separated points in the Grassman manifold.
Probing the Higgs vacuum with general relativity
NASA Technical Reports Server (NTRS)
Mannheim, Philip D.; Kazanas, Demosthenes
1991-01-01
It is shown that the structure of the Higgs vacuum can be revealed in gravitational experiments which probe the Schwarzschild geometry to only one order in MG/r beyond that needed for the classical tests of general relativity. The possibility that deviations from the conventional geometry are at least theoretically conceivable is explored. The deviations obtained provide a diagnostic test for searching for the existence of macroscopic scalar fields and open up the possiblity for further exploring the Higgs mechanism.
Pure connection action principle for general relativity.
Krasnov, Kirill
2011-06-24
It has already been known for two decades that general relativity can be reformulated as a certain gauge theory, so that the only dynamical field is an SO(3) connection and the spacetime metric appears as a derived object. However, no simple action principle realizing these ideas has been available. A new elegant action principle for such a "pure connection" formulation of GR is described.
Probing the Higgs vacuum with general relativity
NASA Technical Reports Server (NTRS)
Mannheim, Philip D.; Kazanas, Demosthenes
1991-01-01
It is shown that the structure of the Higgs vacuum can be revealed in gravitational experiments which probe the Schwarzschild geometry to only one order in MG/r beyond that needed for the classical tests of general relativity. The possibility that deviations from the conventional geometry are at least theoretically conceivable is explored. The deviations obtained provide a diagnostic test for searching for the existence of macroscopic scalar fields and open up the possiblity for further exploring the Higgs mechanism.
Classification of generalized quantum statistics associated with the exceptional Lie (super)algebras
Stoilova, N. I.; Jeugt, J. van der
2007-04-15
Generalized quantum statistics (GQS) associated with a Lie algebra or Lie superalgebra extends the notion of para-Bose or para-Fermi statistics. Such GQS have been classified for all classical simple Lie algebras and basic classical Lie superalgebras. In the current paper we finalize this classification for all exceptional Lie algebras and superalgebras. Since the definition of GQS is closely related to a certain Z grading of the Lie (super)algebra G, our classification reproduces some known Z gradings of exceptional Lie algebras. For exceptional Lie superalgebras such a classification of Z gradings has not been given before.
D'Ariano, Giacomo Mauro
2010-05-04
I will argue that the proposal of establishing operational foundations of Quantum Theory should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational 'principles of the quantumness', I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm 'the universe is a huge quantum computer', reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space-time. In this way Quantum Theory remains the only theory operating the huge computer of the universe.Is the computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam's razor, depending on the mathematical simplicity of QCFT. Here I will just start scratching the surface of QCFT, analyzing simple field theories, including Dirac's. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake the QCFT project, since QCFT makes all such problems manifest, and forces a re-foundation of QFT.
Quantum mechanics, gravity and modified quantization relations.
Calmet, Xavier
2015-08-06
In this paper, we investigate a possible energy scale dependence of the quantization rules and, in particular, from a phenomenological point of view, an energy scale dependence of an effective [Formula: see text] (reduced Planck's constant). We set a bound on the deviation of the value of [Formula: see text] at the muon scale from its usual value using measurements of the anomalous magnetic moment of the muon. Assuming that inflation has taken place, we can conclude that nature is described by a quantum theory at least up to an energy scale of about 10(16) GeV.
General bounds for sender-receiver capacities in multipoint quantum communications
NASA Astrophysics Data System (ADS)
Laurenza, Riccardo; Pirandola, Stefano
2017-09-01
We investigate the maximum rates for transmitting quantum information, distilling entanglement, and distributing secret keys between a sender and a receiver in a multipoint communication scenario, with the assistance of unlimited two-way classical communication involving all parties. First we consider the case where a sender communicates with an arbitrary number of receivers, a so-called quantum broadcast channel. Here we also provide a simple analysis in the bosonic setting where we consider quantum broadcasting through a sequence of beamsplitters. Then, we consider the opposite case where an arbitrary number of senders communicate with a single receiver, a so-called quantum multiple-access channel. Finally, we study the general case of all-in-all quantum communication where an arbitrary number of senders communicate with an arbitrary number of receivers. Since our bounds are formulated for quantum systems of arbitrary dimension, they can be applied to many different physical scenarios involving multipoint quantum communication.
Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices
NASA Astrophysics Data System (ADS)
Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco
2016-10-01
We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.
Generalized dynamic scaling for quantum critical relaxation in imaginary time.
Zhang, Shuyi; Yin, Shuai; Zhong, Fan
2014-10-01
We study the imaginary-time relaxation critical dynamics of a quantum system with a vanishing initial correlation length and an arbitrary initial order parameter M0. We find that in quantum critical dynamics, the behavior of M0 under scale transformations deviates from a simple power law, which was proposed for very small M0 previously. A universal characteristic function is then suggested to describe the rescaled initial magnetization, similar to classical critical dynamics. This characteristic function is shown to be able to describe the quantum critical dynamics in both short- and long-time stages of the evolution. The one-dimensional transverse-field Ising model is employed to numerically determine the specific form of the characteristic function. We demonstrate that it is applicable as long as the system is in the vicinity of the quantum critical point. The universality of the characteristic function is confirmed by numerical simulations of models belonging to the same universality class.
NASA Astrophysics Data System (ADS)
Cao, Meng
The goal of this dissertation is to develop a generally covariant Hamiltonian approach to the generalized harmonic formulation of general relativity. As en route investigations, an important class of coordinate transformations in the context of the 3 + 1 decomposition, foliation preserving transformations, is defined; transformation rules of various 3 + 1 decomposition variables under this change of coordinates are investigated; the notion of covariant time derivative under foliation preserving transformations is defined; gauge conditions of various numerical relativity formulations are rewritten in generally covariant form. The Hamiltonian formulation of the generalized harmonic system is defined in the latter part of this dissertation. With the knowledge of covariant time derivative, the Hamiltonian formulation is extended to achieve general covariance. The Hamiltonian formulation is further proved to be symmetric hyperbolic.
Bulk Rashba Semiconductors and Related Quantum Phenomena.
Bahramy, Mohammad Saeed; Ogawa, Naoki
2017-03-29
Bithmuth tellurohalides BiTeX (X = Cl, Br and I) are model examples of bulk Rashba semiconductors, exhibiting a giant Rashba-type spin splitting among their both valence and conduction bands. Extensive spectroscopic and transport experiments combined with the state-of-the-art first-principles calculations have revealed many unique quantum phenomena emerging from the bulk Rashba effect in these systems. The novel features such as the exotic inter- and intra-band optical transitions, enhanced magneto-optical response, divergent orbital dia-/para-magnetic susceptibility and helical spin textures with a nontrivial Berry's phase in the momentum space are among the salient discoveries, all arising from this effect. Also, it is theoretically proposed and indications have been experimentally reported that bulk Rashba semiconductors such as BiTeI have the capability of becoming a topological insulator under the application of a hydrostatic pressure. Here, we overview these studies and show that BiTeX are an ideal platform to explore the next aspects of quantum matter, which could ultimately be utilized to create spintronic devices with novel functionalities.
Some applications of uncertainty relations in quantum information
NASA Astrophysics Data System (ADS)
Majumdar, A. S.; Pramanik, T.
2016-08-01
We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the Einstein, Podolsky and Rosen (EPR) paradox. Entropic uncertainty relations (EURs) are used to reveal quantum steering for non-Gaussian continuous variable states. EURs for discrete variables are studied in the context of quantum memory where fine-graining yields the optimum lower bound of uncertainty. The fine-grained uncertainty relation is used to obtain connections between uncertainty and the nonlocality of retrieval games for bipartite and tripartite systems. The Robertson-Schrödinger (RS) uncertainty relation is applied for distinguishing pure and mixed states of discrete variables.
Quantum geometry of resurgent perturbative/nonperturbative relations
Basar, Gokce; Dunne, Gerald V.; Unsal, Mithat
2017-05-16
For a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential.more » These are related to the Chebyshev potentials, which are in turn related to certain N = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and ‘special geometry’. These systems inherit a natural modular structure corresponding to Ramanujan’s theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Lastly, our approach is very elementary, using basic classical geometry combined with all-orders WKB.« less
Quantum geometry of resurgent perturbative/nonperturbative relations
NASA Astrophysics Data System (ADS)
Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat
2017-05-01
For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain \\mathcal{N} = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and `special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.
On the Geodesic Hypothesis in General Relativity
NASA Astrophysics Data System (ADS)
Yang, Shiwu
2014-02-01
In this paper, we give a rigorous derivation of Einstein's geodesic hypothesis in general relativity. We use small material bodies governed by the nonlinear Klein-Gordon equations to approximate the test particle. Given a vacuum spacetime , we consider the initial value problem for the Einstein-scalar field system. For all sufficiently small ɛ and δ ≤ ɛ q , q > 1, where δ, ɛ are the amplitude and size of the particle, we show the existence of the solution to the Einstein-scalar field system with the property that the energy of the particle is concentrated along a timelike geodesic. Moreover, the gravitational field produced by is negligibly small in C 1, that is, the spacetime metric g is C 1 close to the given vacuum metric h. These results generalize those obtained by Stuart in (Ann Sci École Norm Sup (4) 37(2):312-362, 2004, J Math Pures Appl (9) 83(5):541-587, 2004).
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity.
Font, José A
2008-01-01
This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has
Balondo Iyela, Daddy; Govaerts, Jan; Hounkonnou, M. Norbert
2013-09-15
Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N= 1 and N= 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N⩾ 3 also exist in the literature, which should be relevant to a complete study of the N⩾ 3 general periodic hierarchies.
NASA Astrophysics Data System (ADS)
Balondo Iyela, Daddy; Govaerts, Jan; Hounkonnou, M. Norbert
2013-09-01
Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N = 1 and N = 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N ⩾ 3 also exist in the literature, which should be relevant to a complete study of the N ⩾ 3 general periodic hierarchies.
Heilmann, R.; Keil, R.; Gräfe, M.; Nolte, S.; Szameit, A.
2014-08-11
We present an innovative approach for ultra-precise phase manipulation in integrated photonic quantum circuits. To this end, we employ generalized directional couplers that utilize a detuning of the propagation constant in optical waveguides by the overlap of adjacent waveguide modes. We demonstrate our findings in experiments with classical as well as quantum light.
Cosmological graviton production in general relativity and related gravity theories
NASA Astrophysics Data System (ADS)
de Garcia Maia, Márcio R.; Barrow, John D.
1994-11-01
A unified description of graviton creation is given for isotropic cosmological models in general relativity, Brans-Dicke theory, and higher-order gravity theories. The Bogolubov coefficents are derived in general and may be specialized to each of the possible gravity theories. The power spectrum and energy density of relic gravitons surviving a variety of early cosmological scenarios are calculated. The possibility of a nonvacuum initial state is allowed for and the problems of imposing an ultraviolet cutoff are analyzed. We distinguish carefully the effects of gravity waves on super- and subhorizon scales. The associated infrared cutoff, or the ``Allen effect,'' is discussed in detail in order to evaluate the dependence of the graviton energy density on the expansion scale factor. It is found that the nonadiabatic evolution of the graviton energy density can occur even during the radiation era when long-wavelength primoridal gravitational waves enter the horizon. Detailed, multistage, cosmological models are set up involving a sequence of changes in the equation of state for general relativity and Brans-Dicke theories. These examples include models with an inflationary phase. The resulting gravitational-wave background is calculated analytically over the whole frequency range in all cases. The limits imposed by nucleosynthesis of helium-4 are found for general relativity. We also investigate the effects of the presence of a thermal sea of gravitons in the initial state prior to gravitational-wave amplification by the expansion and calculate the effects of the small horizon size upon the thermal distributions.
Quantum Fisher Information of Decohered W and GHZ Superposition States with Arbitrary Relative Phase
NASA Astrophysics Data System (ADS)
Erol, Volkan
2017-10-01
Quantum Fisher Information (QFI) is a very useful concept for analyzing situations that require phase sensitivity. It become a popular topic especially in Quantum Metrology domain. In this work, we study the changes in quantum Fisher information (QFI) values for one relative arbitrary phased quantum system consisting of a superposition of N Qubits W and GHZ states. In a recent work (Ozaydin et al. Int. J. Theor. Phys. 52, 2977, 2013), QFI values of this mentioned system for N qubits were studied. In this work, we extend this problem for the changes of QFI values in some noisy channels for the studied system. We show the changes in QFI depending on noise parameters. We report interesting results for different type of decoherence channels. We show the general case results for this problem.
N-dimensional alternate coined quantum walks from a dispersion-relation perspective
NASA Astrophysics Data System (ADS)
Roldán, Eugenio; Di Franco, Carlo; Silva, Fernando; de Valcárcel, Germán J.
2013-02-01
We suggest an alternative definition of N-dimensional coined quantum walk by generalizing a recent proposal [Di Franco , Phys. Rev. Lett.0031-9007PRLTAO10.1103/PhysRevLett.106.080502 106, 080502 (2011)]. This N-dimensional alternate quantum walk, AQW(N), in contrast with the standard definition of the N-dimensional quantum walk, QW(N), requires only a coin qubit. We discuss the quantum diffusion properties of AQW(2) and AQW(3) by analyzing their dispersion relations that reveal, in particular, the existence of diabolical points. This allows us to highlight interesting similarities with other well-known physical phenomena. We also demonstrate that AQW(3) generates considerable genuine multipartite entanglement. Finally, we discuss the implementability of AQW(N).
Quantum Fisher Information of Decohered W and GHZ Superposition States with Arbitrary Relative Phase
NASA Astrophysics Data System (ADS)
Erol, Volkan
2017-07-01
Quantum Fisher Information (QFI) is a very useful concept for analyzing situations that require phase sensitivity. It become a popular topic especially in Quantum Metrology domain. In this work, we study the changes in quantum Fisher information (QFI) values for one relative arbitrary phased quantum system consisting of a superposition of N Qubits W and GHZ states. In a recent work (Ozaydin et al. Int. J. Theor. Phys. 52, 2977, 2013), QFI values of this mentioned system for N qubits were studied. In this work, we extend this problem for the changes of QFI values in some noisy channels for the studied system. We show the changes in QFI depending on noise parameters. We report interesting results for different type of decoherence channels. We show the general case results for this problem.
Energy-Time Uncertainty Relations in Quantum Measurements
NASA Astrophysics Data System (ADS)
Miyadera, Takayuki
2016-11-01
Quantum measurement is a physical process. A system and an apparatus interact for a certain time period (measurement time), and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy-time uncertainty relation, to find that it needs an external system that switches on the interaction between the system and the apparatus. In such a sense this model is not closed. Therefore to treat a measurement process in a fully quantum manner we need to consider a "larger" quantum apparatus which works also as a timing device switching on the interaction. In this setting we prove that a trade-off relation (energy-time uncertainty relation), τ \\cdot Δ H_A ≥ π /4, holds between the energy fluctuation Δ H_A of the quantum apparatus and the measurement time τ . We use this trade-off relation to discuss the spacetime uncertainty relation concerning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus.
New Area Law in General Relativity.
Bousso, Raphael; Engelhardt, Netta
2015-08-21
We report a new area law in general relativity. A future holographic screen is a hypersurface foliated by marginally trapped surfaces. We show that their area increases monotonically along the foliation. Future holographic screens can easily be found in collapsing stars and near a big crunch. Past holographic screens exist in any expanding universe and obey a similar theorem, yielding the first rigorous area law in big bang cosmology. Unlike event horizons, these objects can be identified at finite time and without reference to an asymptotic boundary. The Bousso bound is not used, but it naturally suggests a thermodynamic interpretation of our result.
Testing General Relativity with Atomic Clocks
NASA Astrophysics Data System (ADS)
Reynaud, S.; Salomon, C.; Wolf, P.
2009-12-01
We discuss perspectives for new tests of general relativity which are based on recent technological developments as well as new ideas. We focus our attention on tests performed with atomic clocks and do not repeat arguments present in the other contributions to the present issue (Space Sci. Rev. 2009, This Issue). In particular, we present the scientific motivations of the space projects ACES (Salomon et al. in CR Acad. Sci. IV-2:1313, 2001) and SAGAS (Wolf et al. in Exp. Astron. 23:651, 2009).
New Area Law in General Relativity
NASA Astrophysics Data System (ADS)
Bousso, Raphael; Engelhardt, Netta
2015-08-01
We report a new area law in general relativity. A future holographic screen is a hypersurface foliated by marginally trapped surfaces. We show that their area increases monotonically along the foliation. Future holographic screens can easily be found in collapsing stars and near a big crunch. Past holographic screens exist in any expanding universe and obey a similar theorem, yielding the first rigorous area law in big bang cosmology. Unlike event horizons, these objects can be identified at finite time and without reference to an asymptotic boundary. The Bousso bound is not used, but it naturally suggests a thermodynamic interpretation of our result.
Republication of: On the general relativity theory
NASA Astrophysics Data System (ADS)
Weyl, H.
2009-07-01
This English translation of the paper by H. Weyl, "Zur allgemeinen Relativitätstheorie", Physikalische Zeitschrift 24, 230-232 (1923), in which he formulated the geometrical foundations of a model of an expanding Universe, has been selected by the Editors of General Relativity and Gravitation for publication in the Golden Oldies series of the journal. The paper is accompanied by an editorial note written by Juergen Ehlers and by Weyl's brief biography compiled by Andrzej Krasiński from internet sources, with corrections provided by Weyl's son and grandson.
Solving the Vlasov equation in general relativity
NASA Astrophysics Data System (ADS)
Rasio, Frederic A.; Shapiro, Stuart L.; Teukolsky, Saul A.
1989-09-01
A new numerical method for determining the dynamical evolution of a collisionless system in full general relativity is developed. The method exploits Liouville's theorem to determine the evolution of the distribution function of matter in phase space directly. The distribution function is governed by the collisionless Boltzmann (Vlasov) equation coupled to Einstein's equations for the gravitational field. The method accurately tracks the increasingly complicated fine-grained structure developed by the distribution function due to phase mixing. It can be used to study Newtonian as well as fully relativistic systems. Applications include violent relaxation, the stability of relativistic star clusters, and the collapse of unstable relativistic star clusters to black holes.
A Machian approach to general relativity
NASA Astrophysics Data System (ADS)
Vishwakarma, Ram Gopal
2015-08-01
Mach's principle is surely one of those tantalizingly beautiful concepts in physics which remain elusive. Though general Relativity (GR) was conceived in the spirit of realizing it, the theory failed to fulfill this expectation. Here a study on the implications of imposing Mach's principle on GR with an insight that spacetime has no independent existence without a material background, is presented. This inclusion of the principle in GR turns out to be unexpectedly rewarding. The resulting theory solves many mysteries and averts lingering problems of the conventional forms of GR and cosmology.
A Machian approach to general relativity
NASA Astrophysics Data System (ADS)
Vishwakarma, Ram Gopal
2015-08-01
Mach's principle is surely one of those tantalizingly beautiful concepts in physics which remain elusive. Though general Relativity (GR) was conceived in the spirit of realizing it, the theory failed to fulfill this expectation. Here a study on the implications of imposing Mach.s principle on GR with an insight that spacetime has no independent existence without a material background, is presented. This inclusion of the principle in GR turns out to be unexpectedly rewarding. The resulting theory solves many mysteries and averts lingering problems of the conventional forms of GR and cosmology
Relative Entropy Bounds on Quantum, Private and Repeater Capacities
NASA Astrophysics Data System (ADS)
Christandl, Matthias; Müller-Hermes, Alexander
2017-07-01
We find a strong-converse bound on the private capacity of a quantum channel assisted by unlimited two-way classical communication. The bound is based on the max-relative entropy of entanglement and its proof uses a new inequality for the sandwiched Rényi divergences based on complex interpolation techniques. We provide explicit examples of quantum channels where our bound improves upon both the transposition bound (on the quantum capacity assisted by classical communication) and the bound based on the squashed entanglement. As an application, we study a repeater version of the private capacity assisted by classical communication and provide an example of a quantum channel with high private capacity but negligible private repeater capacity.
Quantum groups as generalized gauge symmetries in WZNW models. Part II. The quantized model
NASA Astrophysics Data System (ADS)
Hadjiivanov, L.; Furlan, P.
2017-07-01
This is the second part of a paper dealing with the "internal" (gauge) symmetry of the Wess-Zumino-Novikov-Witten (WZNW) model on a compact Lie group G. It contains a systematic exposition, for G = SU( n), of the canonical quantization based on the study of the classical model (performed in the first part) following the quantum group symmetric approach first advocated by L.D. Faddeev and collaborators. The internal symmetry of the quantized model is carried by the chiral WZNW zero modes satisfying quadratic exchange relations and an n-linear determinant condition. For generic values of the deformation parameter the Fock representation of the zero modes' algebra gives rise to a model space of U q ( sl( n)). The relevant root of unity case is studied in detail for n = 2 when a "restricted" (finite dimensional) quotient quantum group is shown to appear in a natural way. The module structure of the zero modes' Fock space provides a specific duality with the solutions of the Knizhnik-Zamolodchikov equation for the four point functions of primary fields suggesting the existence of an extended state space of logarithmic CFT type. Combining left and right zero modes (i.e., returning to the 2 D model), the rational CFT structure shows up in a setting reminiscent to covariant quantization of gauge theories in which the restricted quantum group plays the role of a generalized gauge symmetry.
Quantum correlations and distinguishability of quantum states
NASA Astrophysics Data System (ADS)
Spehner, Dominique
2014-07-01
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.
General framework for quantum macroscopicity in terms of coherence
NASA Astrophysics Data System (ADS)
Yadin, Benjamin; Vedral, Vlatko
2016-02-01
We propose a universal language to assess macroscopic quantumness in terms of coherence, with a set of conditions that should be satisfied by any measure of macroscopic coherence. We link the framework to the resource theory of asymmetry. We show that the quantum Fisher information gives a good measure of macroscopic coherence, enabling a rigorous justification of a previously proposed measure of macroscopicity. This picture lets us draw connections between different measures of macroscopicity and evaluate them; we show that another widely studied measure fails one of our criteria.
Generalized nonholonomic mechanics, servomechanisms and related brackets
NASA Astrophysics Data System (ADS)
Cendra, H.; Grillo, S.
2006-02-01
It is well known that nonholonomic systems obeying D'Alembert's principle are described on the Hamiltonian side, after using the Legendre transformation, by the so-called almost-Poisson brackets. In this paper we define the Lagrangian and Hamiltonian sides of a class of generalized nonholonomic systems (GNHS), obeying a generalized version of D'Alembert's principle, such as rubber wheels (like some simplified models of pneumatic tires) and certain servomechanisms (like the controlled inverted pendulum), and show that corresponding equations of motion can also be described in terms of a bracket. We present essentially all possible brackets in terms of which the mentioned equations can be written down, which include the brackets that appear in the literature, and point out those (if any) that are naturally related to each system. In particular, we show there always exists a Leibniz bracket related to a GNHS, and conversely, that every Leibniz system is a GNHS. The control of the inverted pendulum on a cart is studied as an illustrative example.
Functional methods underlying classical mechanics, relativity and quantum theory
NASA Astrophysics Data System (ADS)
Kryukov, A.
2013-04-01
The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is "made" of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.
Unification of Classical and Quantum Mechanics & Theory of Relative Motion
NASA Astrophysics Data System (ADS)
Zheng-Johansson, J. X.
2003-03-01
A systematic survey of relevant pivotal experiments leads us to arrive at (I) vacuum comprises substantial entities called aethers and (II) the velocities of light as measured in vacuum c and by a moving observer c', and the observer's velocity v obey the law of vector addition. (I)-(II) facilitate a General Scheme, which leads to (A) from Newton Mechanics solution for vacuum the fundamental formation of basic material particles having a mass, size, charge, etc. and being a de Broglie wave obeying Quantum Mechanics (B) augmentation in the mass, de Broglie wavevector, etc of a moving particle by a factor γ = 1/[1-(v/c)^2]^1/2 (C) length and time contractions of a moving body as measured in the frame in which the body resides (D) coordinate transformation between an inertial frame at rest and one relatively moving, called Galileo-Lorentz transformation (GLT) (E) using the GLT the prediction of null-fringe shift of the Michelson-Morley experiment and the Doppler effect of electromagnetic waves etc (F) inference of various contemporary empirical rules, incl Uncertainty Relation; etc.
Unification of Classical and Quantum Mechanics & Theory of Relative Motion
NASA Astrophysics Data System (ADS)
Zheng-Johansson, J. X.
2003-03-01
A systematic survey of relevant pivotal experiments leads us to arrive at (I) vacuum comprises substantial entities called aethers and (II) the velocities of light as measured in vacuum c and by a moving observer c', and the observer's velocity v obey the law of vector addition. (I)-(II) facilitate a General Scheme, which lead to (A) the fundamental formation of a basic material particle having a mass, size, charge, etc. and is a de Broglie wave obeying Quantum Mechanics as a result of Newton Mechanics solution (B) augmentation in the mass, de Broglie wavevector, etc of a moving particle by a factor γ =3D 1/[1-(v/c)^2]^1/2 (C) length and time contractions of a moving body as measured in the frame in which the body resides (D) a set of coordinate transformation equations between a inertial frame at rest and one relatively moving, called Galileo-Lorentz transformation (GLT) (E) using the GLT the prediction of null-fringe shift of the Michelson-Morley experiment and the Doppler effect of electromagnetic waves etc (F) inference of various contemporary empirical rules, relations; etc.
NASA Astrophysics Data System (ADS)
Mosonyi, Milán; Ogawa, Tomohiro
2015-03-01
We show that the new quantum extension of Rényi's α-relative entropies, introduced recently by Müller-Lennert et al. (J Math Phys 54:122203, 2013) and Wilde et al. (Commun Math Phys 331(2):593-622, 2014), have an operational interpretation in the strong converse problem of quantum hypothesis testing. Together with related results for the direct part of quantum hypothesis testing, known as the quantum Hoeffding bound, our result suggests that the operationally relevant definition of the quantum Rényi relative entropies depends on the parameter α: for α < 1, the right choice seems to be the traditional definition , whereas for α > 1 the right choice is the newly introduced version .On the way to proving our main result, we show that the new Rényi α-relative entropies are asymptotically attainable by measurements for α > 1. From this, we obtain a new simple proof for their monotonicity under completely positive trace-preserving maps.
NASA Astrophysics Data System (ADS)
Giesel, Kristina
The following sections are included: * Canonical Quantization of General Relativity * General Relativity in Connection Variables * Holonomy-Flux Algebra and its Representation(s) * The Ashtekar-Lewandowski Representation and the Kinematical Hilbert Space of LQG * The Quantum Einstein's Equations of Loop Quantum Gravity * Geometric Operators and Their Properties * Summary * References
Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
Stottmeister, Alexander Thiemann, Thomas
2016-06-15
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).
Multimode squeezing, biphotons and uncertainty relations in polarization quantum optics
NASA Technical Reports Server (NTRS)
Karassiov, V. P.
1994-01-01
The concept of squeezing and uncertainty relations are discussed for multimode quantum light with the consideration of polarization. Using the polarization gauge SU(2) invariance of free electromagnetic fields, we separate the polarization and biphoton degrees of freedom from other ones, and consider uncertainty relations characterizing polarization and biphoton observables. As a consequence, we obtain a new classification of states of unpolarized (and partially polarized) light within quantum optics. We also discuss briefly some interrelations of our analysis with experiments connected with solving some fundamental problems of physics.
Gauge connection formulations for general relativity
NASA Astrophysics Data System (ADS)
González, Diego; Montesinos, Merced
2015-01-01
We report a new class of S O (3 ,C ) and diffeomorphism invariant formulations for general relativity with either a vanishing or a nonvanishing cosmological constant, which depends functionally on a S O (3 ,C ) gauge connection and a complex-valued 4-form via a holomorphic function of the trace of a symmetric 3 ×3 matrix that is constructed from these variables. We present two members of this class, one of which results from the implementation of a method for obtaining action principles belonging to the class. For the case of a nonvanishing cosmological constant, we solve for the complex-valued 4-form and get pure connection action principles. We perform the canonical analysis of the class. The analysis shows that only the Hamiltonian constraint is modified with respect to the Ashtekar formulation and that the members of the class have two physical degrees of freedom per space point.
Motivations for antigravity in General Relativity
NASA Astrophysics Data System (ADS)
Chardin, G.
1997-08-01
We present arguments showing that it is natural to interpret the negative mass part of the Kerr solution as representing the geometry experienced by antimatter. The C, P and T discrete transformations are considered for this geometry. The C and T properties of the proposed identification are found to be in agreement with the usual representation of antimatter. In addition, we conjecture a property of perfect stigmatism through Kerr wormholes which allows General Relativity to mimic antigravity. Kerr wormholes would then act as “supermirrors” reversing the C, P and T images of an object seen through it. This interpretation is subject to several experimental tests and able to provide an explanation, without any free parameter, of the “CP” violation observed in the neutral kaon system.
Rapidly rotating polytropes in general relativity
NASA Technical Reports Server (NTRS)
Cook, Gregory B.; Shapiro, Stuart L.; Teukolsky, Saul A.
1994-01-01
We construct an extensive set of equilibrium sequences of rotating polytropes in general relativity. We determine a number of important physical parameters of such stars, including maximum mass and maximum spin rate. The stability of the configurations against quasi-radial perturbations is diagnosed. Two classes of evolutionary sequences of fixed rest mass and entropy are explored: normal sequences which behave very much like Newtonian evolutionary sequences, and supramassive sequences which exist solely because of relativistic effects. Dissipation leading to loss of angular momentum causes a star to evolve in a quasi-stationary fashion along an evolutionary sequence. Supramassive sequences evolve towards eventual catastrophic collapse to a black hole. Prior to collapse, the star must spin up as it loses angular momentum, an effect which may provide an observational precursor to gravitational collapse to a black hole.
On thick domain walls in general relativity
NASA Technical Reports Server (NTRS)
Goetz, Guenter; Noetzold, Dirk
1989-01-01
Planar scalar field configurations in general relativity differ considerably from those in flat space. It is shown that static domain walls of finite thickness in curved space-time do not possess a reflection symmetry. At infinity, the space-time tends to the Taub vacuum on one side of the wall and to the Minkowski vacuum (Rindler space-time) on the other. Massive test particles are always accelerated towards the Minkowski side, i.e., domain walls are attractive on the Taub side, but repulsive on the Minkowski side (Taub-vacuum cleaner). It is also proved that the pressure in all directions is always negative. Finally, a brief comment is made concerning the possibility of infinite, i.e., bigger than horizon size, domain walls in our universe. All of the results are independent of the form of the potential V(phi) greater than or equal to 0 of the scalar field phi.
Symplectic time integrators for numerical general relativity
Richter, Ronny
2009-05-01
We describe how we use symplectic time integrators in numerical general relativity. Of particular interest is the free symplectic Stoermer-Verlet method and its application to the dynamical part of ADM-like equations.The behavior of this scheme is illustrated on an effectively 1+1-dimensional version of Einstein's equations that we apply to a perturbed Minkowski problem. We discuss differences between symplectic and non-symplectic integrators, showing favorable evolution properties of the symplectic Stoermer-Verlet method in this example.To handle the constraint part of the equations with a symplectic integrator one can use a partially constrained scheme that applies the RATTLE method, a modification of the Stoermer-Verlet method for holonomic constraints.
Black hole mergers: beyond general relativity
NASA Astrophysics Data System (ADS)
Stein, Leo; Okounkova, Maria
2017-01-01
One hundred years after the birth of general relativity, advanced LIGO has finally directly detected gravitational waves. The source: two black holes merging into one. Advanced LIGO will soon provide the opportunity to test GR, using gravitational waves, in the dynamical strong-field regime-a setting where GR has not yet been tested. GR has passed all weak-field tests with flying colors. Yet it should eventually break down, so we must look to the strong-field. To perform strong-field tests of GR, we need waveform models from theories beyond GR. To date there are no numerical simulations of black hole mergers in theories which differ from GR. The main obstacle is the mathematical one of well-posedness. I will explain how to overcome this obstacle, and demonstrate the success of this approach by presenting the first numerical simulations of black hole mergers in a theory beyond GR.
Rapidly rotating polytropes in general relativity
NASA Technical Reports Server (NTRS)
Cook, Gregory B.; Shapiro, Stuart L.; Teukolsky, Saul A.
1994-01-01
We construct an extensive set of equilibrium sequences of rotating polytropes in general relativity. We determine a number of important physical parameters of such stars, including maximum mass and maximum spin rate. The stability of the configurations against quasi-radial perturbations is diagnosed. Two classes of evolutionary sequences of fixed rest mass and entropy are explored: normal sequences which behave very much like Newtonian evolutionary sequences, and supramassive sequences which exist solely because of relativistic effects. Dissipation leading to loss of angular momentum causes a star to evolve in a quasi-stationary fashion along an evolutionary sequence. Supramassive sequences evolve towards eventual catastrophic collapse to a black hole. Prior to collapse, the star must spin up as it loses angular momentum, an effect which may provide an observational precursor to gravitational collapse to a black hole.
The confrontation between general relativity and experiment
NASA Technical Reports Server (NTRS)
Will, C. M.
1980-01-01
Experiments that test the foundations of gravitation theory in terms of the Einstein equivalence principle are discussed along with solar system tests of general relativity at the post-Newtonian level. These include classical (light-deflection, time delay and perihelion shift) tests as well as tests of the strong equivalence principle. The binary pulsar is discussed as an extra-solar-system gravitational testing ground, and attention is given to the multipolarity of the waves and the amount of radiation damping. The mass function, periastron shift, redshift-Doppler parameter and rate of change of the orbit period (Pb) of the binary pulsar are also considered, and it is suggested that the measurement of Pb represents the first observation of the effects of gravitational radiation.
GENERAL: Preservation of quantum states via a super-Zeno effect on ensemble quantum computers
NASA Astrophysics Data System (ADS)
Ren, Ting-Ting; Luo, Jun; Sun, Xian-Ping; Zhan, Ming-Sheng
2009-11-01
Following a recent proposal by Dhar et al (2006 Phys. Rev. Lett. 96 100405), we demonstrate experimentally the preservation of quantum states in a two-qubit system based on a super-Zeno effect using liquid-state nuclear magnetic resonance techniques. Using inverting radiofrequency pulses and delicately selecting time intervals between two pulses, we suppress the effect of decoherence of quantum states. We observe that preservation of the quantum state |11rangle with the super-Zeno effect is three times more efficient than the ordinary one with the standard Zeno effect.
NASA Astrophysics Data System (ADS)
Bogolubov, N. N.; Prykarpatsky, Y. A.
2013-03-01
An approach to describing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the Marsden-Weinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well-known Adler-Kostant-Souriau-Berezin-Kirillov method and the associated R-matrix approach is analyzed. A new generalized exactly solvable spatially one-dimensional quantum superradiance model, describing a charged fermionic medium interacting with external electromagnetic field, is suggested. The Lax type operator spectral problem is presented, the related R-structure is calculated. The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related with the thermodynamical equilibrity of the model, are discussed.
Elliptical galaxies kinematics within general relativity with renormalization group effects
Rodrigues, Davi C.
2012-09-01
The renormalization group framework can be applied to Quantum Field Theory on curved space-time, but there is no proof whether the beta-function of the gravitational coupling indeed goes to zero in the far infrared or not. In a recent paper [1] we have shown that the amount of dark matter inside spiral galaxies may be negligible if a small running of the General Relativity coupling G is present (δG/G{sub 0}∼<10{sup −7} across a galaxy). Here we extend the proposed model to elliptical galaxies and present a detailed analysis on the modeling of NGC 4494 (an ordinary elliptical) and NGC 4374 (a giant elliptical). In order to compare our results to a well known alternative model to the standard dark matter picture, we also evaluate NGC 4374 with MOND. In this galaxy MOND leads to a significative discrepancy with the observed velocity dispersion curve and has a significative tendency towards tangential anisotropy. On the other hand, the approach based on the renormalization group and general relativity (RGGR) could be applied with good results to these elliptical galaxies and is compatible with lower mass-to-light ratios (of about the Kroupa IMF type)
Matrix general relativity: a new look at old problems
NASA Astrophysics Data System (ADS)
Avramidi, Ivan G.
2004-01-01
We develop a novel approach to gravity that we call 'matrix general relativity' (MGR) or 'gravitational chromodynamics' (GCD or GQCD for the quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric two-tensor field) but by a multiplet of such fields, or by a matrix-valued symmetric two-tensor field that satisfies certain conditions. We define the matrix extensions of standard constructions of differential geometry including connections and curvatures, and finally, an invariant functional of the new field that reduces to the standard Einstein action functional in the commutative (diagonal) case. Our main idea is the analogy with Yang Mills theory (QCD and the standard model). We call the new degrees of freedom of gravity associated with the matrix structure 'gravitational colour' or simply 'gravicolour' and introduce a new gauge symmetry associated with this degree of freedom. As in the standard model there are two possibilities. First of all, it is possible that at high energies (say at the Planckian scale) this symmetry is exact (symmetric phase), but at low energies it is badly broken, so that one tensor field remains massless (and gives general relativity) and the other ones become massive with masses of Planckian scale. The second possibility is that the additional degrees of freedom of the gravitational field are confined to the Planckian scale. What one sees at large distances are singlets (invariants) of the new gauge symmetry.
Generalized trace-distance measure connecting quantum and classical non-Markovianity
NASA Astrophysics Data System (ADS)
Wißmann, Steffen; Breuer, Heinz-Peter; Vacchini, Bassano
2015-10-01
We establish a direct connection of quantum Markovianity of an open system to its classical counterpart by generalizing the criterion based on the information flow. Here the flow is characterized by the time evolution of Helstrom matrices, given by the weighted difference of statistical operators, under the action of the quantum dynamical map. It turns out that the introduced criterion is equivalent to P divisibility of a quantum process, namely, divisibility in terms of positive maps, which provides a direct connection to classical Markovian stochastic processes. Moreover, it is shown that mathematical representations similar to those found for the original trace-distance-based measure hold true for the associated generalized measure for quantum non-Markovianity. That is, we prove orthogonality of optimal states showing a maximal information backflow and establish a local and universal representation of the measure. We illustrate some properties of the generalized criterion by means of examples.
An Introduction to General Relativity and Cosmology
NASA Astrophysics Data System (ADS)
Plebanski, Jerzy; Krasinski, Andrzej
2012-09-01
1. How the theory of relativity came into being (a brief historical sketch); Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries; 3. Tensors, tensor densities; 4. Covariant derivatives; 5. Parallel transport and geodesic lines; 6. Curvature of a manifold: flat manifolds; 7. Riemannian geometry; 8. Symmetries of Rieman spaces, invariance of tensors; 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs; 10. The spatially homogeneous Bianchi-type spacetimes; 11. The Petrov classification by the spinor method; Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field; 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory; 14. Spherically symmetric gravitational field of isolated objects; 15. Relativistic hydrodynamics and thermodynamics; 16. Relativistic cosmology I: general geometry; 17. Relativistic cosmology II: the Robertson-Walker geometry; 18. Relativistic cosmology III: the Lemaître-Tolman geometry; 19. Relativistic cosmology IV: generalisations of L-T and related geometries; 20. The Kerr solution; 21. Subjects omitted in this book; References.
An Introduction to General Relativity and Cosmology
NASA Astrophysics Data System (ADS)
Plebanski, Jerzy; Krasinski, Andrzej
2006-08-01
1. How the theory of relativity came into being (a brief historical sketch); Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries; 3. Tensors, tensor densities; 4. Covariant derivatives; 5. Parallel transport and geodesic lines; 6. Curvature of a manifold: flat manifolds; 7. Riemannian geometry; 8. Symmetries of Rieman spaces, invariance of tensors; 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs; 10. The spatially homogeneous Bianchi-type spacetimes; 11. The Petrov classification by the spinor method; Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field; 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory; 14. Spherically symmetric gravitational field of isolated objects; 15. Relativistic hydrodynamics and thermodynamics; 16. Relativistic cosmology I: general geometry; 17. Relativistic cosmology II: the Robertson-Walker geometry; 18. Relativistic cosmology III: the Lemaître-Tolman geometry; 19. Relativistic cosmology IV: generalisations of L-T and related geometries; 20. The Kerr solution; 21. Subjects omitted in this book; References.
Quantum decoherence modulated by special relativity
Cai Jianming; Zhou Zhengwei; Guo Guangcan; Yuan Yefei
2007-10-15
By investigating the evolution of a moving spin-(1/2) Dirac electron coupled with a background magnetic noise, we demonstrate that the effects of special relativity will significantly modify the decoherence properties of the spin state. The dephasing could be much suppressed, and for a sufficiently long time the decoherence even seems to halt. This interesting phenomenon stems from the dressed environment induced by special relativity.
Quantum entanglement for systems of identical bosons: I. General features
NASA Astrophysics Data System (ADS)
Dalton, B. J.; Goold, J.; Garraway, B. M.; Reid, M. D.
2017-02-01
These two accompanying papers are concerned with two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems in which the probabilities for joint measurements on the composite sub-systems are no longer determined from measurement probabilities on the separate sub-systems. There are many aspects of entanglement that can be studied. This two-part review focuses on the meaning of entanglement, the quantum paradoxes associated with entangled states, and the important tests that allow an experimentalist to determine whether a quantum state—in particular, one for massive bosons is entangled. An overall outcome of the review is to distinguish criteria (and hence experiments) for entanglement that fully utilize the symmetrization principle and the super-selection rules that can be applied to bosonic massive particles. In the first paper (I), the background is given for the meaning of entanglement in the context of systems of identical particles. For such systems, the requirement is that the relevant quantum density operators must satisfy the symmetrization principle and that global and local super-selection rules prohibit states in which there are coherences between differing particle numbers. The justification for these requirements is fully discussed. In the second quantization approach that is used, both the system and the sub-systems are modes (or sets of modes) rather than particles, particles being associated with different occupancies of the modes. The definition of entangled states is based on first defining the non-entangled states—after specifying which modes constitute the sub-systems. This work mainly focuses on the two mode entanglement for massive bosons, but is put in the context of tests of local hidden variable theories, where one may not be able to make the above restrictions. The review provides the detailed
Quantum Rényi relative entropies affirm universality of thermodynamics.
Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A K
2015-10-01
We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter α approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.
Monogamy relation in multipartite continuous-variable quantum teleportation
NASA Astrophysics Data System (ADS)
Lee, Jaehak; Ji, Se-Wan; Park, Jiyong; Nha, Hyunchul
2016-12-01
Quantum teleportation (QT) is a fundamentally remarkable communication protocol that also finds many important applications for quantum informatics. Given a quantum entangled resource, it is crucial to know to what extent one can accomplish the QT. This is usually assessed in terms of output fidelity, which can also be regarded as an operational measure of entanglement. In the case of multipartite communication when each communicator possesses a part of an N -partite entangled state, not all pairs of communicators can achieve a high fidelity due to the monogamy property of quantum entanglement. We here investigate how such a monogamy relation arises in multipartite continuous-variable (CV) teleportation, particularly when using a Gaussian entangled state. We show a strict monogamy relation, i.e., a sender cannot achieve a fidelity higher than optimal cloning limit with more than one receiver. While this seems rather natural owing to the no-cloning theorem, a strict monogamy relation still holds even if the sender is allowed to individually manipulate the reduced state in collaboration with each receiver to improve fidelity. The local operations are further extended to non-Gaussian operations such as photon subtraction and addition, and we demonstrate that the Gaussian cloning bound cannot be beaten by more than one pair of communicators. Furthermore, we investigate a quantitative form of monogamy relation in terms of teleportation capability, for which we show that a faithful monogamy inequality does not exist.
Quantum Rényi relative entropies affirm universality of thermodynamics
NASA Astrophysics Data System (ADS)
Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A. K.
2015-10-01
We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter α approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.
Quantum capacitance in monolayers of silicene and related buckled materials
NASA Astrophysics Data System (ADS)
Nawaz, S.; Tahir, M.
2016-02-01
Silicene and related buckled materials are distinct from both the conventional two dimensional electron gas and the famous graphene due to strong spin orbit coupling and the buckled structure. These materials have potential to overcome limitations encountered for graphene, in particular the zero band gap and weak spin orbit coupling. We present a theoretical realization of quantum capacitance which has advantages over the scattering problems of traditional transport measurements. We derive and discuss quantum capacitance as a function of the Fermi energy and temperature taking into account electron-hole puddles through a Gaussian broadening distribution. Our predicted results are very exciting and pave the way for future spintronic and valleytronic devices.
Quantum-memory-assisted entropic uncertainty relations under weak measurements
NASA Astrophysics Data System (ADS)
Li, Lei; Wang, Qing-Wen; Shen, Shu-Qian; Li, Ming
2017-08-01
We investigate quantum-memory-assisted entropic uncertainty relations (EURs) based on weak measurements. It is shown that the lower bound of EUR revealed by weak measurements is always larger than that revealed by the corresponding projective measurements. A series of lower bounds of EUR under both weak measurements and projective measurements are presented. Interestingly, the quantum-memory-assisted EUR based on weak measurements is a monotonically decreasing function of the strength parameter. Furthermore, some information-theoretic inequalities associated with weak measurements are also derived.
Experimental bit commitment based on quantum communication and special relativity.
Lunghi, T; Kaniewski, J; Bussières, F; Houlmann, R; Tomamichel, M; Kent, A; Gisin, N; Wehner, S; Zbinden, H
2013-11-01
Bit commitment is a fundamental cryptographic primitive in which Bob wishes to commit a secret bit to Alice. Perfectly secure bit commitment between two mistrustful parties is impossible through asynchronous exchange of quantum information. Perfect security is however possible when Alice and Bob split into several agents exchanging classical and quantum information at times and locations suitably chosen to satisfy specific relativistic constraints. Here we report on an implementation of a bit commitment protocol using quantum communication and special relativity. Our protocol is based on [A. Kent, Phys. Rev. Lett. 109, 130501 (2012)] and has the advantage that it is practically feasible with arbitrary large separations between the agents in order to maximize the commitment time. By positioning agents in Geneva and Singapore, we obtain a commitment time of 15 ms. A security analysis considering experimental imperfections and finite statistics is presented.
Exotic differentiable structures and general relativity
NASA Astrophysics Data System (ADS)
Brans, Carl H.; Randall, Duane
1993-02-01
We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (“fake” or “exotic”) differentiable structures on topologically simple manifolds such asS 7, ℝ4 andS 3 X ℝ1. Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.
Inflation and bubbles in general relativity
NASA Astrophysics Data System (ADS)
Laguna-Castillo, Pablo; Matzner, Richard A.
1986-11-01
Following Israel's study of singular hypersurfaces and thin shells in general relativity, the complete set of Einstein's field equations in the presence of a bubble boundary SIGMA is reviewed for all spherically symmetric embedding four-geometries M+/-. The mapping that identifies points between the boundaries Σ+ and Σ- is obtained explicitly when the regions M+ and M- are described by a de Sitter and a Minkowski metric, respectively. In addition, the evolution of a bubble with vanishing surface energy density is studied in a spatially flat Robertson-Walker space-time, for region M- radiation dominated with a vanishing cosmological constant, and an energy equation in M+ determined by the matching. It is found that this type of bubble leads to a ``worm-hole'' matching; that is, an infinite extent exterior of a sphere is joined across the wall to another infinite extent exterior of a sphere. Interior-interior matches are also possible. Under this model, solutions for a bubble following a Hubble law are analyzed. Numerical solutions for bubbles with constant tension are also obtained.
NASA Astrophysics Data System (ADS)
Barnum, Howard; Ortiz, Gerardo; Somma, Rolando; Viola, Lorenza
2005-12-01
We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This extends the notion of ordinary entanglement in quantum information theory to a much more general framework. Some important special cases are described, in which the distinguished observables are subspaces of the observables of a quantum system, leading to results like the identification of generalized unentangled states with Lie-group-theoretic coherent states when the special observables form an irreducibly represented Lie algebra. Some open problems, including that of generalizing the semigroup of local operations with classical communication to the convex cones setting, are discussed.
Scaling relations for gaps in fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Murthy, Ganpathy; Park, K.; Shankar, R.; Jain, J. K.
1998-12-01
The microscopic Hamiltonian approach of Murthy and Shankar, which has recently been used to calculate the transport gaps of quantum Hall states with fractions ν=p/(2ps+1), also implies scaling relations between gaps within a single sequence (fixed s) as well as between gaps of corresponding states in different sequences. This work tests these relations for a system of electrons in the lowest Landau level interacting with a model potential cutoff at high momenta due to sample thickness.
Quantum image encryption based on generalized Arnold transform and double random-phase encoding
NASA Astrophysics Data System (ADS)
Zhou, Nan Run; Hua, Tian Xiang; Gong, Li Hua; Pei, Dong Ju; Liao, Qing Hong
2015-04-01
A quantum realization of the generalized Arnold transform is designed. A novel quantum image encryption algorithm based on generalized Arnold transform and double random-phase encoding is proposed. The pixels are scrambled by the generalized Arnold transform, and the gray-level information of images is encoded by the double random-phase operations. The keys of the encryption algorithm include the independent parameters of coefficients matrix, iterative times and classical binary sequences, and thus, the key space is extremely large. Numerical simulations and theoretical analyses demonstrate that the proposed algorithm with good feasibility and effectiveness has lower computational complexity than its classical counterpart.
General model on polarization compensation in satellite-to-ground quantum communication
NASA Astrophysics Data System (ADS)
Li, Ming; Lu, Pengfei; Yu, Zhongyuan; Liu, Yumin; Zhang, Lidong; Yang, Chuanghua
2013-04-01
A general model in satellite-to-ground quantum communication is proposed by investigating the effect of a laser acquisition, pointing, and tracking (APT) system on the polarization state of single photons. The eccentricity of the general model ranges from 0 to 1, which means that a circular orbit can be introduced reasonably. Moreover, the geocentric-equatorial coordinate system, which can utilize the two-line elements, is used in the general model. Two kinds of simulations are performed, and we found that the rotations of polarization state are obviously influenced by the APT system. Our model could be applied in a realistic satellite-to-ground quantum communication system.
NASA Astrophysics Data System (ADS)
Vélez, Mario; Ospina, Juan
2012-06-01
Possible quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant are proposed. Such algorithms are resulting from adaptations of the recently proposed Kauffman's algorithm for the standard Khovanov homology. The method that was applied consists in to write the relevant quantum invariant as the trace of a certain unitary operator and then to compute the trace using the Hadamard test. We apply such method to the quantum computation of the Jones polynomial, HOMFLY polynomial, Chromatic polynomial, Tutte polynomial and Bollobàs- Riordan polynomial. These polynomials are quantum topological invariants for knots, links, graphs and ribbon graphs respectively. The Jones polynomial is categorified by the standard Khovanov homology and the others polynomials are categorified by generalized Khovanov homologies, such as the Khovanov-Rozansky homology and the graph homologies. The algorithm for the Rasmussen's invariant is obtained using the gauge theory; and the recently introduced program of homotopyfication is linked with the super-symmetric quantum mechanics. It is claimed that a new program of analytification could be development from the homotopyfication using the celebrated Atiyah-Singer theorem and its super-symmetric interpretations. It is hoped that the super-symmetric quantum mechanics provides the hardware for the implementation of the proposed quantum algorithms.
General approach to quantum-classical hybrid systems and geometric forces.
Zhang, Qi; Wu, Biao
2006-11-10
We present a general theoretical framework for a hybrid system that is composed of a quantum subsystem and a classical subsystem. We approach such a system with a simple canonical transformation which is particularly effective when the quantum subsystem is dynamically much faster than the classical counterpart, which is commonly the case in hybrid systems. Moreover, this canonical transformation generates a vector potential which, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics and, on the other hand, yields a Lorentz-like geometric force in the slow classical dynamics.
Gamma and Related Functions Generalized for Sequences
ERIC Educational Resources Information Center
Ollerton, R. L.
2008-01-01
Given a sequence g[subscript k] greater than 0, the "g-factorial" product [big product][superscript k] [subscript i=1] g[subscript i] is extended from integer k to real x by generalizing properties of the gamma function [Gamma](x). The Euler-Mascheroni constant [gamma] and the beta and zeta functions are also generalized. Specific examples include…
Gamma and Related Functions Generalized for Sequences
ERIC Educational Resources Information Center
Ollerton, R. L.
2008-01-01
Given a sequence g[subscript k] greater than 0, the "g-factorial" product [big product][superscript k] [subscript i=1] g[subscript i] is extended from integer k to real x by generalizing properties of the gamma function [Gamma](x). The Euler-Mascheroni constant [gamma] and the beta and zeta functions are also generalized. Specific examples include…
Gravitational Wave in Linear General Relativity
NASA Astrophysics Data System (ADS)
Cubillos, D. J.
2017-07-01
General relativity is the best theory currently available to describe the interaction due to gravity. Within Albert Einstein's field equations this interaction is described by means of the spatiotemporal curvature generated by the matter-energy content in the universe. Weyl worked on the existence of perturbations of the curvature of space-time that propagate at the speed of light, which are known as Gravitational Waves, obtained to a first approximation through the linearization of the field equations of Einstein. Weyl's solution consists of taking the field equations in a vacuum and disturbing the metric, using the Minkowski metric slightly perturbed by a factor ɛ greater than zero but much smaller than one. If the feedback effect of the field is neglected, it can be considered as a weak field solution. After introducing the disturbed metric and ignoring ɛ terms of order greater than one, we can find the linearized field equations in terms of the perturbation, which can then be expressed in terms of the Dalambertian operator of the perturbation equalized to zero. This is analogous to the linear wave equation in classical mechanics, which can be interpreted by saying that gravitational effects propagate as waves at the speed of light. In addition to this, by studying the motion of a particle affected by this perturbation through the geodesic equation can show the transversal character of the gravitational wave and its two possible states of polarization. It can be shown that the energy carried by the wave is of the order of 1/c5 where c is the speed of light, which explains that its effects on matter are very small and very difficult to detect.
Quantum Fields Obtained from Convoluted Generalized White Noise Never Have Positive Metric
NASA Astrophysics Data System (ADS)
Albeverio, Sergio; Gottschalk, Hanno
2016-05-01
It is proven that the relativistic quantum fields obtained from analytic continuation of convoluted generalized (Lévy type) noise fields have positive metric, if and only if the noise is Gaussian. This follows as an easy observation from a criterion by Baumann, based on the Dell'Antonio-Robinson-Greenberg theorem, for a relativistic quantum field in positive metric to be a free field.
Candidate General Ontologies for Situating Quantum Field Theory
NASA Astrophysics Data System (ADS)
Simons, Peter
Ontology is traditionally an a priori discipline purveying its categories and principles independently of mere facts, but this arrogance of philosophers has led them into latent or patent incompatibility with good science and has landed them with philosophical aporiai such as the mind-body problem and the universals dispute. So while maintaining the abstractness and systematic universality of ontology it pays to craft one's categories with an eye to the best empirical science, while not necessarily trying to read the ontology off that science. I present desiderata for a systematic ontology and give several reasons why one cannot use physical theory alone as the source of one's a posteriori ontology. With this in mind I survey six ontological theories as possible frameworks for QFT, four briefly, two at greater length. The first is the traditional substanceattribute metaphysic, which is clearly obsolete, and on which I expend little time. The second is its modern logico-linguistic replacement, the ontology of individuals and sets touted as semantic values in logical semantics. This too falls by the wayside for several reasons. A third is the closely related ontology or ontologies of facts, against which I argue on general grounds. A fourth is Whiteheadian process ontology, which is an improvement over the previous three but still leaves several questions unsatisfactorily answered. The most flexible and promising to date is the ontology of tropes and trope bundles, which I have discussed in several places. After expounding this I reject it not because it is false but because it is neither broad nor deep enough. As a final, sixth alternative, I present an ontology of invariant factors inspired in part by Whitehead and in part by remarks of Max Planck, and offer it as a promising future abstract framework within which to situate the physics of QFT.
Categorical Operator Algebraic Foundations of Relational Quantum Theory
NASA Astrophysics Data System (ADS)
Bertozzini, P.
We provide an algebraic formulation of C.Rovelli's relational quantum theory that is based on suitable notions of "non-commutative" higher operator categories, originally developed in the study of categorical non-commutative geometry. As a way to implement C.Rovelli's original intuition on the relational origin of space-time, in the context of our proposed algebraic approach to quantum gravity via Tomita-Takesaki modular theory, we tentatively suggest to use this categorical formalism in order to spectrally reconstruct non-commutative relational space-time geometries from categories of correlation bimodules between operator algebras of observables. Parts of this work are joint collaborations with: Dr.Roberto Conti (Sapienza Universita' di Roma), Assoc.Prof.Wicharn Lewkeeratiyutkul (Chulalongkorn University, Bangkok), Dr.Rachel Dawe Martins (Istituto Superior Tecnico, Lisboa), Dr.Matti Raasakka (Paris 13 University), Dr.Noppakhun Suthichitranont.
What is a singular black hole beyond general relativity?
NASA Astrophysics Data System (ADS)
Bejarano, Cecilia; Olmo, Gonzalo J.; Rubiera-Garcia, Diego
2017-03-01
Exploring the characterization of singular black hole spacetimes, we study the relation between energy density, curvature invariants, and geodesic completeness using a quadratic f (R ) gravity theory coupled to an anisotropic fluid. Working in a metric-affine approach, our models and solutions represent minimal extensions of general relativity (GR) in the sense that they rapidly recover the usual Reissner-Nordström solution from near the inner horizon outwards. The anisotropic fluid helps modify only the innermost geometry. Depending on the values and signs of two parameters on the gravitational and matter sectors, a breakdown of the correlations between the finiteness/divergence of the energy density, the behavior of curvature invariants, and the (in)completeness of geodesics is obtained. We find a variety of configurations with and without wormholes, a case with a de Sitter interior, solutions that mimic nonlinear models of electrodynamics coupled to GR, and configurations with up to four horizons. Our results raise questions regarding what infinities, if any, a quantum version of these theories should regularize.
Capacity of optical communication in loss and noise with general quantum Gaussian receivers
NASA Astrophysics Data System (ADS)
Takeoka, Masahiro; Guha, Saikat
2014-04-01
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated code words with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent-state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations [passive linear optics: beam splitters and phase shifters; second-order nonlinear optics (or active linear optics): squeezers, along with homodyne or heterodyne detection measurements] and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communication, one has to incorporate non-Gaussian, i.e., third- or higher-order nonlinear operations in the receiver. Finally we compare our Gaussian receiver limit with experimentally feasible non-Gaussian receivers and show that in the regime of low received photon flux, it is possible to overcome the Gaussian receiver limit by relatively simple non-Gaussian receivers based on photon counting.
Matrix Results and Techniques in Quantum Information Science and Related Topics
NASA Astrophysics Data System (ADS)
Pelejo, Diane Christine
In this dissertation, we present several matrix-related problems and results motivated by quantum information theory. Some background material of quantum information science will be discussed in chapter 1, while chapter 7 gives a summary of results and concluding remarks. In chapter 2, we look at 2n x 2 n unitary matrices, which describe operations on a closed n-qubit system. We define a set of simple quantum gates, called controlled single qubit gates, and their associated operational cost. We then present a recurrence scheme to decompose a general 2n x 2n unitary matrix to the product of no more than 2n-12n-1 single qubit gates with small number of controls. In chapter 3, we address the problem of finding a specific element phi among a given set of quantum channels S that will produce the optimal value of a scalar function D(rho 1,phi(rho2)), on two fixed quantum states rho 1 and rho2. Some of the functions we considered for D(·,·) are the trace distance, quantum fidelity and quantum relative entropy. We discuss the optimal solution when S is the set of unitary quantum channels, the set of mixed unitary channels, the set of unital quantum channels, and the set of all quantum channels. In chapter 4, we focus on the spectral properties of qubit-qudit bipartite states with a maximally mixed qudit subsystem. More specifically, given positive numbers a1 ≥ ... ≥ a 2n ≥ 0, we want to determine if there exist a 2n x 2n density matrix rho having eigenvalues a1,..., a2n and satisfying tr 1(rho)=1/n In. This problem is a special case of the more general quantum marginal problem. We give the minimal necessary and sufficient conditions on a1,..., a2n for n ≤ 6 and state some observations on general values of n.. In chapter 5, we discuss the numerical method of alternating projections and illustrate its usefulness in: (a) constructing a quantum channel, if it exists, such that phi(rho(1))=sigma(1),...,phi(rho (k))=sigma(k) for given rho (1),...,rho(k) ∈ Dn and
NASA Astrophysics Data System (ADS)
Blair, D. G.; Buckingham, M. J.
Contents: Part A. 1. Rigorous and exact. Classical general relativity: highly non-linear behaviour. Spin, geometry and topology. Approximation methods. Exact solutions. Black hole physics. Alternative theories and torsion. 2. Quantum gravity. Critical accelerations. Quantum gravity. String theories. Cosmic strings, superstrings and supergravity. Quantum cosmology: wavefunction of the universe. Quantum cosmology. 3. Cosmology. Early cosmology and quantum field theory. Supersymmetry, multidimensional cosmology and Kaluza-Klein theory. Theoretical cosmology. Large-scale structure of the universe. Dark matter. Part B. 4. Mathematical astrophysics. Algebraic computing. Numerical relativity. Astrophysics of collapsed objects. Self gravitating systems. History of general relativity. 5. Observational astrophysics. Sources of gravitational radiation. Relativistic astrophysics. Supernovae. Observation of collapsed objects. Cosmic background. 5. Precision experiments. The fifth force. Measuring the gravitational interaction in precision space experiments. Resonant bar antennas. Laser interferometer antennas. Detection of gravitational radiation. Quantum technology for gravitational radiation detection. Precision clocks in general relativity.
Teleportation as a depolarizing quantum channel, relative entropy, and classical capacity.
Bowen, G; Bose, S
2001-12-24
We show that standard teleportation with an arbitrary mixed state resource is equivalent to a generalized depolarizing channel with probabilities given by the maximally entangled components of the resource. This enables the usage of any quantum channel as a generalized depolarizing channel without additional twirling operations. It also provides a nontrivial upper bound on the entanglement of a class of mixed states. Our result allows a consistent and statistically motivated quantification of teleportation success in terms of the relative entropy and this quantification can be related to a classical capacity.
Stupakov, Gennady
2001-04-02
A dispersion relation for a microwave instability of a coasting beam is derived from the Vlasov-Fokker-Plank equation which takes into account the effects of synchrotron damping and quantum fluctuations. This derivation generalizes the standard analysis of the beam stability in which the discussion and damping are usually neglected. Our results are also applicable for a bunched beam when the wavelength of the instability is much smaller than the bunch length.
Superspace and global stability in general relativity
NASA Astrophysics Data System (ADS)
Gurzadyan, A. V.; Kocharyan, A. A.
A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalized Jacobi equation reformulated for pseudo-Riemannian manifolds. We give a direct formalism for dynamical analysis in the superspace, the requisite equation pertinent for stability analysis of the universe by means of generalized covariant and Fermi derivative is derived. Then, the relevant definitions and formulae are retrieved for cosmological models with a scalar field.
General Quantum Meet-in-the-Middle Search Algorithm Based on Target Solution of Fixed Weight
NASA Astrophysics Data System (ADS)
Fu, Xiang-Qun; Bao, Wan-Su; Wang, Xiang; Shi, Jian-Hong
2016-10-01
Similar to the classical meet-in-the-middle algorithm, the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm. Aiming at the target vector of fixed weight, based on the quantum meet-in-the-middle algorithm, the algorithm for searching all n-product vectors with the same weight is presented, whose complexity is better than the exhaustive search algorithm. And the algorithm can reduce the storage complexity of the quantum meet-in-the-middle search algorithm. Then based on the algorithm and the knapsack vector of the Chor-Rivest public-key crypto of fixed weight d, we present a general quantum meet-in-the-middle search algorithm based on the target solution of fixed weight, whose computational complexity is \\sumj = 0d {(O(\\sqrt {Cn - k + 1d - j }) + O(C_kj log C_k^j))} with Σd i =0 Ck i memory cost. And the optimal value of k is given. Compared to the quantum meet-in-the-middle search algorithm for knapsack problem and the quantum algorithm for searching a target solution of fixed weight, the computational complexity of the algorithm is lower. And its storage complexity is smaller than the quantum meet-in-the-middle-algorithm. Supported by the National Basic Research Program of China under Grant No. 2013CB338002 and the National Natural Science Foundation of China under Grant No. 61502526
General coordinate invariance in quantum many-body systems
NASA Astrophysics Data System (ADS)
Brauner, Tomáš; Endlich, Solomon; Monin, Alexander; Penco, Riccardo
2014-11-01
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the background metric and gauge fields, first introduced by Son and Wingate in 2005 and refined in subsequent works, follow naturally from our framework. Our approach makes it clear that Galilei or Poincaré symmetry is by no means a necessary prerequisite for making the theory invariant under coordinate diffeomorphisms. General covariance merely expresses the freedom to choose spacetime coordinates at will, whereas the true, physical symmetries of the system can be separately implemented as "internal" symmetries within the vielbein formalism. A systematic way to implement such symmetries is provided by the coset construction. We illustrate this point by applying our formalism to nonrelativistic s -wave superfluids.
General form of genuine multipartite entanglement quantum channels for teleportation
Chen Pingxing; Zhu Shiyao; Guo, Guangcan
2006-09-15
Recently Yeo and Chua [Phys. Rev. Lett. 96, 060502 (2006)] presented an explicit protocol for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entanglement channel. Here we generalize completely their results to teleporting an arbitrary N-qubit state via genuine N-qubit entanglement channels. And we present the general form of the genuine multipartite entanglement channels, namely, the sufficient and necessary condition the genuine N-qubit entanglement channels must satisfy to teleport an arbitrary N-qubit state.
Sensory Discrimination as Related to General Intelligence.
ERIC Educational Resources Information Center
Acton, G. Scott; Schroeder, David H.
2001-01-01
Attempted to replicate the pitch discrimination findings of previous research and expand them to the modality of color discrimination in a sample of 899 teenagers and adults by correlating 2 sensory discrimination measures with the general factor from a battery of 13 cognitive ability tests. Results suggest that sensory discrimination is…
An Elementary Formalism for General Relativity.
ERIC Educational Resources Information Center
diSessa, Andrea A.
1981-01-01
An elementary formalism is developed for representing curved space-time which allows transparent qualitative explanation of general relativistic effects and is used to make a conceptual analysis of Einstein's principle of equivalence. A final section outlines a number of student activities. (Author/SK)
An Elementary Formalism for General Relativity.
ERIC Educational Resources Information Center
diSessa, Andrea A.
1981-01-01
An elementary formalism is developed for representing curved space-time which allows transparent qualitative explanation of general relativistic effects and is used to make a conceptual analysis of Einstein's principle of equivalence. A final section outlines a number of student activities. (Author/SK)
NASA Astrophysics Data System (ADS)
Radonjić, M.; Popović, D. B.; Prvanović, S.; Burić, N.
2014-02-01
Representation of classical dynamics by unitary transformations has been used to develop a unified description of hybrid classical-quantum systems with a particular type of interaction, and to formulate abstract systems interpolating between classical and quantum ones. We solved the problem of a unitary description of two interpolating systems with general potential interaction. The general solution is used to show that with arbitrary potential interaction between the two interpolating systems the evolution of the so-called unobservable variables is decoupled from that of the observable ones if and only if the interpolation parameters in the two interpolating systems are equal.
Szigeti, Stuart S; Carvalho, Andre R R; Morley, James G; Hush, Michael R
2014-07-11
A "no-knowledge" measurement of an open quantum system yields no information about any system observable; it only returns noise input from the environment. Surprisingly, performing such a no-knowledge measurement can be advantageous. We prove that a system undergoing no-knowledge monitoring has reversible noise, which can be canceled by directly feeding back the measurement signal. We show how no-knowledge feedback control can be used to cancel decoherence in an arbitrary quantum system coupled to a Markovian reservoir that is being monitored. Since no-knowledge feedback does not depend on the system state or Hamiltonian, such decoherence cancellation is guaranteed to be general and robust, and can operate in conjunction with any other quantum control protocol. As an application, we show that no-knowledge feedback could be used to improve the performance of dissipative quantum computers subjected to local loss.
Generalized decoding, effective channels, and simplified security proofs in quantum key distribution
Renes, Joseph M.; Grassl, Markus
2006-08-15
Prepare and measure quantum key distribution protocols can be decomposed into two basic steps: delivery of the signals over a quantum channel and distillation of a secret key from the signal and measurement records by classical processing and public communication. Here we formalize the distillation process for a general protocol in a purely quantum-mechanical framework and demonstrate that it can be viewed as creating an 'effective' quantum channel between the legitimate users Alice and Bob. The process of secret key generation can then be viewed as entanglement distribution using this channel, which enables application of entanglement-based security proofs to essentially any prepare and measure protocol. To ensure secrecy of the key, Alice and Bob must be able to estimate the channel noise from errors in the key, and we further show how symmetries of the distillation process simplify this task. Applying this method, we prove the security of several key distribution protocols based on equiangular spherical codes.
Wu, Feng; Chen, Lingen; Sun, Fengrui; Wu, Chih; Li, Qing
2006-01-01
The purpose of this paper is to establish a model of an irreversible quantum Brayton engine using many noninteracting spin systems as the working substance and consisting of two irreversible adiabatic and two isomagnetic field processes. The time evolution of the total magnetic moment M is determined by solving the generalized quantum master equation of an open system in the Heisenberg picture. The time of two irreversible adiabatic processes is considered based on finite-rate evolution. The relationship between the power output P and the efficiency eta for the irreversible quantum Brayton engine with spin systems is derived. The optimally operating region (or criteria) for the engine is determined. The influences of these important parameters on the performances (P and eta) of the engine are discussed. The results obtained herein will be useful for the further understanding and the selection of the optimal operating conditions for an irreversible quantum Brayton engine with spin systems.
NASA Astrophysics Data System (ADS)
Poisson, Eric
2010-05-01
A few years ago, in my review of Sean Carroll's book in Classical and Quantum Gravity [1], I wrote that while the 1970s was the decade of Weinberg [2] and Misner, Thorne and Wheeler [3], and while the eighties was the decade of Schutz [4] and Wald [5], the 2000s was clearly the decade of Hartle [6] and Carroll [7]. In my opinion, these books continue to stand out in the surprisingly dense crowd of introductory textbooks on general relativity. At the dawn of this new decade I look forward to see what fresh pedagogical insights will be produced next, and who will be revealed as the winners of the 2010s. It is, of course, much too early to tell, but Schutz is back, and he will set the standard just as he did back in 1985. This is the long-awaited second edition of his `First Course', a short, accessible, and very successful introduction to general relativity. The changes from the first edition are modest: Schutz wisely refrained from bloating the text with new topics, and limited himself to updating his discussion of gravitational-wave sources and detectors, neutron-star and black-hole astrophysics, and suggestions for further reading. Most importantly, he completely rewrote the chapter on cosmology, a topic that has evolved enormously since the first edition. The book begins in chapter 1 with a beautiful review of special relativity that emphasizes spacetime geometry and stays away from an algebraic approach based on the Lorentz transformation, which appears only later in the chapter. This is followed up in chapters 2 and 3 with an introduction to vector and tensor analysis in flat spacetime. The point of view is modern (tensors are defined as linear mapping of vectors and one-forms into real numbers) but the presentation is very accessible and avoids an overload of mathematical fine print. In chapter 4 the book introduces the spacetime description of fluids; it is here that the energy-momentum tensor makes its first appearance. The move to curved spacetime is
Highlighting the Mechanism of the Quantum Speedup by Time-Symmetric and Relational Quantum Mechanics
NASA Astrophysics Data System (ADS)
Castagnoli, Giuseppe
2016-03-01
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice's measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one.
Generating matter inhomogeneities in general relativity.
Coley, A A; Lim, W C
2012-05-11
In this Letter we discuss a natural general relativistic mechanism that causes inhomogeneities and hence generates matter perturbations in the early Universe. We concentrate on spikes, both incomplete spikes and recurring spikes, that naturally occur in the initial oscillatory regime of general cosmological models. In particular, we explicitly show that spikes occurring in a class of G2 models lead to inhomogeneities that, due to gravitational instability, leave small residual imprints on matter in the form of matter perturbations. The residual matter overdensities from recurring spikes are not local but form on surfaces. We discuss the potential physical consequences of the residual matter imprints and their possible effect on the subsequent formation of large-scale structure.
Canonical differential calculus on quantum general linear groups and supergroups
NASA Astrophysics Data System (ADS)
Sudbery, A.
1992-06-01
We specify a set of relations between non-commuting matrix elements and their differentials, defined in terms of an R-matrix satisfying the braid relation, which are uniquely determined by the requirements of consistency with the relations between non-commuting coordinates and their differentials. We also give a necessary condition for the existence of a matrix inverse (antipode) in the form of an additional equation to be satisfied by the R-matrix.
A General Paradigm for Public Relations Research.
ERIC Educational Resources Information Center
Whitcomb, Debra
Grunig's decision-situation model is proposed as a comprehensive framework under which various public-relations-related theories may be subsumed. The decision-situation model postulates three dimensions which, taken together, may predict the course of communication behavior: level of involvement, problem recognition, and structural constraints.…
A general framework for the Quantum Zeno and anti-Zeno effects
Chaudhry, Adam Zaman
2016-01-01
Repeated measurements can slow down (the quantum Zeno effect) or speed up (the quantum anti-Zeno effect) the temporal evolution of a quantum system. In this paper, a general treatment of the quantum Zeno and anti-Zeno effects is presented which is valid for an arbitrary system-environment model in the weak system-environment coupling regime. It is shown that the effective lifetime of a quantum state that is subjected to repeated projective measurements depends on the overlap of the spectral density of the environment and a generalized ‘filter function’. This filter function depends on the system-environment Hamiltonian, the state of the environment, and the measurement being performed. Our general framework is then used to study explicitly the Zeno to anti-Zeno crossover behaviour for the spin-boson model where a single two-level system is coupled to a bosonic environment. It is possible to not only reproduce results for the usual population decay case as well as for the pure dephasing model, but to also study the regime where both decay and dephasing take place. These results are then extended to many two-level systems coupled collectively to the bosonic environment to further illustrate the importance of the correct evaluation of the effective decay rate. PMID:27405268
Generalized space and linear momentum operators in quantum mechanics
Costa, Bruno G. da
2014-06-15
We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p{sup ^}{sub q}, and its canonically conjugate deformed position operator x{sup ^}{sub q}. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.
Combined-probability space and certainty or uncertainty relations for a finite-level quantum system
NASA Astrophysics Data System (ADS)
Sehrawat, Arun
2017-08-01
The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys certain quantum constraints, which are triangle inequalities in our case. Such a restricted set of combined vectors, called the combined-probability space, is presented here for a d -level quantum system (qudit). The combined space is a compact convex subset of a Euclidean space, and all its extreme points come from a family of parametric curves. Considering a suitable concave function on the combined space to estimate the uncertainty, we deliver an uncertainty relation by finding its global minimum on the curves for a qudit. If one chooses an appropriate concave (or convex) function, then there is no need to search for the absolute minimum (maximum) over the whole space; it will be on the parametric curves. So these curves are quite useful for establishing an uncertainty (or a certainty) relation for a general pair of settings. We also demonstrate that many known tight certainty or uncertainty relations for a qubit can be obtained with the triangle inequalities.
Some Clarifications on the Relation Between Bohmian Quantum Potential and Mach's Principle
NASA Astrophysics Data System (ADS)
Rahmani, Faramarz; Golshani, Mehdi
2017-10-01
Mach's principle asserts that the inertial mass of a body is related to the distribution of other distant bodies. This means that in the absence of other bodies, a single body has no mass. In this case, talking about motion is not possible, because the detection of motion is possible only relative to other bodies. But in physics we are faced with situations that are not fully Machian. As in the case of general theory of relativity where geodesics exist in the absence of any matter, the motion has meaning. Another example which is the main topic of our discussion, refers to Bohmian quantum mechanics, where the inertial mass of a single particle does not vanish, but is modified. We can call such situations in which motion or mass of a single particle has meaning, pseudo-Machian situations. In this paper, we use the Machian or pseudo-Machian considerations to clarify under what circumstances and how a Machian effect leads us to Bohmian quantum mechanics. Then, we shall get the Bohmian quantum potential and its higher order terms for the Klein-Gordon particle through Machian considerations, without using any quantum mechanical postulate or operator formalism.
Some Clarifications on the Relation Between Bohmian Quantum Potential and Mach's Principle
NASA Astrophysics Data System (ADS)
Rahmani, Faramarz; Golshani, Mehdi
2017-07-01
Mach's principle asserts that the inertial mass of a body is related to the distribution of other distant bodies. This means that in the absence of other bodies, a single body has no mass. In this case, talking about motion is not possible, because the detection of motion is possible only relative to other bodies. But in physics we are faced with situations that are not fully Machian. As in the case of general theory of relativity where geodesics exist in the absence of any matter, the motion has meaning. Another example which is the main topic of our discussion, refers to Bohmian quantum mechanics, where the inertial mass of a single particle does not vanish, but is modified. We can call such situations in which motion or mass of a single particle has meaning, pseudo-Machian situations. In this paper, we use the Machian or pseudo-Machian considerations to clarify under what circumstances and how a Machian effect leads us to Bohmian quantum mechanics. Then, we shall get the Bohmian quantum potential and its higher order terms for the Klein-Gordon particle through Machian considerations, without using any quantum mechanical postulate or operator formalism.
Generalized relativistic harmonic oscillator in minimal length quantum mechanics
NASA Astrophysics Data System (ADS)
Castro, L. B.; E Obispo, A.
2017-07-01
We solve the generalized relativistic harmonic oscillator in 1 + 1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. Furthermore, we also find an isolated solution from the Sturm-Liouville scheme. All cases already analyzed in the literature are obtained as particular cases.
Generalized Uncertainty Relation and Hawking Radiation of the Black Hole
NASA Astrophysics Data System (ADS)
Zhao, Ren; Zhang, Lichun; Wu, Yueqin; Li, Huaifan
2009-08-01
Recently, there has been much attention devoted to the correction to the black hole radiation spectrum and the quantum corrections to Bekenstein-Hawking entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the radiation spectrum of arbitrary dimension Schwarzschild black hole after considering the generalized uncertainty principle. The correction value of Bekenstein-Hawking entropy is derived.
Analytically Solvable Quantum Hamiltonians and Relations to Orthogonal Polynomials
Regniers, G.; Van der Jeugt, J.
2010-06-17
Quantum systems consisting of a linear chain of n harmonic oscillators coupled by a quadratic nearest-neighbour interaction are considered. We investigate when such a system is analytically solvable, in the sense that the eigenvalues and eigenvectors of the interaction matrix have analytically closed expressions. This leads to a relation with Jacobi matrices of systems of discrete orthogonal polynomials. Our study is first performed in the case of canonical quantization. Then we consider these systems under Wigner quantization, leading to solutions in terms of representations of Lie superalgebras. Finally, we show how such analytically solvable Hamiltonians also play a role in another application, that of spin chains used as communication channels in quantum computing. In this context, the analytic solvability leads to closed form expressions for certain transition amplitudes.
Minimax Quantum Tomography: Estimators and Relative Entropy Bounds
Ferrie, Christopher; Blume-Kohout, Robin
2016-03-04
A minimax estimator has the minimum possible error (“risk”) in the worst case. Here we construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O (1/more » $$\\sqrt{N}$$ ) —in contrast to that of classical probability estimation, which is O (1/N) —where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. Lastly, this makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.« less
Minimax Quantum Tomography: Estimators and Relative Entropy Bounds
Ferrie, Christopher; Blume-Kohout, Robin
2016-03-04
A minimax estimator has the minimum possible error (“risk”) in the worst case. Here we construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O (1/$\\sqrt{N}$ ) —in contrast to that of classical probability estimation, which is O (1/N) —where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. Lastly, this makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.
Double-slit experiment with single wave-driven particles and its relation to quantum mechanics.
Andersen, Anders; Madsen, Jacob; Reichelt, Christian; Rosenlund Ahl, Sonja; Lautrup, Benny; Ellegaard, Clive; Levinsen, Mogens T; Bohr, Tomas
2015-07-01
In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.
Double-slit experiment with single wave-driven particles and its relation to quantum mechanics
NASA Astrophysics Data System (ADS)
Andersen, Anders; Madsen, Jacob; Reichelt, Christian; Rosenlund Ahl, Sonja; Lautrup, Benny; Ellegaard, Clive; Levinsen, Mogens T.; Bohr, Tomas
2015-07-01
In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006), 10.1103/PhysRevLett.97.154101] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.
Connection between Newtonian simulations and general relativity
Chisari, Nora Elisa; Zaldarriaga, Matias
2011-06-15
On large scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities, and velocities in a specific coordinate system or gauge. The method of choice for simulating large-scale structure is numerical N-body simulations which are performed in the Newtonian limit. Even though one might worry that the use of the Newtonian approximation would make it impossible to use these simulations to compute properties on very large scales, we show that the simulations are still solving the dynamics correctly even for long modes and we give formulas to obtain the position of particles in the conformal Newtonian gauge given the positions computed in the simulation. We also give formulas to convert from the output coordinates of N-body simulations to the observable coordinates of the particles.
General non-Markovian dynamics of open quantum systems.
Zhang, Wei-Min; Lo, Ping-Yuan; Xiong, Heng-Na; Tu, Matisse Wei-Yuan; Nori, Franco
2012-10-26
We present a general theory of non-Markovian dynamics for open systems of noninteracting fermions (bosons) linearly coupled to thermal environments of noninteracting fermions (bosons). We explore the non-Markovian dynamics by connecting the exact master equations with the nonequilibirum Green's functions. Environmental backactions are fully taken into account. The non-Markovian dynamics consists of nonexponential decays and dissipationless oscillations. Nonexponential decays are induced by the discontinuity in the imaginary part of the self-energy corrections. Dissipationless oscillations arise from band gaps or the finite band structure of spectral densities. The exact analytic solutions for various non-Markovian thermal environments show that non-Markovian dynamics can be largely understood from the environmental-modified spectra of open systems.
Study of quantum correlation swapping with relative entropy methods
NASA Astrophysics Data System (ADS)
Xie, Chuanmei; Liu, Yimin; Chen, Jianlan; Zhang, Zhanjun
2016-02-01
To generate long-distance shared quantum correlations (QCs) for information processing in future quantum networks, recently we proposed the concept of QC repeater and its kernel technique named QC swapping. Besides, we extensively studied the QC swapping between two simple QC resources (i.e., a pair of Werner states) with four different methods to quantify QCs (Xie et al. in Quantum Inf Process 14:653-679, 2015). In this paper, we continue to treat the same issue by employing other three different methods associated with relative entropies, i.e., the MPSVW method (Modi et al. in Phys Rev Lett 104:080501, 2010), the Zhang method (arXiv:1011.4333 [quant-ph]) and the RS method (Rulli and Sarandy in Phys Rev A 84:042109, 2011). We first derive analytic expressions of all QCs which occur during the swapping process and then reveal their properties about monotonicity and threshold. Importantly, we find that a long-distance shared QC can be generated from two short-distance ones via QC swapping indeed. In addition, we simply compare our present results with our previous ones.
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2016-08-01
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.
Fluctuation-dissipation theorem in general relativity and the cosmological constant
Mottola, E.
1992-01-01
Vacuum fluctuations are an essential feature of quantum field theory. Yet, the smallness of the scalar curvature of our universe suggests that the zero-point energy associated with these fluctuations does not curve spacetime. A possible way out of this paradox is suggested by the fact that microscopic fluctuations are generally accompanied by dissipative behavior in macroscopic systems. The intimate relation between the two is expressed by a fluctuation-dissipation theorem which extends to general relativity. The connection between quantum fluctuations and dissipation suggests a mechanism for the conversion of coherent stresses in the curvature of space into ordinary matter or radiation, thereby relaxing the effective cosmological constant'' to zero over time. The expansion of the universe may be the effect of this time-asymmetric relaxation process.
Fluctuation-dissipation theorem in general relativity and the cosmological constant
Mottola, E.
1992-06-01
Vacuum fluctuations are an essential feature of quantum field theory. Yet, the smallness of the scalar curvature of our universe suggests that the zero-point energy associated with these fluctuations does not curve spacetime. A possible way out of this paradox is suggested by the fact that microscopic fluctuations are generally accompanied by dissipative behavior in macroscopic systems. The intimate relation between the two is expressed by a fluctuation-dissipation theorem which extends to general relativity. The connection between quantum fluctuations and dissipation suggests a mechanism for the conversion of coherent stresses in the curvature of space into ordinary matter or radiation, thereby relaxing the effective cosmological ``constant`` to zero over time. The expansion of the universe may be the effect of this time-asymmetric relaxation process.
NASA Technical Reports Server (NTRS)
Moncrief, V.; Teitelboim, C.
1972-01-01
It is shown that if the Hamiltonian constraint of general relativity is imposed as a restriction on the Hamilton principal functional in the classical theory, or on the state functional in the quantum theory, then the momentum constraints are automatically satisfied. This result holds both for closed and open spaces and it means that the full content of the theory is summarized by a single functional equation of the Tomonaga-Schwinger type.
How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?
NASA Astrophysics Data System (ADS)
Yarman, T.; L. Kholmetskii, A.
2011-10-01
We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3 = Constant, where P is the pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work (Yarman et al. 2010 Int. J. Phys. Sci. 5 1524). We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.
Wang, Qin; Wang, Xiang-Bin
2014-01-01
We present a model on the simulation of the measurement-device independent quantum key distribution (MDI-QKD) with phase randomized general sources. It can be used to predict experimental observations of a MDI-QKD with linear channel loss, simulating corresponding values for the gains, the error rates in different basis, and also the final key rates. Our model can be applicable to the MDI-QKDs with arbitrary probabilistic mixture of different photon states or using any coding schemes. Therefore, it is useful in characterizing and evaluating the performance of the MDI-QKD protocol, making it a valuable tool in studying the quantum key distributions. PMID:24728000
The generalized ambiguity function: a bridgework between classical and quantum radar
NASA Astrophysics Data System (ADS)
Gray, John E.; Parks, Allen D.
2016-05-01
We provide a common framework for the measurement problem for radar, sonar, and quantum mechanics by casting them in the common language of quantum mechanics as a Rigged Hilbert Space. This language reveals a more detailed understanding of the underlying interactions of a return signal that are not usually brought out by standard signal processing design techniques. It also provides a means to "post-select" the return signal so the receiver design for radars can be optimized for either a single or multiple operators. Thus, detector design can be optimized for signal interaction with objects, so the algorithm provides a solution to receiver design for general types of interactions.
Cluster-state quantum computing enhanced by high-fidelity generalized measurements.
Biggerstaff, D N; Kaltenbaek, R; Hamel, D R; Weihs, G; Rudolph, T; Resch, K J
2009-12-11
We introduce and implement a technique to extend the quantum computational power of cluster states by replacing some projective measurements with generalized quantum measurements (POVMs). As an experimental demonstration we fully realize an arbitrary three-qubit cluster computation by implementing a tunable linear-optical POVM, as well as fast active feedforward, on a two-qubit photonic cluster state. Over 206 different computations, the average output fidelity is 0.9832+/-0.0002; furthermore the error contribution from our POVM device and feedforward is only of O(10(-3)), less than some recent thresholds for fault-tolerant cluster computing.
Yao, Xing-Can; Fiurásek, Jaromír; Lu, He; Gao, Wei-Bo; Chen, Yu-Ao; Chen, Zeng-Bing; Pan, Jian-Wei
2010-09-17
We experimentally demonstrate an advanced linear-optical programmable quantum processor that combines two elementary single-qubit programmable quantum gates. We show that this scheme enables direct experimental probing of quantum commutation relations for Pauli operators acting on polarization states of single photons. Depending on a state of two-qubit program register, we can probe either commutation or anticommutation relations. Very good agreement between theory and experiment is observed, indicating high-quality performance of the implemented quantum processor.
Uncertainty relations in quantum optics. Is the photon intelligent?
NASA Astrophysics Data System (ADS)
Przanowski, Maciej; García-Compeán, Hugo; Tosiek, Jaromir; Turrubiates, Francisco J.
2016-10-01
The Robertson-Schrödinger, Heisenberg-Robertson and Trifonov uncertainty relations for arbitrary two functions f1 and f2 depending on the quantum phase and the number of photons respectively, are given. Intelligent states and states which minimize locally the product of uncertainties (Δf1) 2 ṡ(Δf2) 2 or the sum (Δf1) 2 +(Δf2) 2 are investigated for the cases f1 = ϕ , exp(iϕ) , exp(- iϕ) , cos ϕ , sin ϕ and f2 = n.
Foundation of quantum mechanics from the principle of relativity
Nottale, Laurent
2007-04-28
We briefly recall the main steps by which we suggest to found quantum mechanics and gauge field theories on the principle of relativity, once it is extended to scale transformations of the reference system. The wave functions are constructed as consequences of the nondifferentiability of a continuous space-time, while the Schroedinger and Dirac equations are obtained from its geodesics equations. In this framework, the gauge fields emerge as manifestation of the fractal geometry, and the gauge charges as the conservative quantities which are built from its internal symmetries.
Recent advances toward a general purpose linear-scaling quantum force field.
Giese, Timothy J; Huang, Ming; Chen, Haoyuan; York, Darrin M
2014-09-16
Conspectus There is need in the molecular simulation community to develop new quantum mechanical (QM) methods that can be routinely applied to the simulation of large molecular systems in complex, heterogeneous condensed phase environments. Although conventional methods, such as the hybrid quantum mechanical/molecular mechanical (QM/MM) method, are adequate for many problems, there remain other applications that demand a fully quantum mechanical approach. QM methods are generally required in applications that involve changes in electronic structure, such as when chemical bond formation or cleavage occurs, when molecules respond to one another through polarization or charge transfer, or when matter interacts with electromagnetic fields. A full QM treatment, rather than QM/MM, is necessary when these features present themselves over a wide spatial range that, in some cases, may span the entire system. Specific examples include the study of catalytic events that involve delocalized changes in chemical bonds, charge transfer, or extensive polarization of the macromolecular environment; drug discovery applications, where the wide range of nonstandard residues and protonation states are challenging to model with purely empirical MM force fields; and the interpretation of spectroscopic observables. Unfortunately, the enormous computational cost of conventional QM methods limit their practical application to small systems. Linear-scaling electronic structure methods (LSQMs) make possible the calculation of large systems but are still too computationally intensive to be applied with the degree of configurational sampling often required to make meaningful comparison with experiment. In this work, we present advances in the development of a quantum mechanical force field (QMFF) suitable for application to biological macromolecules and condensed phase simulations. QMFFs leverage the benefits provided by the LSQM and QM/MM approaches to produce a fully QM method that is able to
Large-scale tides in general relativity
NASA Astrophysics Data System (ADS)
Ip, Hiu Yan; Schmidt, Fabian
2017-02-01
Density perturbations in cosmology, i.e. spherically symmetric adiabatic perturbations of a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime, are locally exactly equivalent to a different FLRW solution, as long as their wavelength is much larger than the sound horizon of all fluid components. This fact is known as the "separate universe" paradigm. However, no such relation is known for anisotropic adiabatic perturbations, which correspond to an FLRW spacetime with large-scale tidal fields. Here, we provide a closed, fully relativistic set of evolutionary equations for the nonlinear evolution of such modes, based on the conformal Fermi (CFC) frame. We show explicitly that the tidal effects are encoded by the Weyl tensor, and are hence entirely different from an anisotropic Bianchi I spacetime, where the anisotropy is sourced by the Ricci tensor. In order to close the system, certain higher derivative terms have to be dropped. We show that this approximation is equivalent to the local tidal approximation of Hui and Bertschinger [1]. We also show that this very simple set of equations matches the exact evolution of the density field at second order, but fails at third and higher order. This provides a useful, easy-to-use framework for computing the fully relativistic growth of structure at second order.
Linear derivative Cartan formulation of general relativity
NASA Astrophysics Data System (ADS)
Kummer, W.; Schütz, H.
2005-07-01
Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz invariance is implemented in a formulation of Einstein gravity (with or without cosmological term) in terms of initially completely independent vielbein and spin connection variables and auxiliary two-form fields. In the systematic study of all possible embeddings of Einstein gravity into that formulation with auxiliary fields, the introduction of a “bi-complex” algebra possesses crucial technical advantages. Certain components of the new two-form fields directly provide canonical momenta for spatial components of all Cartan variables, whereas the remaining ones act as Lagrange multipliers for a large number of constraints, some of which have been proposed already in different, less radical approaches. The time-like components of the Cartan variables play that role for the Lorentz constraints and others associated to the vierbein fields. Although also some ternary ones appear, we show that relations exist between these constraints, and how the Lagrange multipliers are to be determined to take care of second class ones. We believe that our formulation of standard Einstein gravity as a gauge theory with consistent local Poincaré algebra is superior to earlier similar attempts.
Derived relations and generalized alteration of preferences.
Valdivia-Salas, Sonsoles; Dougher, Michael J; Luciano, Carmen
2013-06-01
The present study examined the role of derived relations in the generalizability of the evaluative conditioning effect. Healthy university students participated. Four geometrical shapes were first established as discriminative stimuli for the contingent presentation of pictograms (B1, B2, C1, and C2, respectively). We then assessed the reinforcing properties of B1 versus B2, and C1 versus C2 by using simultaneous discrimination tasks: at baseline (baseline assessment), after pairing B1 with aversive slides plus noise and B2 with pleasant slides (test I), and after employing equivalence training and testing to establish B1 as equivalent to C1 and B2 as equivalent to C2 (test II). Most participants (82%) in the experimental condition, as compared with the control conditions (17% and 10%), selected the discriminative shapes for B2 (test I) and C2 (test II) on most trials, replicating and extending previous findings. Subsequently, the geometrical shapes were established as equivalent to the letters X, Y, W, and Z, respectively, which then served as antecedent stimuli in simultaneous discrimination tasks as before (test III). As was expected, only participants in the experimental condition showed preference for the novel letters that were established as equivalent to B2-producing and C2-producing shapes. These findings suggest that the evaluative conditioning effect may extend far beyond the stimulus being de/valuated and narrow the behavioral repertoire.
Momentum in general relativity: local versus quasilocal conservation laws
NASA Astrophysics Data System (ADS)
Epp, Richard J.; McGrath, Paul L.; Mann, Robert B.
2013-10-01
We construct a general relativistic conservation law for linear and angular momentum for matter and gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous construction of a general relativistic energy conservation law with the same features (McGrath et al 2012 Class. Quantum Grav. 29 215012). Our approach uses the Brown and York (1993 Phys. Rev. D 47 1407-19) quasilocal stress-energy-momentum tensor for matter and gravitational fields, plus the concept of a rigid quasilocal frame (RQF) introduced in (Epp et al 2009 Class. Quantum Grav. 26 035015; 2012 Classical and Quantum Gravity: Theory, Analysis, and Applications (Nova Science)). The RQF approach allows us to construct, in a generic spacetime, frames of reference whose boundaries are rigid (their shape and size do not change with time), and that have precisely the same six arbitrary time-dependent degrees of freedom as the accelerating and tumbling rigid frames we are familiar with in Newtonian mechanics. These RQFs, in turn, give rise to a completely general conservation law for the six components of momentum (three linear and three angular) of a finite system of matter and gravitational fields. We compare in detail this quasilocal RQF approach to constructing conservation laws with the usual local one based on spacetime symmetries, and discuss the shortcomings of the latter. These RQF conservation laws lead to a deeper understanding of physics in the form of simple, exact, operational definitions of gravitational energy and momentum fluxes, which in turn reveal, for the first time, the exact, detailed mechanisms of gravitational energy and momentum transfer taking place in a wide variety of physical phenomena, including a simple falling apple. As a concrete example, we derive a general relativistic version of Archimedes’ law that we apply to understand electrostatic weight and buoyant force in the context of a Reissner
BOOK REVIEW: Advanced Mechanics and General Relativity Advanced Mechanics and General Relativity
NASA Astrophysics Data System (ADS)
Louko, Jorma
2011-04-01
Joel Franklin's textbook `Advanced Mechanics and General Relativity' comprises two partially overlapping, partially complementary introductory paths into general relativity at advanced undergraduate level. Path I starts with the Lagrangian and Hamiltonian formulations of Newtonian point particle motion, emphasising the action principle and the connection between symmetries and conservation laws. The concepts are then adapted to point particle motion in Minkowski space, introducing Lorentz transformations as symmetries of the action. There follows a focused development of tensor calculus, parallel transport and curvature, using examples from Newtonian mechanics and special relativity, culminating in the field equations of general relativity. The Schwarzschild solution is analysed, including a detailed discussion of the tidal forces on a radially infalling observer. Basics of gravitational radiation are examined, highlighting the similarities to and differences from electromagnetic radiation. The final topics in Path I are equatorial geodesics in Kerr and the motion of a relativistic string in Minkowski space. Path II starts by introducing scalar field theory on Minkowski space as a limit of point masses connected by springs, emphasising the action principle, conservation laws and the energy-momentum tensor. The action principle for electromagnetism is introduced, and the coupling of electromagnetism to a complex scalar field is developed in a detailed and pedagogical fashion. A free symmetric second-rank tensor field on Minkowski space is introduced, and the action principle of general relativity is recovered from coupling the second-rank tensor to its own energy-momentum tensor. Path II then merges with Path I and, supplanted with judicious early selections from Path I, can proceed to the Schwarzschild solution. The choice of material in each path is logical and focused. A notable example in Path I is that Lorentz transformations in Minkowki space are introduced
Is there a philosophy of time compatible with relativity and quantum mechanics?
NASA Astrophysics Data System (ADS)
Besnard, Fabien
2012-06-01
The goal of this text is to study the compatibility of three main philosophical theories of time (presentism, possibilism, and eternalism) with special relativity, general relativity, and quantum mechanics. We will show that possibilism is compatible with these physical theories, but only at two conditions: the past of an observer must be understood as his causal past, and there must be some mechanism forbidding closed timelike curves. We will also argue that provided one adopts Everett's interpretation of QM, eternalism can be phrased in a natural way which is compatible with these three theories. We emphasize the fact that reality is observer-independent in eternalism only.
Krishna, S.; Shukla, A.; Malik, R.P.
2014-12-15
Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSY invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.
General theory of measurement with two copies of a quantum state.
Bendersky, Ariel; Paz, Juan Pablo; Cunha, Marcelo Terra
2009-07-24
We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that mu can label a set of outcomes of a measurement on two copies if and only if there is a family of maps C_{micro} such that the probability Prob(micro) is the fidelity of each map, i.e., Prob(micro) = Tr[rhoC_{micro}(rho)]. Here, the map C_{micro} must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure).
NASA Astrophysics Data System (ADS)
Wang, Xiao-Jun; An, Long-Xi; Yu, Xu-Tao; Zhang, Zai-Chen
2017-10-01
A multilayer quantum secret sharing protocol based on GHZ state is proposed. Alice has the secret carried by quantum state and wants to distribute this secret to multiple agent nodes in the network. In this protocol, the secret is transmitted and shared layer by layer from root Alice to layered agents. The number of agents in each layer is a geometric sequence with a specific common ratio. By sharing GHZ maximally entangled states and making generalized Bell basis measurement, one qubit state can be distributed to multiparty agents and the secret is shared. Only when all agents at the last layer cooperate together, the secret can be recovered. Compared with other protocols based on the entangled state, this protocol adopts layered construction so that secret can be distributed to more agents with fewer particles GHZ state. This quantum secret sharing protocol can be used in wireless network to ensure the security of information delivery.
NASA Astrophysics Data System (ADS)
Sassoli de Bianchi, Massimiliano
2012-04-01
We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of "fuzzy" and "free-flight" sojourn times that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they should not be called "times."
NASA Astrophysics Data System (ADS)
Yu, Min; Fang, Mao-Fa
2017-09-01
The dynamic properties of the quantum-memory-assisted entropic uncertainty relation for a system comprised of a qubit to be measured and a memory qubit are investigated. We explore the behaviors of the entropic uncertainty and its lower bound in three different cases: Only one of the two qubits interacts with an external environment and subjects to quantum-jump-based feedback control, or both of the two qubits independently experience their own environments and local quantum-jump-based feedback control. Our results reveal that the quantum-jump-based feedback control with an appropriate feedback parameter can reduce the entropic uncertainty and its lower bound, and for the three different scenarios, the reduction in the uncertainty relates to different physical quantities. Besides, we find out that the quantum-jump-based feedback control not only can remarkably decrease the entropic uncertainty, but also can make the uncertainty reach its lower bound where the dynamical map becomes unital.
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
Yeh, L. |
1993-06-23
After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented.
Lipparini, Filippo; Scalmani, Giovanni; Frisch, Michael J.; Lagardère, Louis; Stamm, Benjamin; Cancès, Eric; Maday, Yvon; Piquemal, Jean-Philip; Mennucci, Benedetta
2014-11-14
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.
Zhang, Jun; Zhang, Yang; Yu, Chang-shui
2015-06-29
The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodecki's bound entangled state are investigated in details.
NASA Astrophysics Data System (ADS)
Zhang, Jun; Zhang, Yang; Yu, Chang-Shui
2015-06-01
The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodecki’s bound entangled state are investigated in details.
A general transfer-function approach to noise filtering in open-loop quantum control
NASA Astrophysics Data System (ADS)
Viola, Lorenza
2015-03-01
Hamiltonian engineering via unitary open-loop quantum control provides a versatile and experimentally validated framework for manipulating a broad class of non-Markovian open quantum systems of interest, with applications ranging from dynamical decoupling and dynamically corrected quantum gates, to noise spectroscopy and quantum simulation. In this context, transfer-function techniques directly motivated by control engineering have proved invaluable for obtaining a transparent picture of the controlled dynamics in the frequency domain and for quantitatively analyzing performance. In this talk, I will show how to identify a computationally tractable set of ``fundamental filter functions,'' out of which arbitrary filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. I will show, in particular, how the resulting notion of ``filtering order'' reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the ``cancellation order,'' traditionally defined in the Magnus sense. Implications for current quantum control experiments will be discussed. Work supported by the U.S. Army Research Office under Contract No. W911NF-14-1-0682.
Towards Implementation of a Generalized Architecture for High-Level Quantum Programming Language
NASA Astrophysics Data System (ADS)
Ameen, El-Mahdy M.; Ali, Hesham A.; Salem, Mofreh M.; Badawy, Mahmoud
2017-08-01
This paper investigates a novel architecture to the problem of quantum computer programming. A generalized architecture for a high-level quantum programming language has been proposed. Therefore, the programming evolution from the complicated quantum-based programming to the high-level quantum independent programming will be achieved. The proposed architecture receives the high-level source code and, automatically transforms it into the equivalent quantum representation. This architecture involves two layers which are the programmer layer and the compilation layer. These layers have been implemented in the state of the art of three main stages; pre-classification, classification, and post-classification stages respectively. The basic building block of each stage has been divided into subsequent phases. Each phase has been implemented to perform the required transformations from one representation to another. A verification process was exposed using a case study to investigate the ability of the compiler to perform all transformation processes. Experimental results showed that the efficacy of the proposed compiler achieves a correspondence correlation coefficient about R ≈ 1 between outputs and the targets. Also, an obvious achievement has been utilized with respect to the consumed time in the optimization process compared to other techniques. In the online optimization process, the consumed time has increased exponentially against the amount of accuracy needed. However, in the proposed offline optimization process has increased gradually.
NASA Astrophysics Data System (ADS)
Yang, Yuxiang; Chiribella, Giulio; Adesso, Gerardo
2014-10-01
Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines often remains a nontrivial problem. To address such a problem, one first needs to establish the best classical solutions, which set benchmarks that must be beaten by any implementation claiming to harness quantum features for an enhanced performance. Here we introduce and develop a self-contained formalism to obtain the ultimate, generally probabilistic benchmarks for quantum information protocols including teleportation and approximate cloning, with arbitrary ensembles of input states generated by a group action, so-called Gilmore-Perelomov coherent states. This allows us to construct explicit fidelity thresholds for the transmission of multimode Gaussian and non-Gaussian states of continuous-variable systems, as well as qubit and qudit pure states drawn according to nonuniform distributions on the Bloch hypersphere, which accurately model the current laboratory facilities. The performance of deterministic classical procedures such as square-root measurement strategies is further compared with the optimal probabilistic benchmarks, and the state-of-the-art performance of experimental quantum implementations against our newly derived thresholds is discussed. This work provides a comprehensive collection of directly useful criteria for the reliable certification of quantum communication technologies.
Histories approach to general relativity: I. The spacetime character of the canonical description
NASA Astrophysics Data System (ADS)
Savvidou, Ntina
2004-01-01
The problem of time in canonical quantum gravity is related to the fact that the canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to be a dynamical, fluctuating quantity in quantum gravity. We show how this problem can be solved in the histories formulation of general relativity. We implement the 3 + 1 decomposition using metric-dependent foliations which remain spacelike with respect to all possible Lorentzian metrics. This allows us to find an explicit relation of covariant and canonical quantities which preserves the spacetime character of the canonical description. In this new construction, we also have the coexistence of the spacetime diffeomorphisms group, Diff(M), and the Dirac algebra of constraints.
Fleming, C.H.; Roura, Albert; Hu, B.L.
2011-05-15
Research Highlights: > We study the model of a quantum oscillator linearly coupled to a bath of oscillators. > We derive the master equation and solutions for general spectra and temperatures. > We generalize to cases with an external force and arbitrary number of oscillators. > Other derivations have incorrect diffusion and force response for nonlocal damping. > We give exact results for ohmic, sub-ohmic and supra-ohmic environments. - Abstract: We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. The flexibility of our approach allows for an immediate generalization to cases with an external force and with an arbitrary number of Brownian oscillators. More importantly, we point out an important mathematical subtlety concerning boundary-value problems for integro-differential equations which led to incorrect master equation coefficients and impacts on the description of nonlocal dissipation effects in all earlier derivations. Furthermore, we provide explicit, exact analytical results for the master equation coefficients and its solutions in a wide variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with a finite cut-off.
29 CFR 778.5 - Relation to other laws generally.
Code of Federal Regulations, 2010 CFR
2010-07-01
... POLICY OR INTERPRETATION NOT DIRECTLY RELATED TO REGULATIONS OVERTIME COMPENSATION General Considerations..., and the payment of overtime compensation computed on bases different from those set forth in the...
Fermi-edge singularity and related interaction induced phenomena in multilevel quantum dots
NASA Astrophysics Data System (ADS)
Goremykina, A. S.; Sukhorukov, E. V.
2017-04-01
We study the manifestation of the nonperturbative effects of interaction in sequential tunneling between a quasi-one-dimensional system of chiral quantum Hall edge channels and a multilevel quantum dot (QD). We use the formal scattering theory approach to the bosonization technique to present an alternative derivation of the Fermi-edge singularity effect and demonstrate the origin of its universality. This approach allows us to address, within the same framework, plasmon-assisted sequential tunneling to relatively large dots and investigate the interaction-induced level broadening. The results are generalized by taking into account the dispersion in the spectrum of plasmons in the QD. We then discuss their modification in the presence of neutral modes, which can be realized either in a QD with two chiral strongly interacting edge channels or in a three-dimensional QD in the Coulomb blockade regime. In the former case a universal behavior of the tunneling rate is discovered.
Quantum field theory with a preferred direction: The very special relativity framework
NASA Astrophysics Data System (ADS)
Lee, Cheng-Yang
2016-02-01
The theory of very special relativity (VSR) proposed by Cohen and Glashow contains an intrinsic preferred direction. Starting from the irreducible unitary representation of the inhomogeneous VSR group I S I M (2 ), we present a rigorous construction of quantum field theory with a preferred direction. We find that although the particles and their quantum fields between the VSR and Lorentz sectors are physically different, they share many similarities. The massive spin-half and spin-one vector fields are local and satisfy the Dirac and Proca equations, respectively. This result can be generalized to higher-spin field theories. By studying the Yukawa and standard gauge interactions, we obtain a qualitative understanding on the effects of the preferred direction. Its effect is manifest for polarized processes but are otherwise absent.
The classical-quantum boundary for correlations: Discord and related measures
NASA Astrophysics Data System (ADS)
Modi, Kavan; Brodutch, Aharon; Cable, Hugo; Paterek, Tomasz; Vedral, Vlatko
2012-10-01
One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.
Quantum diffusion with drift and the Einstein relation. I
De Roeck, Wojciech; Fröhlich, Jürg; Schnelli, Kevin
2014-07-15
We study the dynamics of a quantum particle hopping on a simple cubic lattice and driven by a constant external force. It is coupled to an array of identical, independent thermal reservoirs consisting of free, massless Bose fields, one at each site of the lattice. When the particle visits a site x of the lattice it can emit or absorb field quanta of the reservoir at x. Under the assumption that the coupling between the particle and the reservoirs and the driving force are sufficiently small, we establish the following results: The ergodic average over time of the state of the particle approaches a non-equilibrium steady state describing a non-zero mean drift of the particle. Its motion around the mean drift is diffusive, and the diffusion constant and the drift velocity are related to one another by the Einstein relation.
Position-momentum uncertainty relations in the presence of quantum memory
Furrer, Fabian; Berta, Mario; Tomamichel, Marco; Scholz, Volkher B.; Christandl, Matthias
2014-12-15
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.
NASA Astrophysics Data System (ADS)
Colosi, Daniele; Dohse, Max
2017-04-01
We use the General Boundary Formulation (GBF) of Quantum Field Theory to compute the S-matrix for a general interacting scalar field in a wide class of curved spacetimes. As a by-product we obtain the general expression of the Feynman propagator for the scalar field, defined in the following three types of spacetime regions. First, there are the familiar interval regions (e.g. a time interval times all of space). Second, we consider the rod hypercylinder regions (all of time times a solid ball in space). Third, the tube hypercylinders (all of time times a solid shell in space) are related to interval regions, and result from removing a smaller rod from a concentric larger one. Using the Schrödinger representation for the quantum states combined with Feynman's path integral quantization, we obtain the S-matrix as the asymptotic limit of the GBF amplitude associated with finite interval, and rod regions. For interval regions, whose boundary consists of two Cauchy surfaces, the asymptotic GBF-amplitude becomes the standard S-matrix. Our work generalizes previous results (obtained in Minkowski, Rindler, de Sitter, and Anti de Sitter spacetimes) to a wide class of curved spacetimes.
NASA Astrophysics Data System (ADS)
Tan, Xiaoqing; Zhang, Xiaoqian
2016-05-01
We propose two controlled quantum secure communication schemes by entanglement distillation or generalized measurement. The sender Alice, the receiver Bob and the controllers David and Cliff take part in the whole schemes. The supervisors David and Cliff can control the information transmitted from Alice to Bob by adjusting the local measurement angles θ _4 and θ _3. Bob can verify his secret information by classical one-way function after communication. The average amount of information is analyzed and compared for these two methods by MATLAB. The generalized measurement is a better scheme. Our schemes are secure against some well-known attacks because classical encryption and decoy states are used to ensure the security of the classical channel and the quantum channel.
NASA Astrophysics Data System (ADS)
Yahiaoui, S. A.; Bentaiba, M.
2012-11-01
In the context of the factorization method, we investigate the pseudo-Hermitian coherent states and their Hermitian counterpart coherent states under the generalized quantum condition in the framework of a position-dependent mass. By considering a specific modification in the superpotential, suitable annihilation and creation operators are constructed in order to reproduce the Hermitian counterpart Hamiltonian in the factorized form. We show that by means of these ladder operators, we can construct a wide range of exactly solvable potentials as well as their accompanying coherent states. Alternatively, we explore the relationship between the pseudo-Hermitian Hamiltonian and its Hermitian counterparts, obtained from a similarity transformation, to construct the associated pseudo-Hermitian coherent states. These latter preserve the structure of Perelomov’s states and minimize the generalized position-momentum uncertainty principle. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Denseness of Ashtekar Lewandowski states and a generalized cut-off in loop quantum gravity
NASA Astrophysics Data System (ADS)
Velhinho, J. M.
2005-07-01
We show that the set of states of the Ashtekar Isham Lewandowski holonomy algebra defined by elements of the Ashtekar Lewandowski Hilbert space is dense in the space of all states. We consider weak convergence properties of a modified version of the cut-off procedure currently in use in loop quantum gravity. This version is adapted to vector states rather than to general distributions.
Quantum generalization of the classical rotating solutions of the O(N) model
NASA Astrophysics Data System (ADS)
Vautherin, D.; Matsui, T.
1998-10-01
Analytic solutions of the mean field evolution equations for an N-component scalar field with O(N) symmetry are presented. These solutions correspond to rotations in isospin space. They represent generalizations of the classical solutions obtained earlier by Anselm and Ryskin. As compared to classical solutions new effects arise because of the coupling between the average value of the field and quantum fluctuations.
General immunity and superadditivity of two-way Gaussian quantum cryptography.
Ottaviani, Carlo; Pirandola, Stefano
2016-03-01
We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks.
General immunity and superadditivity of two-way Gaussian quantum cryptography
Ottaviani, Carlo; Pirandola, Stefano
2016-01-01
We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks. PMID:26928053
BOOK REVIEW: Equations of Motion in General Relativity Equations of Motion in General Relativity
NASA Astrophysics Data System (ADS)
Schäfer, Gerhard
2012-03-01
Devoted exclusively to the problem of motion in general relativity, this book by H. Asada, T. Futamase, and P. A. Hogan is highly welcome to close up a gap in the book sector presenting a concise account of theoretical developments and results on gravitational equations of motion achieved since the discovery of the binary neutron star system PSR 1913+16 in 1974. For the most part, the book is concerned with the development and application of the important post-Newtonian approximation (PNA) framework which allows for highly efficient approximate analytic solutions of the Einstein field equations for many-body systems in terms of a slow-motion and weak-field ordering parameter. That approximation scheme is shown to be applicable also to the external motion of strongly self-gravitating objects if their internal dynamics is frozen in (strong field point particle limit) and the external conditions fit. Relying on the expertise of the authors, the PNA framework is presented in a form which, at the 1PNA level, had become famous through the work by Einstein, Infeld and Hoffmann in 1938; therein, surface integrals over gravitational field expressions in the outside-body regime play a crucial role. Other approaches which also succeeded with the highest achieved PNA level so far are mentioned too, if not fully exhaustively with respect to the highest, the 3.5PNA level which contains the inverse power of the speed of light to the seventh order. Regarding the 3PNA, the reader gains a clear understanding of how the equations of motion for binary systems with compact components come about. Remarkably, no deviation from four-dimensional space-time is needed. Various explicit analytic expressions are derived for binary systems: the periastron advance and the orbital period at the 2PNA, the orbital decay through gravitational radiation reaction at the 2.5PNA, and effects of the gravitational spin-orbit and spin-spin couplings on the orbital motion. Also the propagation of light
General Relativity: The most beautiful of theories. Applications and trends after 100 years
NASA Astrophysics Data System (ADS)
Rovelli, Carlo
2015-02-01
Generalising Newton's law of gravitation, general relativity is one of the pillars of modern physics. While applications in the beginning were restricted to isolated effects such as a proper understanding of Mercury's orbit, the second half of the twentieth century saw a massive development of applications. These include cosmology, gravitational waves, and even very practical results for satellite based positioning systems as well as different approaches to unite general relativity with another very successful branch of physics - quantum theory. On the occassion of general relativity's centennial, leading scientists in the different branches of gravitational research review the history and recent advances in the main fields of applications of the theory, which was referred to by Lev Landau as "the most beautiful of the existing physical theories".
Unsharpness of generalized measurement and its effects in entropic uncertainty relations
Baek, Kyunghyun; Son, Wonmin
2016-01-01
Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we suggest a new class of entropic uncertainty relation that differentiates quantum uncertainty from device imperfection due to the unsharpness of measurement. In order to quantify the unsharpness, we suggest and analyze the quantity that characterizes the uncertainty in the measuring device, based on Shannon entropy. Using the quantity, we obtain a new lower bound of entropic uncertainty with unsharpness and it has been shown that the relation can also be obtained under the scenario that sharp observables are affected by the white noise and amplitude damping. PMID:27456466
Perturbative Quantum Gravity and its Relation to Gauge Theory.
Bern, Zvi
2002-01-01
In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.
Metric on the space of quantum states from relative entropy. Tomographic reconstruction
NASA Astrophysics Data System (ADS)
Man'ko, Vladimir I.; Marmo, Giuseppe; Ventriglia, Franco; Vitale, Patrizia
2017-08-01
In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential calculus. The cases N=2, N=3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher-Rao metric for the space of quantum tomograms and derived a reconstruction formula of the quantum metric of density states out of the tomographic one. A new inequality obtained for probabilities of three spin-1/2 projections in three perpendicular directions is proposed to be checked in experiments with superconducting circuits.
Uncertainty under quantum measures and quantum memory
NASA Astrophysics Data System (ADS)
Xiao, Yunlong; Jing, Naihuan; Li-Jost, Xianqing
2017-04-01
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty relation will vary. Based on the knowledge of correlations between the measured particle and quantum memory, we have investigated the entropic uncertainty relations for two and multiple measurements and generalized the lower bounds on the sum of Shannon entropies without quantum side information to those that allow quantum memory. In particular, we have obtained generalization of Kaniewski-Tomamichel-Wehner's bound for effective measures and majorization bounds for noneffective measures to allow quantum side information. Furthermore, we have derived several strong bounds for the entropic uncertainty relations in the presence of quantum memory for two and multiple measurements. Finally, potential applications of our results to entanglement witnesses are discussed via the entropic uncertainty relation in the absence of quantum memory.
NASA Astrophysics Data System (ADS)
Pang, Belinda; Ma, Yiqiu; Miao, Haixing; Chen, Yanbei
2017-01-01
We relate the radiation of gravitational waves (GW) by a light interferometer with cavity arms (such as LIGO) to its quantum limited sensitivity as a detector of GW's, thereby demonstrating a reciprocity relation between the interferometer's function as a detector and emitter. We derive the pairwise interactions among the cavity optical field, the cavity end mirror, and the gravitational perturbation from the action principle. We quantize these degrees of freedom to calculate the GW's generated by a quantum object. We find that the rate of gravitational wave generation is related to the so-called quantum Cramer Rao bound of the detector, which is a general result from linear measurement theory that gives the fundamental limit to a detector's sensitivity. We show that increasing the maximal sensitivity for the interferometer also increases its GW radiation. This finding may point towards a new paradigm for improving detector sensitivity by maximizing GW radiator.
Quantum corrections to the generalized Proca theory via a matter field
NASA Astrophysics Data System (ADS)
Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab
2017-09-01
We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.
General quantum two-player games, their gate operators, and Nash equilibria
NASA Astrophysics Data System (ADS)
Bolonek-Lasoń, Katarzyna
2015-02-01
Two-player N-strategy games quantized according to the Eisert-Lewenstein-Wilkens scheme [Phys. Rev. Lett. 83, 3077 (1999)] are considered. Group-theoretical methods are applied to the problem of finding a general form of gate operators (entanglers) under the assumption that the set of classical pure strategies is contained in the set of pure quantum ones. The role of the stability group of the initial state of the game is stressed. As an example, it is shown that maximally entangled games do not admit nontrivial pure Nash strategies. The general arguments are supported by explicit computations performed in the three-strategy case.
NASA Astrophysics Data System (ADS)
Farouk, Ahmed; Zakaria, Magdy; Megahed, Adel; Omara, Fatma A.
2015-11-01
In this paper, we generalize a secured direct communication process between N users with partial and full cooperation of quantum server. So, N - 1 disjointed users u1, u2, …, uN-1 can transmit a secret message of classical bits to a remote user uN by utilizing the property of dense coding and Pauli unitary transformations. The authentication process between the quantum server and the users are validated by EPR entangled pair and CNOT gate. Afterwards, the remained EPR will generate shared GHZ states which are used for directly transmitting the secret message. The partial cooperation process indicates that N - 1 users can transmit a secret message directly to a remote user uN through a quantum channel. Furthermore, N - 1 users and a remote user uN can communicate without an established quantum channel among them by a full cooperation process. The security analysis of authentication and communication processes against many types of attacks proved that the attacker cannot gain any information during intercepting either authentication or communication processes. Hence, the security of transmitted message among N users is ensured as the attacker introduces an error probability irrespective of the sequence of measurement.
Digital-analog quantum simulation of generalized Dicke models with superconducting circuits
Lamata, Lucas
2017-01-01
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits. PMID:28256559
Digital-analog quantum simulation of generalized Dicke models with superconducting circuits.
Lamata, Lucas
2017-03-03
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.
General response formula and application to topological insulator in quantum open system.
Shen, H Z; Qin, M; Shao, X Q; Yi, X X
2015-11-01
It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.
Digital-analog quantum simulation of generalized Dicke models with superconducting circuits
NASA Astrophysics Data System (ADS)
Lamata, Lucas
2017-03-01
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.
Farouk, Ahmed; Zakaria, Magdy; Megahed, Adel; Omara, Fatma A.
2015-01-01
In this paper, we generalize a secured direct communication process between N users with partial and full cooperation of quantum server. So, N − 1 disjointed users u1, u2, …, uN−1 can transmit a secret message of classical bits to a remote user uN by utilizing the property of dense coding and Pauli unitary transformations. The authentication process between the quantum server and the users are validated by EPR entangled pair and CNOT gate. Afterwards, the remained EPR will generate shared GHZ states which are used for directly transmitting the secret message. The partial cooperation process indicates that N − 1 users can transmit a secret message directly to a remote user uN through a quantum channel. Furthermore, N − 1 users and a remote user uN can communicate without an established quantum channel among them by a full cooperation process. The security analysis of authentication and communication processes against many types of attacks proved that the attacker cannot gain any information during intercepting either authentication or communication processes. Hence, the security of transmitted message among N users is ensured as the attacker introduces an error probability irrespective of the sequence of measurement. PMID:26577473
Farouk, Ahmed; Zakaria, Magdy; Megahed, Adel; Omara, Fatma A
2015-11-18
In this paper, we generalize a secured direct communication process between N users with partial and full cooperation of quantum server. So, N - 1 disjointed users u1, u2, …, uN-1 can transmit a secret message of classical bits to a remote user uN by utilizing the property of dense coding and Pauli unitary transformations. The authentication process between the quantum server and the users are validated by EPR entangled pair and CNOT gate. Afterwards, the remained EPR will generate shared GHZ states which are used for directly transmitting the secret message. The partial cooperation process indicates that N - 1 users can transmit a secret message directly to a remote user uN through a quantum channel. Furthermore, N - 1 users and a remote user uN can communicate without an established quantum channel among them by a full cooperation process. The security analysis of authentication and communication processes against many types of attacks proved that the attacker cannot gain any information during intercepting either authentication or communication processes. Hence, the security of transmitted message among N users is ensured as the attacker introduces an error probability irrespective of the sequence of measurement.
Geodesic Motion in General Relativity:. Lares in Earth's Gravity
NASA Astrophysics Data System (ADS)
Ciufolini, I.; Gurzadyan, V. G.; Penrose, R.; Paolozzi, A.
2013-11-01
According to General Relativity, as distinct from Newtonian gravity, motion under gravity is treated by a theory that deals, initially, only with test particles. At the same time, satellite measurements deal with extended bodies. We discuss the correspondence between geodesic motion in General Relativity and the motion of an extended body by means of the Ehlers-Geroch theorem, and in the context of the recently launched LAser RElativity Satellite (LARES). Being possibly the highest mean density orbiting body in the Solar system, this satellite provides the best realization of a test particle ever reached experimentally and provides a unique possibility for testing the predictions of General Relativity.
NASA Astrophysics Data System (ADS)
Eftekhari, F.; Tavassoly, M. K.
In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coherent states. The suQ(1, 1) algebra as a nonlinear deformed algebra realization of the introduced states is established. In addition, the corresponding even and odd nonlinear charge coherent states have also been introduced. The formalism has the potentiality to be applied to systems either with known "nonlinearity function" f(n) or solvable quantum system with known "discrete nondegenerate spectrum" en. As some physical appearances, a few known physical systems in the two mentioned categories have been considered. Finally, since the construction of nonclassical states is a central topic of quantum optics, nonclassical features and quantum statistical properties of the introduced states have been investigated by evaluating single- and two-mode squeezing, su(1, 1)-squeezing, Mandel parameter and antibunching effect (via g-correlation function) as well as some of their generalized forms we have introduced in the present paper.
Xing, Jian; Zhang, Yu-Ran; Liu, Shang; Chang, Yan-Chun; Yue, Jie-Dong; Fan, Heng; Pan, Xin-Yu
2017-05-31
One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of quantum information, the uncertainty principle can be formulated as entropic uncertainty relations with two measurements for a quantum bit (qubit) in two-dimensional system. New entropic uncertainty relations are studied for a higher-dimensional quantum state with multiple measurements, and the uncertainty bounds can be tighter than that expected from two measurements settings and cannot result from qubits system with or without a quantum memory. Here we report the first room-temperature experimental testing of the entropic uncertainty relations with three measurements in a natural three-dimensional solid-state system: the nitrogen-vacancy center in pure diamond. The experimental results confirm the entropic uncertainty relations for multiple measurements. Our result represents a more precise demonstrating of the fundamental uncertainty principle of quantum mechanics.
Is Relativistic Quantum Mechanics Compatible with Special Relativity?
NASA Astrophysics Data System (ADS)
Lavenda, B. H.
2001-05-01
The transformation from a time-dependent random walk to quantum mechanics converts a modified Bessel function into an ordinary one together with a phase factor e,ir/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order of the Bessel function. Assuming equal probabilities for jumps ± 1 , the normalized modified Bessel function of an imaginary argument is the solution of the finite difference differential Schrödinger equation whereas the same function of a real argument satisfies the diffusion equation. In the nonrelativistic limit, the stability condition of the difference scheme contains the mass whereas in the ultrarelativistic limit only the velocity of light appears. Particle waves in the nonrelativistic limit become elastic waves in the ultrarelativistic limit with a phase shift in the frequency and wave number of 7r/2. The ordinary Bessel function satisfies a second order recurrence relation which is a finite difference differential wave equation, using non-nearest neighbors, whose solutions are the chirality components of a free-particle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the Klein-Gordon equation but does not admit a solution in terms of ordinary Bessel functions. However, a sign change of the mass term permits a solution in terms of a modified Bessel function whose recurrence formulas produce all the results of special relativity. The Lorentz transformation maximizes the integral of the modified Bessel function and determines the paths of steepest descent in the classical limit. If the definitions of frequency and wave number in terms of the phase were used in special relativity, the condition that the frame be inertial would equate the superluminal phase velocity with the particle velocity in violation of causality. In order to get surfaces of constant phase to move at the group velocity, an
Covariance and time regained in canonical general relativity
Kouletsis, I.
2008-09-15
Canonical vacuum gravity is expressed in generally covariant form in order that spacetime diffeomorphisms be represented within its equal-time phase space. In accordance with the principle of general covariance and ideas developed within history phase-space formalisms in [I. Kouletsis and K. V. Kuchar, Phys. Rev. D 65, 125026 (2002)], [K. Savvidou, Classical Quantum Gravity 18, 3611 (2001)], [K. Savvidou, Classical Quantum Gravity 21, 615 (2004)], [K. Savvidou, Classical Quantum Gravity 21, 631 (2004)], the time mapping T: M{yields}R and the space mapping X: M{yields}{sigma} that define the Dirac-Arnowitt-Deser-Misner (ADM) foliation are incorporated into the framework of the Hilbert variational principle. The resulting canonical action encompasses all individual Dirac-ADM actions, corresponding to different choices of foliating vacuum spacetimes by spacelike hypersurfaces. The equal-time phase space P=(g{sub ij},p{sup ij},Y{sup {alpha}},P{sub {alpha}}) includes the embeddings Y{sup {alpha}}: {sigma}{yields}M and their conjugate momenta P{sub {alpha}}. It is constrained by eight first-class constraints. The constraint surface C is determined by the super-Hamiltonian and supermomentum constraints of vacuum gravity and the vanishing of the embedding momenta. Deformations of the time and space mappings, {delta}T and {delta}X, and spacetime diffeomorphisms, V(set-membership sign)LDiffM, induce symplectic diffeomorphisms of P. While the generator D{sub ({delta}T,{delta}X)} of deformations depends on all eight constraints, the generator D{sub V} of spacetime diffeomorphisms depends only on the embedding momentum constraints. As a result, spacetime observables, namely, dynamical variables F on P that are invariant under spacetime diffeomorphisms, (F,D{sub V})|{sub C}=0, are not necessarily invariant under the deformations of the mappings, (F,D{sub ({delta}T,{delta}X)})|{sub C}{ne}0, nor are they constants of the motion, (F,{integral}d{sup 3}xH)|{sub C}{ne}0. Dirac
NASA Astrophysics Data System (ADS)
Kotas, Ronald
2014-03-01
The concept of General Relativity is not compatible with Quantum Mechanics. General Relativity is not real science, only a fallacy concept with no definitive proofs. It is not based on reality. Light and other radiation are not bent by General Relativity, only by Newtonian Refractions in the Sun's very hot Corona. The planet Mercury orbital perihelion is not a proof of General Relativity; it is fully and logically explained by Newtonian Mechanics. The dynamic 2/3rds ratio of Mercury's day-to-year ratio is profound and a Nuclear Quantum Gravitational function, not General Relativity. The Red Shift is a Nuclear Quantum Gravitational effect, not General Relativity. The so-called gravitational lens is also where refraction of gaseous matter, dust or real objects are not considered. No ``gravity waves'' have ever been detected by any LIGO site in the world. No material ``frame dragging'' has been detected by the Gravity B probe. The reason is that there is no space fabric to cause these effects. It should be perfectly clear that General Relativity has no definitive proofs and is not a real or correct description of Science. Nuclear Quantum Gravitation is a clear explanation of Gravity/Gravitation with 31 proofs and indications, and is compatible with Quantum and Newtonian Mechanics.
Private quantum computation: an introduction to blind quantum computing and related protocols
NASA Astrophysics Data System (ADS)
Fitzsimons, Joseph F.
2017-06-01
Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have emerged which seek to marry these concepts for the purpose of securing computation rather than communication. These protocols address the task of securely delegating quantum computation to an untrusted device while maintaining the privacy, and in some instances the integrity, of the computation. We present a review of the progress to date in this emerging area.
General quantum-mechanical setting for field-antifield formalism as a hyper-gauge theory
NASA Astrophysics Data System (ADS)
Batalin, Igor A.; Lavrov, Peter M.
2016-09-01
A general quantum-mechanical setting is proposed for the field-antifield formalism as a unique hyper-gauge theory in the field-antifield space. We formulate a Schr\\"odinger-type equation to describe the quantum evolution in a "current time" purely formal in its nature. The corresponding Hamiltonian is defined in the form of a supercommutator of the delta-operator with a hyper-gauge Fermion. The initial wave function is restricted to be annihilated with the delta-operator. The Schr\\"odinger's equation is resolved in a closed form of the path integral, whose action contains the symmetric Weyl's symbol of the Hamiltonian. We take the path integral explicitly in the case of being a hyper-gauge Fermion an arbitrary function rather than an operator.
von Neumann measurement-related matrices and the nullity condition for quantum correlation
NASA Astrophysics Data System (ADS)
Zhao, MingJing; Ma, Teng; Zhang, TingGui; Fei, Shao-Ming
2016-12-01
We study von Neumann measurement-related matrices, and the nullity condition of quantum correlation. We investigate the properties of these matrices that are related to a von Neumann measurement. It is shown that these ( m 2 - 1) × ( m 2 - 1) matrices are idempotent, and have rank m - 1. These properties give rise to necessary conditions for the nullity of quantum correlations in bipartite systems. Finally, as an example we discuss quantum correlation in Bell diagonal states.
General Relativity Theory - Well Proven and Also Incomplete: Further Arguments
NASA Astrophysics Data System (ADS)
Brandes, Jürgen
In the former article "General Relativity Theory - well proven and also incomplete?" with a few arguments it was proven that general relativity (GRT) makes contradictory predictions about the total energy of a particle resting in the gravitational field. With a few further arguments it was proven that this contradiction is resolved by expanding general relativity. General relativity is contradictious in energy questions since on one side the total energy of a particle resting in the gravitational field is lower than its rest mass (there is energy needed to pull out the particle from the gravitational field) while on the other side it is equal to its rest mass (this is a consequence of the equivalence principle). In the following article these considerations are generalized to a moving particle. A particle moving in the gravitational field has a total energy less than its rest mass times the relativistic γ-factor since there is energy needed to pull the particle out without changing its velocity. On the other side total energy of a moving particle is equal to its rest mass times the relativistic γ-factor (this is a consequence of the equivalence principle, too). This contradiction is resolved by expanding general relativity in the same manner as above. The other fact: Though it is not the aim of the author to reject general relativity but to expand it, he is treated as some uncritical anti-relativist - since the start of his considerations and meanwhile for more than 20 years.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
NASA Astrophysics Data System (ADS)
Lake, Kayll
2010-12-01
, Hoenselaers C and Herlt E 2003 Exact Solutions of Einstein's Field Equations (Second Edition) (Cambridge: Cambridge University Press) [2] Pretorius F and Israel W 1998 Class. Quantum Grav.15 2289 [3] Wiltshire D, Visser M and Scott S (ed) 2008 The Kerr Spacetime: Rotating Black Holes in General Relativity (Cambridge: Cambridge University Press) [4] Coley A, Hervik S and Pelavas N 2009 Class. Quantum Grav. 26 025013 [5] Plebański J and Krasiński A 2006 An Introduction to General Relativity and Cosmology (Cambridge: Cambridge University Press)
Contradictory character of general relativity. The relativistic theory of gravitation
Logunov, A.A.; Loskutov, Y.M.
1986-11-01
It is shown that in its general form general relativity is unsatisfactory. In particular, its predictions for the gravitational time delay of a radio signal and the period of revolution of a satellite are ambiguous. At the same time, it is shown that the relativistic theory of gravitation is free of such shortcomings and agrees with all reliably established experimental facts.
2. GENERAL VIEW SOUTHEAST DEPICTING THE RELATION (LEFT TO RIGHT) ...
2. GENERAL VIEW SOUTHEAST DEPICTING THE RELATION (LEFT TO RIGHT) OF 25, 35, 119 AND 125 CONTRA COSTA ST. - Point Richmond Historic District, Hillside & Contra Costa Streets, Richmond, Contra Costa County, CA
Relativistic theory of gravitation and criticism of general relativity
Logunov, A.A.; Loskutov, Yu.M.; Mestvirishvili, M.A.
1988-05-01
Two questions are discussed: (1) the invalidity of the general theory of relativity as a physical theory of gravitation and (2) the construction of a relativistic theory of gravitation possessing all attributes of field theories.
Conservative form of Boltzmann's equation in general relativity
NASA Astrophysics Data System (ADS)
Shibata, Masaru; Nagakura, Hiroki; Sekiguchi, Yuichiro; Yamada, Shoichi
2014-04-01
We derive a conservative form of Boltzmann's equation in general relativity, which is concisely written. Several explicit forms of this equation are written for black-hole spacetime with several coordinate conditions in real spacetime and momentum-space coordinates.