A general theory of quantum relativity
NASA Astrophysics Data System (ADS)
Minic, Djordje; Tze, Chia-Hsiung
2004-02-01
The geometric form of standard quantum mechanics is compatible with the two postulates: (1) the laws of physics are invariant under the choice of experimental setup and (2) every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite-dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics.
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
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.
Generalized Uncertainty Relation in the Non-commutative Quantum Mechanics
NASA Astrophysics Data System (ADS)
Chung, Won Sang
2016-06-01
In this paper the non-commutative quantum mechanics (NCQM) with the generalized uncertainty relations {Δ } x1 {Δ } x2 ≥ {θ}/{2}, {Δ} p1 {Δ } p2 ≥ {bar{θ}}/{2}, {Δ } xi {Δ } pi ≥ {hbar _{eff}}/{2} is discussed. Four each uncertainty relation, wave functions saturating each uncertainty relation are explicitly constructed. The unitary operators relating the non-commutative position and momentum operators to the commutative position and momentum operators are also investigated. We also discuss the uncertainty relation related to the harmonic oscillator.
The Cavenish Experiment, General Relativity, Nuclear Quantum Gravitation
NASA Astrophysics Data System (ADS)
Kotas, Ronald R.
2008-04-01
The Cavendish Experiment - Demonstration clearly shows the Gravitational attraction between two masses, which is a force proportional to the Newtonian mechanics. General Relativity fails the Cavendish Experiment because there is no force between two gravitating masses but instead pictures a fallacious time-space concept. GR has no definitive proofs. The very hot corona and not GR cause the bending of light near and about the Sun The Perihelion of Mercury, the 43 arc seconds is 3.8 x 10-12 of the total and is not a proof of GR. This Perihelion rotation is nothing more than another mode of Newtonian mechanics explained by Newtonian mechanics. Each orbit is an ellipse, a Newtonian function that adds together because of Newtonian functions and accounts for any movement and advancement of Mercury. Because of gravity and speed changes, clocks change, time does not change. Other proofs are not valid because they are Quantum effects or plainly Newtonian refractions. Nuclear Quantum Gravitation clearly explains the gravitational force between two gravitating masses because of alternating electromagnetic functions in nuclei of matter. Some 20 proofs and indications prove this, plainly and clearly. Any gravity theory that does not conform to the Cavendish demonstration is not a viable theory of gravity. With Nuclear Quantum Gravitation, the Forces are plainly and coherently unified.
Tighter quantum uncertainty relations following from a general probabilistic bound
NASA Astrophysics Data System (ADS)
Fröwis, Florian; Schmied, Roman; Gisin, Nicolas
2015-07-01
Uncertainty relations (URs) such as the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from estimation theory, a Cramér-Rao-like bound. The Heisenberg-Robertson UR is then obtained by using the Born rule and the Schrödinger equation. This allows a clear separation of the probabilistic nature of quantum mechanics from the Hilbert space structure and the dynamical law. It also simplifies the interpretation of the bound. In addition, the Heisenberg-Robertson UR is tightened for mixed states by replacing one variance by the quantum Fisher information. Thermal states of Hamiltonians with evenly gapped energy levels are shown to saturate the tighter bound for natural choices of the operators. This example is further extended to Gaussian states of a harmonic oscillator. For many-qubit systems, we illustrate the interplay between entanglement and the structure of the operators that saturate the UR with spin-squeezed states and Dicke states.
Quantum electrodynamical corrections to a magnetic dipole in general relativity
NASA Astrophysics Data System (ADS)
Pétri, J.
2016-03-01
Magnetized neutron stars are privileged places where strong electromagnetic fields as high as BQ = 4.4 × 109 T exist, giving rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). These corrections need to be included to the general relativistic (GR) description of a magnetic dipole supposed to be anchored in the neutron star. In this paper, these QED and GR perturbations to the standard flat space-time dipole are calculated to the lowest order in the fine structure constant αsf and to any order in the ratio Rs/R where R is the neutron star radius and Rs its Schwarzschild radius. Following our new 3+1 formalism developed in a previous work, we compute the multipolar non-linear corrections to this dipole and demonstrate the presence of a small dipolar ℓ = 1 and hexapolar ℓ = 3 component.
Can a sub-quantum medium be provided by General Relativity?
NASA Astrophysics Data System (ADS)
Andersen, Thomas C.
2016-03-01
Emergent Quantum Mechanics (EmQM) seeks to construct quantum mechanical theory and behaviour from classical underpinnings. This paper explores the possibility that the field of classical general relativity (GR) could supply a sub-quantum medium for these subquantum mechanics. Firstly, I present arguments which show that GR satisfies many of the a priori requirements for a sub-quantum medium. Secondly, some potential obstacles to using GR as the underlying field are noted, for example field strength (isn't gravity a very weak force?) and spin 2. Thirdly, the ability of dynamical exchange processes to create very strong effective fields is demonstrated through the use of a simple model, which solves many of the issues raised in the second section. I conclude that there appears to be enough evidence to pursue this direction of study further, particularly as this line of research also has the possibility to help unify quantum mechanics and general relativity.
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.
Non-locality in quantum field theory due to general relativity
NASA Astrophysics Data System (ADS)
Calmet, Xavier; Croon, Djuna; Fritz, Christopher
2015-12-01
We show that general relativity coupled to a quantum field theory generically leads to non-local effects in the matter sector. These non-local effects can be described by non-local higher dimensional operators which remarkably have an approximate shift symmetry. When applied to inflationary models, our results imply that small non-Gaussianities are a generic feature of models based on general relativity coupled to matter fields. However, these effects are too small to be observable in the cosmic microwave background.
A 3+1 formalism for quantum electrodynamical corrections to Maxwell equations in general relativity
NASA Astrophysics Data System (ADS)
Pétri, J.
2015-08-01
Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover, strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of BQ = 4.4 × 109 T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polarization properties, it is important to include general relativistic (GR) effects simultaneously with non-linear electrodynamics. This can be achieved through a 3+1 formalism known in general relativity and that incorporates QED perturbations to Maxwell equations. Starting from the lowest order corrections to the Lagrangian for the electromagnetic field, as given for instance by Born-Infeld or Euler-Heisenberg theory, we derive the non-linear Maxwell equations in general relativity including quantum vacuum effects. We also derive a prescription for the force-free limit and show that these equations can be solved with classical finite volume methods for hyperbolic conservation laws. It is therefore straightforward to include general relativity and QED in the description of neutron star magnetospheres by using standard classical numerical techniques borrowed from Maxwell and Newton theory. As an application, we show that spin-down luminosity corrections associated with QED effects are negligible with respect to GR corrections.
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. PMID:15889967
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.
Two Phases of the Non-Commutative Quantum Mechanics with the Generalized Uncertainty Relations
NASA Astrophysics Data System (ADS)
Chung, Won Sang
2016-04-01
We consider the quantum mechanics on the noncommutative plane with the generalized uncertainty relations {Δ } x1 {Δ } x2 ge frac {θ }{2}, {Δ } p1 {Δ } p2 ge frac {bar {θ }}{2}, {Δ } xi {Δ } pi ge frac {hbar }{2}, {Δ } x1 {Δ } p2 ge frac {η }{2}. We show that the model has two essentially different phases which is determined by kappa = 1 + frac {1}{hbar 2 } (η 2 - θ bar {θ }). We construct a operator hat {π }i commuting with hat {x}j and discuss the harmonic oscillator model in two dimensional non-commutative space for three case κ > 0, κ = 0, κ < 0. Finally, we discuss the thermodynamics of a particle whose hamiltonian is related to the harmonic oscillator model in two dimensional non-commutative space.
Relativity and Quantum Mechanics
Braendas, Erkki J.
2007-12-26
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.
Unifying the Geometry of General Relativity with the Virtual Particle Nature of Quantum Theory
NASA Astrophysics Data System (ADS)
Laubenstein, John
2007-03-01
General Relativity (GR) and Quantum Electro-Dynamics (QED) utilize different underlying assumptions regarding the nature of vacuum and space-time. GR requires the actual geometry of space-time to change in the presence of mass resulting in gravitation. QED operates within flat space-time and propagates forces through the exchange of virtual photons. Efforts to unify these theories are -- despite their mathematical elegance -- complex, cumbersome and incomplete. The inability to achieve unification may suggest a need to re-think basic conceptual models. The IWPD Research Center has found evidence suggesting that time -- as a unique degree of freedom -- may be illusionary. Our research suggests that time may be ``embedded'' within a spatial dimension through a geometric manipulation of the light cone in Minkowski space-time. This interpretation of space-time provides predictions that are experimentally verifiable and suggests a conceptual path for the unification of GR and QED.
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.
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)
Santos, A. P.; Silva, R.; Alcaniz, J. S.; Anselmo, D. H. A. L.
2011-08-01
A deduction of generalized quantum entropies within the Tsallis and Kaniadakis frameworks is derived using a generalization of the ordinary multinomial coefficient. This generalization is based on the respective deformed multiplication and division. We show that the two above entropies are consistent with ones arbitrarily assumed at other contexts.
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.
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 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.
How the Jones polynomial give rise to physical states of quantum general relativity
Bruegmann, B. ); Gambini, R. ); Pullin, J. )
1993-01-01
Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by considering loop functionals which are knot invariants, there remains the puzzle why several of the known knot invariants are also solutions to the hamiltonian constraint. We show how the Jones polynomial gives rise to an infinite set of solutions to all the constraints of quantum gravity thereby illuminating the structure of the space of solutions and suggesting the existence of a deep connection between quantum gravity and knot theory at a dynamical level.
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.
NASA Astrophysics Data System (ADS)
Roupas, Zacharias
2015-06-01
In [1], the thermal equilibrium of static, spherically symmetric perfect fluids in General Relativity was studied. I would like to elaborate three points relevant to the results of [1]. The first point is only a clarification, summarized in theorem 1 below, of results that appear in [1]. The following two points correct the error in [1], stating that the condition for thermodynamic stability, found in [1], is referring to the microcanonical ensemble, while it was referring to the canonical one. In theorems 2 and 3, specific cases for which equivalence of dynamical and thermodynamic stability holds are specified.
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.
Quantum thermodynamics of general quantum processes
NASA Astrophysics Data System (ADS)
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.
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. PMID:25871066
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 Quantum Interference Principle and Duality Computer
NASA Astrophysics Data System (ADS)
Long, Gui-Lu
2006-05-01
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.
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.
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.
Recent advances in general relativity
Janis, A.I.; Porter, J.R.
1992-01-01
The papers included in this book arose from a Discussion Conference on Recent Advances in General Relativity, which was held at the University of Pittsburgh, May 3-5, 1990, in honor of Ted Newman on the occasion of his 60th birthday. The book opens with a contribution outlining successes and problems of general relativity. Two contributions are devoted to quantum gravity. Discussions are included about general relativistic astrophysics, mathematics, and gravitational radiation. There are also workshop reports on classical gravity and quantum gravity.
Complementarity relations for quantum coherence
NASA Astrophysics Data System (ADS)
Cheng, Shuming; Hall, Michael J. W.
2015-10-01
Various measures have been suggested recently for quantifying the coherence of a quantum state with respect to a given basis. We first use two of these, the l1-norm and relative entropy measures, to investigate tradeoffs between the coherences of mutually unbiased bases. Results include relations between coherence, uncertainty, and purity; tight general bounds restricting the coherences of mutually unbiased bases; and an exact complementarity relation for qubit coherences. We further define the average coherence of a quantum state. For the l1-norm measure this is related to a natural "coherence radius" for the state and leads to a conjecture for an l2-norm measure of coherence. For relative entropy the average coherence is determined by the difference between the von Neumann entropy and the quantum subentropy of the state and leads to upper bounds for the latter quantity. Finally, we point out that the relative entropy of coherence is a special case of G-asymmetry, which immediately yields several operational interpretations in contexts as diverse as frame alignment, quantum communication, and metrology, and suggests generalizing the property of quantum coherence to arbitrary groups of physical transformations.
Speed limits in general relativity
NASA Astrophysics Data System (ADS)
Low, Robert J.
1999-02-01
Some standard results on the initial value problem of general relativity in matter are reviewed. These results are applied first to show that in a well defined sense, finite perturbations in the gravitational field travel no faster than light, and second to show that it is impossible to construct a warp drive as considered by Alcubierre (1994 The warp drive: hyper-fast travel within general relativity Class. Quantum Grav. 11 L73-7) in the absence of exotic matter.
Deformed symmetries from quantum relational observables
NASA Astrophysics Data System (ADS)
Girelli, Florian; Poulin, David
2007-05-01
Deformed Special Relativity (DSR) is a candidate phenomenological theory to describe the Quantum Gravitational (QG) semi-classical regime. A possible interpretation of DSR can be derived from the notion of deformed reference frame. Observables in (quantum) General Relativity can be constructed from (quantum) reference frame - a physical observable is then a relation between a system of interest and the reference frame. We present a toy model and study an example of such quantum relational observables. We show how the intrinsic quantum nature of the reference frame naturally leads to a deformation of the symmetries, comforting DSR to be a good candidate to describe the QG semi-classical regime.
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…
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
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.
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)
Uncertainty Relation for a Quantum Open System
NASA Astrophysics Data System (ADS)
Hu, B. L.; Zhang, Yuhong
We derive the uncertainty relation for a quantum open system consisting of a Brownian particle interacting with a bath of quantum oscillators at finite temperature. We examine how the quantum and thermal fluctuations of the environment contribute to the uncertainty in the canonical variables of the system. We show that upon contact with the bath (assumed to be ohmic in this paper) the system evolves from a quantum-dominated state to a thermal-dominated state in a time which is the same as the decoherence time in similar models in the discussion of quantum to classical transition. This offers some insight into the physical mechanisms involved in the environment-induced decoherence process. We obtain closed analytic expressions for this generalized uncertainty relation under the conditions of high temperature and weak damping, separately. We also consider under these conditions an arbitrarily squeezed initial state and show how the squeeze parameter enters in the generalized uncertainty relation. Using these results we examine the transition of the system from a quantum pure state to a nonequilibrium quantum statistical state and to an equilibrium quantum statistical state. The three stages are marked by the decoherence time and the relaxation time, respectively. With these observations we explicate the physical conditions under which the two basic postulates of quantum statistical mechanics become valid. We also comment on the inappropriate usage of the word “classicality” in many decoherence studies of quantum to classical transition.
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.
Correspondence between quantum and classical information: Generalized quantum measurements
Grishanin, Boris A.; Zadkov, Victor N.
2006-04-15
The concept of generalized quantum measurement is introduced as a transformation that sets a one-to-one correspondence between the initial states of the measured object system and final states of the object-meter system with the help of a classical informational index, unambiguously linked to a classically compatible set of quantum states. It is shown that the generalized quantum measurement concept covers all key types of quantum measurement--standard projective, entangling, fuzzy, and generalized measurements with a partial or complete destruction of initial information associated with the object. A special class of soft quantum measurements as a basic model for the fuzzy measurements widespread in physics is introduced and its information properties are studied in detail. Also, a special class of partially destructive measurements mapping all states of the Hilbert space of a finite-dimensional quantum system onto the basis states of an infinite-dimensional quantum system is considered.
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)
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 Astrophysics Data System (ADS)
Blandford, Roger D.
2016-01-01
A hundred years after its birth, general relativity has become a highly successful theory in the sese that it has passed many experimental and observational tests and finds widespread application to diverse set of cosmic phenomena. It remains an accurate research field as more tests are deployed, epitomized by the exciting prospect of detecting gravitational radiation directly. General realtivity is the essential foundation of modern cosmology and underlies our detailed description of the black holes and neutron stars that are ultimately responsible for the most powerful and dramatic cosmic sources. The interface with physics on both the largest and the smallest scales continues to be very fertile. In this talk I will attempt to highlight some key steps along the way to general relativity today.
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.
Reformulating the Quantum Uncertainty Relation.
Li, Jun-Li; Qiao, Cong-Feng
2015-01-01
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. PMID:26234197
Reformulating the Quantum Uncertainty Relation
NASA Astrophysics Data System (ADS)
Li, Jun-Li; Qiao, Cong-Feng
2015-08-01
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.
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.
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
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.
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…
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.
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.
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.
Relating quantum discord with the quantum dense coding capacity
NASA Astrophysics Data System (ADS)
Wang, Xin; Qiu, Liang; Li, Song; Zhang, Chi; Ye, Bin
2015-01-01
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.
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.
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…
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.
Uncertainty characteristics of generalized quantum measurements
NASA Astrophysics Data System (ADS)
Hofmann, Holger F.
2003-02-01
The effects of any quantum measurement can be described by a collection of measurement operators {Mm} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the measurement process that are valid for arbitrary input states. The motivation of these concepts is explained from a quantum communication viewpoint. It is shown that the intuitive interpretation of uncertainty as a relation between measurement resolution and disturbance provides a valid description of measurement back action. Possible applications to quantum cryptography, quantum cloning, and teleportation are discussed.
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.
Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-06-01
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 quantum key distribution in higher dimension
NASA Astrophysics Data System (ADS)
Xiong, Zhao-Xi; Shi, Han-Duo; Wang, Yi-Nan; Jing, Li; Lei, Jin; Mu, Liang-Zhu; Fan, Heng
2012-01-01
We study a general quantum key distribution protocol in higher dimension. In this protocol, quantum states in arbitrary g+1 (1≤g≤d) out of all d+1 mutually unbiased bases in a d-dimensional system can be used for the key encoding. This provides a natural generalization of the quantum key distribution in higher dimension and recovers the previously known results for g=1 and d. In our investigation, we study Eve's attack by two slightly different approaches. One is considering the optimal cloner of Eve, and the other, defined as the optimal attack, is maximizing Eve's information. We derive results for both approaches and show the deviation of the optimal cloner from the optimal attack. With our systematic investigation of the quantum key distribution protocols in higher dimension, one may balance the security gain and the implementation cost by changing the number of bases in the key encoding. As a side product, we also prove the equivalency between the optimal phase covariant quantum cloning machine and the optimal cloner for the g=d-1 quantum key distribution.
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.
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.
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)
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
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.
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.
Majorization entropic uncertainty relations for quantum operations
NASA Astrophysics Data System (ADS)
Rastegin, Alexey E.; Życzkowski, Karol
2016-09-01
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an extension of the previous formulation, which deals with submatrices of a unitary matrix relating orthogonal bases in which measurements are performed. Two classes of majorization relations are considered: one related to the tensor product of probability vectors and another one related to their direct sum. We explicitly discuss an example of a pair of one-qubit operations, each of them represented by two Kraus operators. In the particular case of quantum maps describing orthogonal measurements the presented formulation reduces to earlier results derived for measurements in orthogonal bases. The presented approach allows us also to bound the entropy characterizing results of a single generalized measurement.
Fourth order deformed general relativity
NASA Astrophysics Data System (ADS)
Cuttell, Peter D.; Sakellariadou, Mairi
2014-11-01
Whenever the condition of anomaly freedom is imposed within the framework of effective approaches to loop quantum cosmology, one seems to conclude that a deformation of general covariance is required. Here, starting from a general deformation we regain an effective gravitational Lagrangian including terms up to fourth order in extrinsic curvature. We subsequently constrain the form of the corrections for the homogeneous case, and then investigate the conditions for the occurrence of a big bounce and the realization of an inflationary era, in the presence of a perfect fluid or scalar field.
Generalized quantum statistics and Lie (super)algebras
NASA Astrophysics Data System (ADS)
Stoilova, N. I.
2016-03-01
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?
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
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
Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies
NASA Astrophysics Data System (ADS)
Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette
2014-05-01
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.
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.
Generalized parametrization dependence in quantum gravity
NASA Astrophysics Data System (ADS)
Gies, Holger; Knorr, Benjamin; Lippoldt, Stefan
2015-10-01
We critically examine the gauge and field-parametrization dependence of renormalization group flows in the vicinity of non-Gaußian fixed points in quantum gravity. While physical observables are independent of such calculational specifications, the construction of quantum gravity field theories typically relies on off-shell quantities such as β functions and generating functionals and thus face potential stability issues with regard to such generalized parametrizations. We analyze a two-parameter class of covariant gauge conditions, the role of momentum-dependent field rescalings and a class of field parametrizations. Using the product of Newton and cosmological constant as an indicator, the principle of minimum sensitivity identifies stationary points in this parametrization space which show a remarkable insensitivity to the parametrization. In the most insensitive cases, the quantized gravity system exhibits a non-Gaußian UV stable fixed point, lending further support to asymptotically safe quantum gravity. One of the stationary points facilitates an analytical determination of the quantum gravity phase diagram and features ultraviolet and infrared complete RG trajectories with a classical regime.
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.
Entanglement of multipartite quantum states and the generalized quantum search
NASA Astrophysics Data System (ADS)
Gingrich, Robert Michael
2002-09-01
In chapter 2 various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. It is shown that the entanglement monotones of any multipartite pure state uniquely determine the orbit of that state. It follows that there must be an entanglement monotone for three-qubit pure states which depends on the Kempe invariant defined in [1]. A form for such an entanglement monotone is proposed. A theorem is proved that significantly reduces the number of entanglement monotones that must be looked at to find the maximal probability of transforming one multipartite state to another. In chapter 3 Grover's unstructured quantum search algorithm is generalized to use an arbitrary starting superposition and an arbitrary unitary matrix. A formula for the probability of the generalized Grover's algorithm succeeding after n iterations is derived. This formula is used to determine the optimal strategy for using the unstructured quantum search algorithm. The speedup obtained illustrates that a hybrid use of quantum computing and classical computing techniques can yield a performance that is better than either alone. The analysis is extended to the case of a society of k quantum searches acting in parallel. In chapter 4 the positive map Gamma : rho → (Trrho) - rho is introduced as a separability criterion. Any separable state is mapped by the tensor product of Gamma and the identity in to a non-negative operator, which provides a necessary condition for separability. If Gamma acts on a two-dimensional subsystem, then it is equivalent to partial transposition and therefore also sufficient for 2 x 2 and 2 x 3 systems. Finally, a connection between this map for two qubits and complex conjugation in the "magic" basis [2] is displayed.
General Relativity: an Einstein Centenary Survey
NASA Astrophysics Data System (ADS)
Hawking, Stephen; Israel, W.
2010-03-01
List of contributors; Preface; 1. An introductory survey S. W. Hawking and W. Israel; 2. The confrontation between gravitation theory and experiment C. M. Will; 3. Gravitational-radiation experiments D. H. Douglass and V. B. Braginsky; 4. The initial value problem and the dynamical formulation of general relativity A. E. Fischer and J. E. Marsden; 5. Global structure of spacetimes R. Geroch and G. T. Horowitz; 6. The general theory of the mechanical, electromagnetic and thermodynamic properties of black holes B. Carter; 7. An introduction to the theory of the Kerr metric and its peturbations S. Chandrasekhar; 8. Black hole astrophysics R. D. Blandford and K. S. Thorne; 9. The big bang cosmology - enigmas and nostrums R. H. Dicke and P. J. E. Peebles; 10. Cosmology and the early universe Ya B. Zel'dovitch; 11. Anisotropic and inhomogeneous relativistic cosmologies M. A. H. MacCallum; 12. Singularities and time-asymmetry R. Penrose; 13. Quantum field theory in curved spacetime G. W. Gibbons; 14. Quantum gravity: the new synthesis B. S. DeWitt; 15. The path-integral approach to quantum gravity S. W. Hawking; 16. Ultraviolet divergences in quantum theories of gravitation S. Weinberg; References; Index.
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
Generalized Kronig-Penney model for ultracold atomic quantum systems
NASA Astrophysics Data System (ADS)
Negretti, A.; Gerritsma, R.; Idziaszek, Z.; Schmidt-Kaler, F.; Calarco, T.
2014-10-01
We study the properties of a quantum particle interacting with a one-dimensional structure of equidistant scattering centers. We derive an analytical expression for the dispersion relation and for the Bloch functions in the presence of both even and odd scattering waves within the pseudopotential approximation. This generalizes the well-known solid-state physics textbook result known as the Kronig-Penney model. Our generalized model can be used to describe systems such as degenerate Fermi gases interacting with ions or with another neutral atomic species confined in an optical lattice, thus enabling the investigation of polaron or Kondo physics within a simple formalism. We focus our attention on the specific atom-ion system and compare our findings with quantum defect theory. Excellent agreement is obtained within the regime of validity of the pseudopotential approximation. This enables us to derive a Bose-Hubbard Hamiltonian for a degenerate quantum Bose gas in a linear chain of ions.
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
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.
Factorization in the quantum mechanics with the generalized uncertainty principle
NASA Astrophysics Data System (ADS)
Chung, Won Sang
2015-07-01
In this paper, we discuss the quantum mechanics with the generalized uncertainty principle (GUP) where the commutation relation is given by [x̂,p̂] = iℏ(1 + αp̂ + βp̂2). For this algebra, we obtain the eigenfunction of the momentum operator. We also study the GUP corrected quantum particle in a box. Finally, we apply the factorization method to the harmonic oscillator in the presence of a minimal observable length and obtain the energy eigenvalues by applying the perturbation method.
Uncertainty relation revisited from quantum estimation theory
Watanabe, Yu; Sagawa, Takahiro; Ueda, Masahito
2011-10-15
We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.
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.
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
2016-07-01
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.
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.
General unifying features of controlled quantum phenomena
Pechen, Alexander; Brif, Constantin; Wu, Rebing; Chakrabarti, Raj; Rabitz, Herschel
2010-09-15
Many proposals have been put forth for controlling quantum phenomena, including open-loop, adaptive feedback, and real-time feedback control. Each of these approaches has been viewed as operationally, and even physically, distinct from the others. This work shows that all such scenarios inherently share the same fundamental control features residing in the topology of the landscape relating the target physical observable to the applied controls. This unified foundation may provide a basis for development of hybrid control schemes that would combine the advantages of the existing approaches to achieve the best overall performance.
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 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)
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.
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/
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.
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.
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.
2016-05-01
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.
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
Relativity of representations in quantum mechanics
NASA Astrophysics Data System (ADS)
de la Torre, A. C.
2002-03-01
Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity of the representations of the abstract formulation of quantum mechanics, two examples of representations related to the operators αX+(1-α)P and 1/2(XP+PX) are presented.
Testing general relativity on accelerators
NASA Astrophysics Data System (ADS)
Kalaydzhyan, Tigran
2015-11-01
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 to 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. 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.
Energy loss in general relativity
Cooperstock, F.I.; Lim, P.H.
1987-07-15
Implicit assumptions regarding continuity in energy-loss calculations in general relativity are examined. The Arnowitt-Deser-Misner energy integral is treated in a new manner as a universal vehicle for energy loss. Two explicit examples are given: the electric dipole radiation flux is computed using general relativity as well as the gravitational-radiation flux from a linear mass quadrupole oscillator. In this approach, the latter is seen as a nonlinear problem in the sense that the lower-order metric serves as a source for the required order metric as computed within the wave front. Logarithmic terms which threaten to induce divergences, as has been found in other works, are averted by functions of integration which are required to sustain the gauge conditions and finally yield the usual fluxes.
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
Discrete Hamiltonian for general relativity
NASA Astrophysics Data System (ADS)
Ziprick, Jonathan; Gegenberg, Jack
2016-02-01
Beginning from the Ashtekar formulation of general relativity, we derive a physical Hamiltonian written in terms of (classical) loop gravity variables. This is done by defining the gravitational fields within a complex of three-dimensional cells and imposing that curvature and torsion vanish within each cell. The resulting theory is holographic, with the bulk dynamics being captured completely by degrees of freedom living on cell boundaries. Quantization is readily obtainable by existing methods.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Bodendorfer, N.; Zipfel, A.
2016-08-01
Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level. To this end, we generalise the previously proposed quantum reduction by dropping the gauge fixing condition on the radial diffeomorphisms, thus allowing us to make direct contact with previous work on reduced quantisation. A dictionary between spherically symmetric variables and observables with respect to the reduction constraints in the full theory is discussed, as well as an embedding of reduced quantum states to a subsector of the quantum symmetry reduced full theory states. On this full theory subsector, the quantum algebra of the mentioned observables is computed and shown to qualitatively reproduce the quantum algebra of the reduced variables in the large quantum number limit for a specific choice of regularisation. Insufficiencies in recovering the reduced algebra quantitatively from the full theory are attributed to the oversimplified full theory quantum states we use.
Generalized Einstein relation in tilted periodic potential: a semiclassical approach.
Shit, Anindita; Chattopadhyay, Sudip; Banik, Suman Kumar; Chaudhuri, Jyotipratim Ray
2010-06-17
This paper concerns the investigation of the quantum motion of a system in a dissipative Ohmic heat bath in the presence of an external field using the traditional system-reservoir model. Using physically motivated initial conditions, we then obtain the c-number of the generalized quantum Langevin equation by which we calculate the quantum correction terms using a perturbation technique. As a result of this, one can apply a classical differential equation-based approach to consider quantum diffusion in a tilted periodic potential, and thus our approach is easy to use. We use our expression to calculate the Einstein relation for the quantum Brownian particle in a ratchet-type potential in a very simple closed analytical form using a suitable and convenient approximation. It is found that the diffusion rate is independent of the detailed form of the potential both in quantum and classical regimes, which is the main essence of this work. PMID:20481540
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.
Quantum stochastic walks: A generalization of classical random walks and quantum walks
NASA Astrophysics Data System (ADS)
Whitfield, James D.; Rodríguez-Rosario, César A.; Aspuru-Guzik, Alán
2010-02-01
We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.
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.
Friction Forces in General Relativity
NASA Astrophysics Data System (ADS)
Bini, D.; Gregoris, D.; Rosquist, K.
2015-01-01
Friction forces play an important role in a wide class of phenomena both in the contexts of classical mechanics and general relativity. This paper discusses the Poynting-Robertson approach to the description of the motion of a massive test particle inside a perfect fluid undergoing dissipative effects in curved space. Specific cases of motions 1) inside a photon gas near a Schwarzschild black hole; 2) inside a photon gas in the Tolman metric are then discussed with applications to models of accretion disks of a black hole and to motion inside a static radiation dominated Universe.
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.)
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.
General monogamy property of global quantum discord and the application
Liu, Si-Yuan; Zhang, Yu-Ran; Zhao, Li-Ming; Yang, Wen-Li; Fan, Heng
2014-09-15
We provide a family of general monogamy inequalities for global quantum discord (GQD), which can be considered as an extension of the usual discord monogamy inequality. It can be shown that those inequalities are satisfied under the similar condition for the holding of usual monogamy relation. We find that there is an intrinsic connection among them. Furthermore, we present a different type of monogamy inequality and prove that it holds under the condition that the bipartite GQDs do not increase when tracing out some subsystems. We also study the residual GQD based on the second type of monogamy inequality. As applications of those quantities, we investigate the GQDs and residual GQD in characterizing the quantum phase transition in the transverse field Ising model.
General monogamy property of global quantum discord and the application
NASA Astrophysics Data System (ADS)
Liu, Si-Yuan; Zhang, Yu-Ran; Zhao, Li-Ming; Yang, Wen-Li; Fan, Heng
2014-09-01
We provide a family of general monogamy inequalities for global quantum discord (GQD), which can be considered as an extension of the usual discord monogamy inequality. It can be shown that those inequalities are satisfied under the similar condition for the holding of usual monogamy relation. We find that there is an intrinsic connection among them. Furthermore, we present a different type of monogamy inequality and prove that it holds under the condition that the bipartite GQDs do not increase when tracing out some subsystems. We also study the residual GQD based on the second type of monogamy inequality. As applications of those quantities, we investigate the GQDs and residual GQD in characterizing the quantum phase transition in the transverse field Ising model.
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.
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.
A Generalized Detailed Balance Relation
NASA Astrophysics Data System (ADS)
Ruelle, David
2016-06-01
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.
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.
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. PMID:25531675
NASA Astrophysics Data System (ADS)
Li, Zhuo; Xing, Li-Juan; Wang, Xin-Mei
2008-01-01
We construct a family of quantum maximum-distance-separable (MDS) codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be unified under these codes in the sense that when a quantum MDS code exists, then a quantum code of this type with the same parameters also exists. Thus, as far as is known at present, they are the most important family of quantum MDS codes.
Quantum stochastic walks: A generalization of classical random walks and quantum walks
NASA Astrophysics Data System (ADS)
Aspuru-Guzik, Alan
2010-03-01
We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases, but also includes more general probability distributions. As an example, we study the QSW on a line, the QW to CRW transition and transitions to genearlized QSWs that go beyond the CRW and QW. QSWs provide a new framework to the study of quantum algorithms as well as of quantum walks with environmental effects.
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
Generalization of continuous-variable quantum cloning with linear optics
NASA Astrophysics Data System (ADS)
Zhai, Zehui; Guo, Juan; Gao, Jiangrui
2006-05-01
We propose an asymmetric quantum cloning scheme. Based on the proposal and experiment by Andersen [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.
Generalized Uncertainty Relations in the Non-commutative Plane
NASA Astrophysics Data System (ADS)
Chung, Won Sang
2015-09-01
In this paper we study two-dimensional noncommutative quantum mechanics (NCQM) with the generalized uncertainty relations . We find the new NCQM algebra from the generalized uncertainty relations. We construct a operator commuting with and discuss two possibilities; One is the case that also commutes with and another is the case that does not commute with . For both case we consider a motion of a charged particle in a magnetic field with a harmonic oscillator potential in the noncommutative plane.
Quantum description of light propagation in generalized media
NASA Astrophysics Data System (ADS)
Häyrynen, Teppo; Oksanen, Jani
2016-02-01
Linear quantum input-output relation based models are widely applied to describe the light propagation in a lossy medium. The details of the interaction and the associated added noise depend on whether the device is configured to operate as an amplifier or an attenuator. Using the traveling wave (TW) approach, we generalize the linear material model to simultaneously account for both the emission and absorption processes and to have point-wise defined noise field statistics and intensity dependent interaction strengths. Thus, our approach describes the quantum input-output relations of linear media with net attenuation, amplification or transparency without pre-selection of the operation point. The TW approach is then applied to investigate materials at thermal equilibrium, inverted materials, the transparency limit where losses are compensated, and the saturating amplifiers. We also apply the approach to investigate media in nonuniform states which can be e.g. consequences of a temperature gradient over the medium or a position dependent inversion of the amplifier. Furthermore, by using the generalized model we investigate devices with intensity dependent interactions and show how an initial thermal field transforms to a field having coherent statistics due to gain saturation.
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. PMID:27065436
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. PMID:25353748
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.
Quantum measurement and uncertainty relations in photon polarization
NASA Astrophysics Data System (ADS)
Edamatsu, Keiichi
2016-07-01
Recent theoretical and experimental studies have given raise to new aspects in quantum measurements and error-disturbance uncertainty relations. After a brief review of these issues, we present an experimental test of the error-disturbance uncertainty relations in photon polarization measurements. Using a generalized, strength-variable measurement of a single photon polarization state, we experimentally evaluate the error and disturbance in the measurement process and demonstrate the validity of recently proposed uncertainty relations.
General relativity in Newtonian form
NASA Astrophysics Data System (ADS)
Gautreau, Ronald
1990-06-01
It is shown how the use of coordinates where time is measured with clocks moving radially in a spherically symmetric gravitational field leads to general relativistic dynamical expressions that are exactly identical to corresponding expressions in Newtonian theory. The general formalism is developed for the case where the stress-energy tensor is that of a perfect fluid. Expressions like the Newtonian inverse square gravitational law, the Newtonian equation of continuity for fluid flow, Newtonian conservation of energy, etc., follow quite naturally from the fully-fledged exact general relativistic equations. Specific examples involving cosmology and gravitational collapse are given.
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.
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.
Quantum classical transition in scale relativity
NASA Astrophysics Data System (ADS)
Célérier, Marie-Noëlle; Nottale, Laurent
2004-01-01
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The Schrödinger and Klein-Gordon equations are demonstrated as geodesic equations in this framework. A development of the intrinsic properties of this theory, using the mathematical tool of Hamilton's bi-quaternions, leads us to a derivation of the Dirac equation within the scale-relativity paradigm. The complex form of the wavefunction in the Schrödinger and Klein-Gordon equations follows from the non-differentiability of the geometry, since it involves a breaking of the invariance under the reflection symmetry on the (proper) time differential element (ds harr -ds). This mechanism is generalized for obtaining the bi-quaternionic nature of the Dirac spinor by adding a further symmetry breaking due to non-differentiability, namely the differential coordinate reflection symmetry (dxmgr harr -dxmgr) and by requiring invariance under the parity and time inversion. The Pauli equation is recovered as a non-motion-relativistic approximation of the Dirac equation.
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.
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.
On quantum Rényi entropies: A new generalization and some properties
NASA Astrophysics Data System (ADS)
Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco
2013-12-01
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.
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.
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.
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.
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.
Quasilocal mass in general relativity.
Wang, Mu-Tao; Yau, Shing-Tung
2009-01-16
There have been many attempts to define the notion of quasilocal mass for a spacelike two surface in spacetime by the Hamilton-Jacobi analysis. The essential difficulty in this approach is to identify the right choice of the background configuration to be subtracted from the physical Hamiltonian. Quasilocal mass should be non-negative for surfaces in general spacetime and zero for surfaces in flat spacetime. In this Letter, we propose a new definition of gauge-independent quasilocal mass and prove that it has the desired properties. PMID:19257261
A quantum modification of relative cohomology
NASA Astrophysics Data System (ADS)
Zhang, Dong; Chen, Bohui; Du, Cheng-Yong
2015-12-01
In this paper, we give a quantum modification of the relative cup product on H*(X, S;ℝ) by using Gromov-Witten invariants when S is a compact codimension 2k symplectic submanifold of the compact symplectic manifold (X, ω).
Quantum phases for a generalized harmonic oscillator
NASA Astrophysics Data System (ADS)
Bracken, Paul
2008-03-01
An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.
Generally covariant quantum mechanics on noncommutative configuration spaces
Kopf, Tomas; Paschke, Mario
2007-11-15
We generalize the previously given algebraic version of 'Feynman's proof of Maxwell's equations' to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such spaces, which, in contrast to most examples discussed in the literature, does not rely on a distinguished set of coordinates. We give a detailed account of several examples, e.g., C{sup {infinity}}(Q)xM{sub n}(C) which leads to non-Abelian Yang-Mills theories, and of noncommutative tori T{sub {theta}}{sup d}. Moreover, we examine models over the Moyal-deformed plane R{sub {theta}}{sup 2}. Assuming the conservation of electrical charges, we show that in this case the canonical uncertainty relation [x{sub k},x{sub l}]=ig{sub kl} with metric g{sub kl} is only consistent if g{sub kl} is constant.
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.
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.
Generalized Limits for Single-Parameter Quantum Estimation
Boixo, Sergio; Flammia, Steven T.; Caves, Carlton M.; Geremia, JM
2007-03-02
We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multisystem interactions. For a Hamiltonian with k-system parameter-sensitive terms, the quantum limit scales as 1/N{sup k}, where N is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter-independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.
Multiple-event probability in general-relativistic quantum mechanics
Hellmann, Frank; Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo
2007-04-15
We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse.
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.
Beyond relativity and quantum mechanics: space physics
NASA Astrophysics Data System (ADS)
Lindner, Henry H.
2011-09-01
Albert Einstein imposed an observer-based epistemology upon physics. Relativity and Quantum Mechanics limit physics to describing and modeling the observer's sensations and measurements. Their "underlying reality" consists only of ideas that serve to model the observer's experience. These positivistic models cannot be used to form physical theories of Cosmic phenomena. To do this, we must again remove the observer from the center of physics. When we relate motion to Cosmic space instead of to observers and we attempt to explain the causes of Cosmic phenomena, we are forced to admit that Cosmic space is a substance. We need a new physics of space. We can begin by replacing Relativity with a modified Lorentzian-Newtonian model of spatial flow, and Quantum Mechanics with a wave-based theory of light and electrons. Space physics will require the reinterpretation of all known phenomena, concepts, and mathematical models.
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.
In Pursuit of General Behavioral Relations.
ERIC Educational Resources Information Center
Mace, F. Charles
1996-01-01
Discusses behavioral momentum and the general behavioral relation between the persistence of behavior and the rate of reinforcement obtained in a given situation. Strategies for establishing the generality of behavioral relations are reviewed, followed by a brief summary of evidence for the generality of behavioral momentum. (Author/CR)
Reciprocal relativity of noninertial frames: quantum mechanics
NASA Astrophysics Data System (ADS)
Low, Stephen G.
2007-04-01
Noninertial transformations on time-position-momentum-energy space {t, q, p, e} with invariant Born-Green metric ds^{2}=-d t^{2}+\\frac{1}{c^{2}}\\,d q^{2}+\\frac{1}{b^{2}} \\big(d p^{2}-\\frac{1}{c^{2}}\\,d e^{2}\\big) and the symplectic metric -de ∧ dt + dp ∧ dq are studied. This {\\cal U}1,3) group of transformations contains the Lorentz group as the inertial special case and, in the limit of small forces and velocities, reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds2 = -dt2. The {\\cal U}( 1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. In the limit of b → ∞, spacetime is invariant. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary representations of its central extension. The same method of projective representations for the inhomogeneous {\\cal U}( 1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous {\\cal U}( 1,3) group is the cover of the quaplectic group {\\cal Q}( 1,3) ={\\cal U}( 1,3) \\otimes _{s}{\\cal H}(4) . {\\cal H}( 4) is the Weyl-Heisenberg group. The {\\cal H}( 4) group, and the associated Heisenberg commutation relations central to quantum mechanics, results directly from requiring projective representations. A set of second-order wave equations result from the representations of the Casimir operators.
Certifying the quantumness of a generalized coherent control scenario
NASA Astrophysics Data System (ADS)
Scholak, Torsten; Brumer, Paul
2014-11-01
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.
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. PMID:25429946
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.
Generalized coherent states under deformed quantum mechanics with maximum momentum
NASA Astrophysics Data System (ADS)
Ching, Chee Leong; Ng, Wei Khim
2013-10-01
Following the Gazeau-Klauder approach, we construct generalized coherent states (GCS) as the quantum simulator to examine the deformed quantum mechanics, which exhibits an intrinsic maximum momentum. We study deformed harmonic oscillators and compute their probability distribution and entropy of states exactly. Also, a particle in an infinite potential box is studied perturbatively. In particular, unlike usual quantum mechanics, the present deformed case increases the entropy of the Planck scale quantum optical system. Furthermore, for simplicity, we obtain the modified uncertainty principle (MUP) with the perturbative treatment up to leading order. MUP turns out to increase generally. However, for certain values of γ (a parameter of GCS), it is possible that the MUP will vanish and hence will exhibit the classical characteristic. This is interpreted as the manifestation of the intrinsic high-momentum cutoff at lower momentum in a perturbative treatment. Although the GCS saturates the minimal uncertainty in a simultaneous measurement of physical position and momentum operators, thus constituting the squeezed states, complete coherency is impossible in quantum gravitational physics. The Mandel Q number is calculated, and it is shown that the statistics can be Poissonian and super-/sub-Poissonian depending on γ. The equation of motion is studied, and both Ehrenfest’s theorem and the correspondence principle are recovered. Fractional revival times are obtained through the autocorrelation, and they indicate that the superposition of a classical-like subwave packet is natural in GCS. We also contrast our results with the string-motivated (Snyder) type of deformed quantum mechanics, which incorporates a minimum position uncertainty rather than a maximum momentum. With the advances of quantum optics technology, it might be possible to realize some of these distinguishing quantum-gravitational features within the domain of future experiments.
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. PMID:12570532
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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 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…
Experimental realization of generalized qubit measurements based on quantum walks
NASA Astrophysics Data System (ADS)
Zhao, Yuan-yuan; Yu, Neng-kun; Kurzyński, Paweł; Xiang, Guo-yong; Li, Chuan-Feng; Guo, Guang-Can
2015-04-01
We report an experimental implementation of a single-qubit generalized measurement scenario, the positive-operator valued measure (POVM), based on a quantum walk model. The qubit is encoded in a single-photon polarization. The photon performs a quantum walk on an array of optical elements, where the polarization-dependent translation is performed via birefringent beam displacers and a change of the polarization is implemented with the help of wave plates. We implement: (i) trine POVM, i.e., the POVM elements uniformly distributed on an equatorial plane of the Bloch sphere; (ii) symmetric-informationally-complete (SIC) POVM; and (iii) unambiguous discrimination of two nonorthogonal qubit 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.
Role of information theoretic uncertainty relations in quantum theory
NASA Astrophysics Data System (ADS)
Jizba, Petr; Dunningham, Jacob A.; Joo, Jaewoo
2015-04-01
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.
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.
A generalization of Fermat's principle for classical and quantum systems
NASA Astrophysics Data System (ADS)
Elsayed, Tarek A.
2014-09-01
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in many-dimensional spaces describing dynamical systems (i.e., the quantum Hilbert space and the classical phase and configuration space). We propose that if the notion of a metric distance is well defined in that space and the velocity of the representative point of the system is an invariant of motion, then a generalized version of Fermat's principle will hold. We substantiate this conjecture for time-independent quantum systems and for a classical system consisting of coupled harmonic oscillators. An exception to this principle is the configuration space of a charged particle in a constant magnetic field; in this case the principle is valid in a frame rotating by half the Larmor frequency, not the stationary lab frame.
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
"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.
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)
Quantum rms error and Heisenberg's error-disturbance relation
NASA Astrophysics Data System (ADS)
Busch, Paul
2014-09-01
Reports on experiments recently performed in Vienna [Erhard et al, Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, a Heisenberg-type tradeoff relation for joint measurements of position and momentum has been formulated and proven in [Phys. Rev. Lett. 111, 160405 (2013)]. Here I show how the apparent conflict is resolved by a careful consideration of the quantum generalization of the notion of root-mean-square error. The claim of a violation of Heisenberg's principle is untenable as it is based on a historically wrong attribution of an incorrect relation to Heisenberg, which is in fact trivially violated. We review a new general trade-off relation for the necessary errors in approximate joint measurements of incompatible qubit observables that is in the spirit of Heisenberg's intuitions. The experiments mentioned may directly be used to test this new error inequality.
Recovering General Relativity from Massive Gravity
Babichev, E.; Deffayet, C.; Ziour, R.
2009-11-13
We obtain static, spherically symmetric, and asymptotically flat numerical solutions of massive gravity with a source. Those solutions show, for the first time explicitly, a recovery of the Schwarzschild solution of general relativity via the so-called Vainshtein mechanism.
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)
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
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.
Generalized Kraus operators and generators of quantum dynamical semigroups
NASA Astrophysics Data System (ADS)
Alazzawi, Sabina; Baumgartner, Bernhard
2015-09-01
Quantum dynamical semigroups play an important role in the description of physical processes such as diffusion, radiative decay or other non-equilibrium events. Taking strongly continuous and trace preserving semigroups into consideration, we show that, under a special criterion, the generator of such a group admits a certain generalized standard form, thereby shedding new light on known approaches in this direction. Furthermore, we illustrate our analysis in concrete examples.
Quantum black hole in the generalized uncertainty principle framework
Bina, A.; Moslehi, A.; Jalalzadeh, S.
2010-01-15
In this paper we study the effects of the generalized uncertainty principle (GUP) on canonical quantum gravity of black holes. Through the use of modified partition function that involves the effects of the GUP, we obtain the thermodynamical properties of the Schwarzschild black hole. We also calculate the Hawking temperature and entropy for the modification of the Schwarzschild black hole in the presence of the GUP.
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.
On the general constraints in single qubit quantum process tomography
NASA Astrophysics Data System (ADS)
Bhandari, Ramesh; Peters, Nicholas A.
2016-05-01
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.
On the general constraints in single qubit quantum process tomography
Bhandari, Ramesh; Peters, Nicholas A.
2016-01-01
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. PMID:27188691
Generalized directed loop method for quantum Monte Carlo simulations.
Alet, Fabien; Wessel, Stefan; Troyer, Matthias
2005-03-01
Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world-line segments. Using linear programming techniques to solve the generalized equations, we look for optimal construction schemes for directed loops. This also allows for an extension of the directed loop scheme to general lattice models, such as high-spin or bosonic models. The resulting algorithms are bounce free in larger regions of parameter space than the original directed loop algorithm. The generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes. In contrast to general expectations, we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables, because of the nonuniqueness of the bounce-free solutions. We therefore propose different general strategies to further minimize autocorrelations, which can be used as supplementary requirements in any directed loop scheme. We show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency; however, we find that the optimal strategy depends not only on the model parameters but also on the observable of interest. PMID:15903632
Comparison of quantum discord and relative entropy in some bipartite quantum systems
NASA Astrophysics Data System (ADS)
Mahdian, M.; Arjmandi, M. B.
2016-04-01
The study of quantum correlations in high-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the quantum state to the closest classical-classical state. In particular, we establish relations between relative entropy and quantum discord quantifiers obtained by means of orthogonal projection measurements. We show that for symmetrical X-states density matrices the quantum discord is equal to relative entropy. At the end of paper, various examples of X-states such as two-qubit and qubit-qutrit have been demonstrated.
General very special relativity is Finsler geometry
Gibbons, G. W.; Gomis, Joaquim; Pope, C. N.
2007-10-15
We ask whether Cohen and Glashow's very special relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved space-time with a cosmological constant. We show that its symmetry group ISIM(2) does admit a 2-parameter family of continuous deformations, but none of these give rise to noncommutative translations analogous to those of the de Sitter deformation of the Poincare group: space-time remains flat. Only a 1-parameter family DISIM{sub b}(2) of deformations of SIM(2) is physically acceptable. Since this could arise through quantum corrections, its implications for tests of Lorentz violations via the Cohen-Glashow proposal should be taken into account. The Lorentz-violating point-particle action invariant under DISIM{sub b}(2) is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive DISIM{sub b}(2)-invariant wave equations for particles of spins 0, (1/2), and 1. The experimental bound, |b|<10{sup -26}, raises the question 'Why is the dimensionless constant b so small in very special relativity?'.
Nonlinear SUSY General Relativity Theory and Significances
NASA Astrophysics Data System (ADS)
Shima, Kazunari; Tsuda, Motomu
2012-02-01
We show some interesting consequences of the nonliear supersymmetric general relativity theory(NLSUSYGR) on particle physics, cosmology and their relations. They may geiv new insights into the SUSY breaking mechanism, dark energy, dark matter and the low enegy superpartner particles which are compatible with the recent LHC data.
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.
Autonomous quantum to classical transitions and the generalized imaging theorem
NASA Astrophysics Data System (ADS)
Briggs, John S.; Feagin, James M.
2016-03-01
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. Here 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. Currently, 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.
Connection between measurement disturbance relation and multipartite quantum correlation
NASA Astrophysics Data System (ADS)
Li, Jun-Li; Du, Kun; Qiao, Cong-Feng
2015-01-01
It is found that the measurement disturbance relation (MDR) determines the strength of quantum correlation and hence is one of the essential facets of the nature of quantum nonlocality. In reverse, the exact form of MDR may be ascertained through measuring the correlation function. To this aim, an optical experimental scheme is proposed. Moreover, by virtue of the correlation function, we find that the quantum entanglement, the quantum nonlocality, and the uncertainty principle can be explicitly correlated.
General Relativity Theory: Recognition through Time
NASA Astrophysics Data System (ADS)
Alexandrov, A. N.; Vavilova, I. B.; Zhdanov, V. I.; Zhuk, A. I.; Kudrya, Yu. N.; Parnovsky, S. L.; Fedorova, E. V.; Yatskiv, Ya. S.
2015-10-01
The book provides an overview of the current state of the General Relativity Theory on the eve of its centennial. The authors describe briefly the basis of this theory, systematize experimental verifications and outline the main areas of its applications in astrophysics, cosmology and astrometry in the light of the last decade. For researchers and students specializing in the Relativity Theory as well as for anyone interested in Relativity Theory, relativistic astrophysics and cosmology.
A Generalized Geometric Measurement of Quantum Discord: Exact Treatment
NASA Astrophysics Data System (ADS)
Cui, Hai-Tao; Tian, Jun-Long; Yang, Gui
2016-02-01
A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin-Meshkov-Glick and Dicke model. Supported by National Natural Science Foundation of China under Grant No. 11005002 and 11475004, New Century Excellent Talent of M.O.E (NCET-11-0937), and Sponsoring Program of Excellent Younger Teachers in universities in Henan Province under Grant No. 2010GGJS-181
A Generalized Geometric Measurement of Quantum Discord: Exact Treatment
NASA Astrophysics Data System (ADS)
Cui, Hai-Tao; Tian, Jun-Long; Yang, Gui
2016-02-01
A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin–Meshkov–Glick and Dicke model. Supported by National Natural Science Foundation of China under Grant No. 11005002 and 11475004, New Century Excellent Talent of M.O.E (NCET-11-0937), and Sponsoring Program of Excellent Younger Teachers in universities in Henan Province under Grant No. 2010GGJS-181
Expanding General Relativity's Space by S-Denying
NASA Astrophysics Data System (ADS)
Rabounski, Dmitri; Smarandache, Florentins; Borissova, Larissa
2016-05-01
Applying the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space - i.e. changing one (or even all) of the conditions to be partially true and partially false. Obtaining five kinds of expanded space-time for General Relativity. Kind I permits the space-time to be in collapse. Kind II permits the space-time to change its own signature. Kind III has peculiarities, linked to the third signature condition. Kind IV permits regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons. Kind V is common for kinds I, II, III, and IV.
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.
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 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. PMID:27091160
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.
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.
Generating perfect fluid spheres in general relativity
NASA Astrophysics Data System (ADS)
Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke
2005-06-01
Ever since Karl Schwarzschild’s 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star—a static spherically symmetric blob of fluid with position-independent density—the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.
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.
Tests of General Relativity with GW150914.
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; 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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 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. PMID:27314708
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.
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.
Tests of General Relativity with GW150914
NASA Astrophysics Data System (ADS)
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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.; 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.
Multiconfigurational quantum propagation with trajectory-guided generalized coherent states
NASA Astrophysics Data System (ADS)
Grigolo, Adriano; Viscondi, Thiago F.; de Aguiar, Marcus A. M.
2016-03-01
A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively.
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
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 collapse rules from the maximum relative entropy principle
NASA Astrophysics Data System (ADS)
Hellmann, Frank; Kamiński, Wojciech; Paweł Kostecki, Ryszard
2016-01-01
We show that the von Neumann-Lüders collapse rules in quantum mechanics always select the unique state that maximises the quantum relative entropy with respect to the premeasurement state, subject to the constraint that the postmeasurement state has to be compatible with the knowledge gained in the measurement. This way we provide an information theoretic characterisation of quantum collapse rules by means of the maximum relative entropy principle.
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.
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.
Geoids in general relativity: geoid quasilocal frames
NASA Astrophysics Data System (ADS)
Oltean, Marius; Epp, Richard J.; McGrath, Paul L.; Mann, Robert B.
2016-05-01
We develop, in the context of general relativity, the notion of a geoid—a surface of constant ‘gravitational potential’. In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general and operationally useful construction called a quasilocal frame—that is, a choice of a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume. We study the geometric properties of these geoid quasilocal frames, and construct solutions for them in some simple spacetimes. We then compare these results—focusing on the computationally tractable scenario of a non-rotating body with a quadrupole perturbation—against their counterparts in Newtonian gravity (the setting for current applications of the geoid), and we compute general-relativistic corrections to some measurable geometric quantities.
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.
Confronting general relativity with further cosmological data
Daniel, Scott F.; Linder, Eric V.
2010-11-15
Deviations from general relativity in order to explain cosmic acceleration generically have both time and scale-dependent signatures in cosmological data. We extend our previous work by investigating model-independent gravitational deviations in bins of redshift and length scale, by incorporating further cosmological probes such as temperature-galaxy and galaxy-galaxy cross-correlations, and by examining correlations between deviations. Markov Chain Monte Carlo likelihood analysis of the model-independent parameters fitting current data indicates that at low redshift general relativity deviates from the best fit at the 99% confidence level. We trace this to two different properties of the CFHTLS weak lensing data set and demonstrate that COSMOS weak lensing data does not show such deviation. Upcoming galaxy survey data will greatly improve the ability to test time and scale-dependent extensions to gravity and we calculate the constraints that the BigBOSS galaxy redshift survey could enable.
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.
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
Quantum dynamics in continuum for proton transport--generalized correlation.
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
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.
Fluctuation relation for quantum heat engines and refrigerators
NASA Astrophysics Data System (ADS)
Campisi, Michele
2014-06-01
At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoirs of temperatures TC ⩽ TH can outperform the ideal Carnot engine:
Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation
NASA Astrophysics Data System (ADS)
Zhang, Ming-Liang; Ka, Being J.; Geva, Eitan
2006-07-01
The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics, and the inhomogeneous term accounts for initial system-bath correlations. In this paper, we propose a new approach for calculating the memory kernel and inhomogeneous term for arbitrary initial state and system-bath coupling. The memory kernel and inhomogeneous term are obtained by numerically solving a single inhomogeneous Volterra equation of the second kind for each. The new approach can accommodate a very wide range of projection operators, and requires projection-free two-time correlation functions as input. An application to the case of a two-state system with diagonal coupling to an arbitrary bath is described in detail. Finally, the utility and self-consistency of the formalism are demonstrated by an explicit calculation on a spin-boson model.
General relativity and cosmic structure formation
NASA Astrophysics Data System (ADS)
Adamek, Julian; Daverio, David; Durrer, Ruth; Kunz, Martin
2016-04-01
Numerical simulations are a versatile tool for providing insight into the complicated process of structure formation in cosmology. This process is mainly governed by gravity, which is the dominant force on large scales. At present, a century after the formulation of general relativity, numerical codes for structure formation still employ Newton’s law of gravitation. This approximation relies on the two assumptions that gravitational fields are weak and that they originate from non-relativistic matter. Whereas the former seems well justified on cosmological scales, the latter imposes restrictions on the nature of the `dark’ components of the Universe (dark matter and dark energy), which are, however, poorly understood. Here we present the first simulations of cosmic structure formation using equations consistently derived from general relativity. We study in detail the small relativistic effects for a standard lambda cold dark matter cosmology that cannot be obtained within a purely Newtonian framework. Our particle-mesh N-body code computes all six degrees of freedom of the metric and consistently solves the geodesic equation for particles, taking into account the relativistic potentials and the frame-dragging force. This conceptually clean approach is very general and can be applied to various settings where the Newtonian approximation fails or becomes inaccurate, ranging from simulations of models with dynamical dark energy or warm/hot dark matter to core collapse supernova explosions.
Testing General Relativity with Atom Interferometry
Dimopoulos, Savas; Graham, Peter W.; Hogan, Jason M.; Kasevich, Mark A.
2007-03-16
The unprecedented precision of atom interferometry will soon lead to laboratory tests of general relativity to levels that will rival or exceed those reached by astrophysical observations. We propose such an experiment that will initially test the equivalence principle to 1 part in 10{sup 15} (300 times better than the current limit), and 1 part in 10{sup 17} in the future. It will also probe general relativistic effects--such as the nonlinear three-graviton coupling, the gravity of an atom's kinetic energy, and the falling of light--to several decimals. In contrast with astrophysical observations, laboratory tests can isolate these effects via their different functional dependence on experimental variables.
Testing general relativity with atom interferometry.
Dimopoulos, Savas; Graham, Peter W; Hogan, Jason M; Kasevich, Mark A
2007-03-16
The unprecedented precision of atom interferometry will soon lead to laboratory tests of general relativity to levels that will rival or exceed those reached by astrophysical observations. We propose such an experiment that will initially test the equivalence principle to 1 part in 10(15) (300 times better than the current limit), and 1 part in 10(17) in the future. It will also probe general relativistic effects - such as the nonlinear three-graviton coupling, the gravity of an atom's kinetic energy, and the falling of light - to several decimals. In contrast with astrophysical observations, laboratory tests can isolate these effects via their different functional dependence on experimental variables. PMID:17501039
Weakly coupled gravity beyond general relativity
NASA Astrophysics Data System (ADS)
Camanho, Xián O.; Edelstein, José D.; Zhiboedov, Alexander
2015-11-01
We explore four-dimensional (4D) weakly coupled gravity beyond general relativity in an on-shell language, focusing on the graviton three-point vertex. This admits a novel structure which can be attributed to a term cubic in the Riemann tensor. We consider a generalization of the Shapiro time delay experiment that involves polarized gravitons and show that the new vertex leads to causality violation. Fixing the problem demands the inclusion of an infinite tower of massive higher spin states. Perturbative string theory provides an example of this phenomenon, the only known so far. Interestingly enough, the same argument being applied to inflation suggests that stringy signatures may be hidden in the non-Gaussianities of the primordial gravity wave spectrum.
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, E.V .; Khmil, S. V.
2006-08-01
Theoretical basis of the General Relativity theory (GR), its experimental tests as well as GR applications were briefly summarized in the new textbook devoted to the World Year of Physics-2005 (authors - Yatskiv Ya.S., Alexandrov A.N., Vavilova I.B., Zhdanov V.I., Kudrya Yu.N., Parnovsky S.L., Fedorova E.V., Khmil S.V., Kyiv:Akademperiodika, 2005, 288 p.). The monograph addresses scientists, post-graduate students, and students specialized in the natural sciences as well as everyone who takes a great interest in GR. Special attention is paid on Relativistic Reference Systems, as an attachment to this book, including attachment to this book where the Resolution of the XXIV IAU General Assembly is given (in Ukrainian).
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).
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.
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.
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. PMID:26066137
Subdiffusive and superdiffusive quantum transport and generalized duality
Sassetti, M.; Schomerus, H.; Weiss, U.
1996-02-01
As a generic model for transport of interacting fermions through a barrier or interstitials in a lattice, quantum Brownian motion in a periodic potential is studied. There is a duality transformation between the continuous coordinate or phase representation and the discrete momentum or charge representation for general frequency-dependent damping. Sub-Ohmic friction is mapped on super-Ohmic friction, and vice versa. The mapping is exact for arbitrary barrier height and valid at any temperature. Thus all features of the continuous model can be investigated from analytical or numerical analysis of the discrete model. Nonperturbative results for the frequency-dependent linear mobility including subdiffusive and superdiffusive behaviors are reported. {copyright} {ital 1996 The American Physical Society.}
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. PMID:26340179
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.
Mesh and measure in early general relativity
NASA Astrophysics Data System (ADS)
Darrigol, Olivier
2015-11-01
In the early days of general relativity, several of Einstein's readers misunderstood the role of coordinates or "mesh-system" in ways that threatened the basic predictions of the theory. This confusion largely derived from intrinsic defects of Einstein's first systematic exposition of his theory. A few of Einstein's followers, including Arthur Eddington, Hermann Weyl, and Max von Laue, identified the interpretive difficulties and solved them by combining a deeply geometrical understanding of the theory with detailed attention to the concrete conditions of measurement.
Epicycles and Poincare resonances in general relativity
Koekoek, G.; Holten, J. W. van
2011-03-15
The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this paper we construct an improved parametrized version of the method, and discuss some subtleties in its application related to secular motions in first as well as in higher-order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.
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.
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.
General Properties of Overlap Operators in Disordered Quantum Spin Systems
NASA Astrophysics Data System (ADS)
Itoi, C.
2016-04-01
We study short-range quantum spin systems with Gaussian disorder. We obtain quantum mechanical extensions of the Ghirlanda-Guerra identities. We discuss properties of overlap spin operators with these identities.
Quantum quenches in the Luttinger model and its close relatives
NASA Astrophysics Data System (ADS)
Cazalilla, M. A.; Chung, Ming-Chiang
2016-06-01
A number of results on quantum quenches in the Luttinger and related models are surveyed with emphasis on post-quench correlations. For the Luttinger model and initial gaussian states, we discuss both sudden and smooth quenches of the interaction and the emergence of a steady state described by a generalized Gibbs ensemble. Comparisons between analytics and numerics, and the question of universality or lack thereof are also discussed. The relevance of the theoretical results to current and future experiments in the fields of ultracold atomic gases and mesoscopic systems of electrons is also briefly touched upon. Wherever possible, our approach is pedagogical and self-contained. This work is dedicated to the memory of our colleague Alejandro Muramatsu.
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
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.
Permutation-symmetry related selection rules in spinor quantum gases
NASA Astrophysics Data System (ADS)
Yurovsky, Vladimir
2014-05-01
Selection rules constraining possible transitions between states of quantum systems can be derived from the system symmetry. Invariance over permutations of indistinguishable particles, contained in each physical system, is one of the basic symmetries. Consider a many-body system with separable spin and spatial degrees of freedom of particles with arbitrary spins s. Eigenfunctions of such systems can be expressed as a sum of products of spin and spatial functions, which form irreducible representations (irreps) of the symmetric group. The quantum numbers are the Young diagrams λ = [λ1 , ... ,λ2 s + 1 ] . The selection rules for a general k-body interactions allow transitions between the states λ and λ' only if ∑m=12s+1 |λm -λm'| <= 2 k . For s = 1 / 2 , the Young diagrams are unambiguously related to the total spin, and if k = 1 , we get the conventional selection rule for dipole transitions. However, if s > 1 / 2 , the rules cannot be expressed in terms of spins. The selection rules provide a way of control over the formation of many-body entangled states, belonging to multidimensional, non-Abelian irreps of the symmetric group. The effects can be observed with spinor atoms in an optical lattice in the Mott-insulator regime.
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.
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.
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.
Spherical shock waves in general relativity
Nutku, Y. )
1991-11-15
We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-{ital N} vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-{ital N} Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the {ital C}{sup 0}-form of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.
General relativity from a thermodynamic perspective
NASA Astrophysics Data System (ADS)
Padmanabhan, T.
2014-03-01
I show that the gravitational dynamics in a bulk region of space can be connected to a thermodynamic description in the boundary of that region, thereby providing clear physical interpretations of several mathematical features of classical general relativity: (1) The Noether charge contained in a bulk region, associated with a specific time evolution vector field, has a direct thermodynamic interpretation as the gravitational heat content of the boundary surface. (2) This result, in turn, shows that all static spacetimes maintain holographic equipartition in the following sense: In these spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk. (3) In a general, evolving spacetime, the rate of change of gravitational momentum is related to the difference between the number of bulk and boundary degrees of freedom. It is this departure from the holographic equipartition which drives the time evolution of the spacetime. (4) When the equations of motion hold, the (naturally defined) total energy of the gravity plus matter within a bulk region, will be equal to the boundary heat content. (5) After motivating the need for an alternate description of gravity (if we have to solve the cosmological constant problem), I describe a thermodynamic variational principle based on null surfaces to achieve this goal. The concept of gravitational heat density of the null surfaces arises naturally from the Noether charge associated with the null congruence. The variational principle, in fact, extremises the total heat content of the matter plus gravity system. Several variations on this theme and implications are described.
NASA Astrophysics Data System (ADS)
Johnson, David T.
Quantum mechanics is an extremely successful and accurate physical theory, yet since its inception, it has been afflicted with numerous conceptual difficulties. The primary subject of this thesis is the theory of entropic quantum dynamics (EQD), which seeks to avoid these conceptual problems by interpreting quantum theory from an informational perspective. We begin by reviewing Cox's work in describing probability theory as a means of rationally and consistently quantifying uncertainties. We then discuss how probabilities can be updated according to either Bayes' theorem or the extended method of maximum entropy (ME). After that discussion, we review the work of Caticha and Giffin that shows that Bayes' theorem is a special case of ME. This important result demonstrates that the ME method is the general method for updating probabilities. We then review some motivating difficulties in quantum mechanics before discussing Caticha's work in deriving quantum theory from the approach of entropic dynamics, which concludes our review. After entropic dynamics is introduced, we develop the concepts of symmetries and transformations from an informational perspective. The primary result is the formulation of a symmetry condition that any transformation must satisfy in order to qualify as a symmetry in EQD. We then proceed to apply this condition to the extended Galilean transformation. This transformation is of interest as it exhibits features of both special and general relativity. The transformation yields a gravitational potential that arises from an equivalence of information. We conclude the thesis with a discussion of the measurement problem in quantum mechanics. We discuss the difficulties that arise in the standard quantum mechanical approach to measurement before developing our theory of entropic measurement. In entropic dynamics, position is the only observable. We show how a theory built on this one observable can account for the multitude of measurements present in
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.
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.
Dispersion Relation of Linear Waves in Quantum Magnetoplasmas
NASA Astrophysics Data System (ADS)
Zhu, Jun
2016-07-01
The quantum magnetohydrodynamic (QMHD) model is applied in investigating the propagation of linear waves in quantum magnetoplasmas. Using the QMHD model, the dispersion equation for quantum magnetoplasmas and the dispersion relations of linear waves are deduced. Results show that quantum effects affect the propagation of electron plasma waves and extraordinary waves (X waves). When we select the plasma parameters of the laser-based plasma compression (LBPC) schemes for calculation, the quantum correction cannot be neglected. Meanwhile, the corrections produced by the Fermi degeneracy pressure and Bohm potential are compared under different plasma parameter conditions. supported by National Natural Science Foundation of China (No. 11447125) and the Research Training Program for Undergraduates of Shanxi University of China (Nos. 2014012167, 2015013182)
Quantum mechanics, gravity and modified quantization relations.
Calmet, Xavier
2015-08-01
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. PMID:26124253
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.
NASA Astrophysics Data System (ADS)
Qiu, Liang; Tang, Gang; Yang, Xian-qing; Wang, An-min
2014-02-01
In order to define quantum correlations, there are two important paradigms in quantum information theory, viz. the information-theoretic and the entanglement-separability ones. In this paper, we give an analytical relation between two measures of quantum correlations. One of them is related to the monogamy of squared bipartite quantum discord, which is a information-theoretic multipartite quantum correlation measure, while the other is the generalized geometric measure which lies in the entanglement-separability paradigm. We find a certain cone-like region on the two-dimensional spaces spanned by the two measures. Moreover, we have investigated the quantum phase transition with the two measures in the anisotropic spin XXZ model by exploiting the quantum renormalization group method.
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)
The quantum Ising chain with a generalized defect
NASA Astrophysics Data System (ADS)
Grimm, Uwe
1990-08-01
The finite-size scaling properties of the quantum Ising chain with different types of generalized defects are studied. This not only means an alteration of the coupling constant as previously examined, but also an additional arbitrary transformation in the algebra of observables at one site of the chain. One can distinguish between two classes of generalized defects: on the one hand those which do not affect the finite-size integrability of the Ising chain, and on the other hand those that destroy this property. In this context, finite-size integrability is always understood as a synonym for the possibility to write the hamiltonian of the finite chain as a bilinear expression in fermionic operators by means of a Jordan-Wigner transformation. Concerning the first type of defect, an exact solution for the scaling spectrum is obtained for the most universal defect that preserves the global Z2 symmetry of the chain. It is shown that in the continuum limit this yields the same result as for one properly chosen ordinary defect, that is changing the coupling constant only, and thus the finite-size scaling spectra can be described by irreps of a shifted u(1) Kac-Moody algebra. The other type of defect is examined by means of numerical finite-size calculations. In contrast to the first case, these calculations suggest a non-continuous dependence of the scaling dimensions on the defect parameters. A conjecture for the operator content involving only one primary field of a Virasoro algebra with central charge c= {1}/{2} is given.
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.
Generalized Spearman estimators of relative dose.
Morton, R
1981-06-01
In a biological assay the expected response may be transformed to a variable bounded between 0 and 1. If the transformed response is regarded as analogous to the tolerance distribution function, the mean of that distribution may be estimated for the standard and test preparations, and a simple estimator of the relative potency obtained. The special case where the identity transformation is used for a quantal response corresponds to Spearman's estimator, and our generalization has similar unbiasedness properties to that estimator. Asymptotic results are derived when the intervals between dose levels decrease and the sample of each dose level simultaneously increases. These results are evaluated for the case with equal sample sizes at regularly spaced values of the dose metameter. An approximate test for similarity is proposed. If the tolerance distribution is known up to a scale parameter, then the transformation may be chosen so that the estimator is asymptotically fully efficient. An application to the thermal disinfestation of wheat is given. PMID:7272411
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.
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.
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo Mauro
2010-05-01
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.
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…
Energy-Time Uncertainty Relations in Quantum Measurements
NASA Astrophysics Data System (ADS)
Miyadera, Takayuki
2016-06-01
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 hbar /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.
Becerra, F E; Fan, J; Migdall, A
2013-01-01
Generalized quantum measurements implemented to allow for measurement outcomes termed inconclusive can perform perfect discrimination of non-orthogonal states, a task which is impossible using only measurements with definitive outcomes. Here we demonstrate such generalized quantum measurements for unambiguous discrimination of four non-orthogonal coherent states and obtain their quantum mechanical description, the positive-operator valued measure. For practical realizations of this positive-operator valued measure, where noise and realistic imperfections prevent perfect unambiguous discrimination, we show that our experimental implementation outperforms any ideal standard-quantum-limited measurement performing the same non-ideal unambiguous state discrimination task for coherent states with low mean photon numbers. PMID:23774177
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.
GENERAL: Efficient quantum secure communication with a publicly known key
NASA Astrophysics Data System (ADS)
Li, Chun-Yan; Li, Xi-Han; Deng, Fu-Guo; Zhou, Hong-Yu
2008-07-01
This paper presents a simple way for an eavesdropper to eavesdrop freely the secret message in the experimental realization of quantum communication protocol proposed by Beige et al (2002 Acta Phys. Pol. A 101 357). Moreover, it introduces an efficient quantum secure communication protocol based on a publicly known key with decoy photons and two biased bases by modifying the original protocol. The total efficiency of this new protocol is double that of the original one. With a low noise quantum channel, this protocol can be used for transmitting a secret message. At present, this protocol is good for generating a private key efficiently.
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
2016-03-01
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.
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.
General Relativity, Scalar Fields and Cosmic Strings.
NASA Astrophysics Data System (ADS)
Burd, Adrian Benedict
1987-09-01
Available from UMI in association with The British Library. This thesis is divided into three, essentially self-contained, parts. In the first part we examine the structure of classical three-dimensional space-times. Here, we review and extend what is known about the gravitational theories in these models. We investigate the non-existence of a Newtonian limit to the relativistic theories showing that in the presence of certain matter terms, Newtonian gravity can be obtained as a suitable weak-field limit. We present a number of new, exact static and non-static solutions to the equations of three-dimensional general relativity with scalar field and perfect fluid sources. We comment on the relationship between the stiff perfect fluid and the scalar field. Motivated by the Kaluza-Klein procedure of dimensional reduction we find some exact scalar field solutions which have analogues in four-dimensions. We also present classification schemes based on the group of motions of homogeneous space-times and on the Cotton -York tensor. The description of the general cosmological solution in the vicinity of the singularity is given in terms of the number of arbitrary spatial functions independently specified on a space-like hypersurface. We also study a series approximation to the space-time in the vicinity of the cosmological singularity. Some conjectures are made concerning the space-time singularities. We present two exact cosmological solutions containing self-interacting scalar fields. The models exhibit an inflationary behaviour. We also present an anisotropic cosmological model. The second part of the thesis contains a study of certain cosmological models which have self-interacting scalar fields obeying an exponential potential. We use the techniques of phase portrait analysis to study the N-dimensional cosmological models as well as certain anisotropic models. The latter involves the analysis of a three-dimensional system of equations and we review the relevant theory
Generalized reduction criterion for separability of quantum states
NASA Astrophysics Data System (ADS)
Albeverio, Sergio; Chen, Kai; Fei, Shao-Ming
2003-12-01
A necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L. A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The separability criterion naturally generalizes the reduction separability criterion introduced independently in the previous work [M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999) and N. J. Cerf, C. Adami, and R. M. Gingrich, Phys. Rev. A 60, 898 (1999)]. In special cases, it recovers the previous reduction criterion and the recent generalized partial transposition criterion [K. Chen and L. A. Wu, Phys. Lett. A 306, 14 (2002)]. The criterion involves only simple matrix manipulations and can therefore be easily applied.
Ascertaining the uncertainty relations via quantum correlations
NASA Astrophysics Data System (ADS)
Li, Jun-Li; Du, Kun; Qiao, Cong-Feng
2014-02-01
We propose a new scheme to express the uncertainty principle in the form of inequality of the bipartite correlation functions for a given multipartite state, which provides an experimentally feasible and model-independent way to verify various uncertainty and measurement disturbance relations. By virtue of this scheme, the implementation of experimental measurement on the measurement disturbance relation to a variety of physical systems becomes practical. The inequality in turn, also imposes a constraint on the strength of correlation, i.e. it determines the maximum value of the correlation function for two-body system and a monogamy relation of the bipartite correlation functions for multipartite system.
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.
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.
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)
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)
Heilmann, R.; Keil, R.; Gräfe, M.; Nolte, S.; Szameit, A.
2014-08-01
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.
Direct measurement of general quantum states using strong measurement
NASA Astrophysics Data System (ADS)
Zou, Ping; Zhang, Zhi-Ming; Song, Wei
2015-05-01
The direct state measurement (DSM) based on the weak measurement has the advantage of simplicity, versatility, and directness. However, the weak measurement will introduce an unavoidable error in the reconstructed quantum state. We modify the DSM by replacing the weak coupling between the system and the pointer by a strong one, and present two procedures for measuring quantum states, one of which can give the wave function or the density matrix directly. We can also measure the Dirac distribution of a discrete system directly. Furthermore, we propose quantum circuits for realizing these procedures, and the main body of the circuits consists of Toffoli gates. By numerical simulation, we find that our scheme can eliminate the biased error effectively.
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.
Information, fidelity, and reversibility in general quantum measurements
NASA Astrophysics Data System (ADS)
Terashima, Hiroaki
2016-02-01
We present the amount of information, fidelity, and reversibility obtained by arbitrary quantum measurements on completely unknown states. These quantities are expressed as functions of the singular values of a measurement operator corresponding to the obtained outcome. As an example, we consider a class of quantum measurements with highly degenerate singular values to discuss trade-offs among information, fidelity, and reversibility. The trade-offs are at the level of a single outcome, in the sense that the quantities pertain to each single outcome rather than the average over all possible outcomes.
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
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 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. PMID:26565222
Generalized guidance equation for peaked quantum solitons and effective gravity
NASA Astrophysics Data System (ADS)
Durt, Thomas
2016-04-01
Bouncing oil droplets have been shown to follow de Broglie-Bohm–like trajectories and at the same time they exhibit attractive and repulsive pseudo-gravitation. We propose a model aimed at rendering account of these phenomenological observations. It inspires, in a more speculative approach, a toy model for quantum gravity.
Decoherence in generalized measurement and the quantum Zeno paradox
NASA Astrophysics Data System (ADS)
Mack, Gerhard; Wallentowitz, Sascha; Toschek, Peter E.
2014-07-01
In the development of quantum mechanics, the evolution of a quantum system was a controversial item. The duality of unitary evolution and state reduction as proposed by John von Neumann was widely felt unsatisfactory. Among the various attempts to reconcile the two incompatible modes of dynamics, the model of decoherence has turned out rather convincing. While the debate has been going on mainly by reasoning the consequences of gedanken experiments, the technical progress has made available techniques of addressing real experiments, even on an individual quantum object. In particular, the impeded evolution of an atom under continuous or reiterated measurement, predicted long ago, has been proven. The procedure of such an experiment-as with many a more conventional one-includes sequences of alternating time intervals of preparation and detection, known as “pump-probe”, or “drive-probe” measurements. We discuss this procedure in the context of the decoherence model. The emergence of pointer states of the meter is outlined. We show compatibility of this approach with photon counting, and emphasize the importance of information transfer in the course of measurement. Qualitative conditions having been considered so far necessary and sufficient criteria for meeting the “quantum Zeno paradox” are being quantified.
On the quantum discord of general X states
NASA Astrophysics Data System (ADS)
Yurischev, M. A.
2015-09-01
Quantum discord Q is a function of density matrix elements. The domain of such a function in the case of two-qubit system with X density matrix may consist of three subdomains at most: two ones where the quantum discord is expressed in closed analytical forms ( and ) and an intermediate subdomain for which, to extract the quantum discord , it is required to solve numerically a one-dimensional minimization problem to find the optimal measurement angle . Hence, the quantum discord is given by a piecewise analytical-numerical formula . It is shown that the boundaries between the subdomains consist of bifurcation points. The subdomains are discovered in the dynamical phase flip channel model, in the anisotropic spin systems at thermal equilibrium, and in the heteronuclear dimers in an external magnetic field. We found that the transitions between subdomain and and ones occur suddenly, but continuously and smoothly, i.e., nonanalyticity is hidden and can be observed in higher order derivatives of discord function.
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.
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.
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. PMID:24237497
Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
NASA Astrophysics Data System (ADS)
Stottmeister, Alexander; Thiemann, Thomas
2016-06-01
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).
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
Generalized Lifshitz-Kosevich scaling at quantum criticality from the holographic correspondence
Hartnoll, Sean A.; Hofman, Diego M.
2010-04-15
We characterize quantum oscillations in the magnetic susceptibility of a quantum critical non-Fermi liquid. The computation is performed in a strongly interacting regime using the nonperturbative holographic correspondence. The temperature dependence of the amplitude of the oscillations is shown to depend on a critical exponent nu. For general nu the temperature scaling is distinct from the textbook Lifshitz-Kosevich formula. At the ''marginal'' value nu=(1/2), the Lifshitz-Kosevich formula is recovered despite strong interactions. As a by-product of our analysis we present a formalism for computing the amplitude of quantum oscillations for general fermionic theories very efficiently.
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.
The tau lepton in general relativity
Nienart, L.
1988-01-01
This dissertation presents the results of an investigation into trying to see how the mass of the tau lepton can arise from general Relativistic considerations. The formalism was applied earlier to electrons and predicted both the electron's mass and the muon's mass. The tau leptons mass will be found by considering the contribution of a non-zero magnetic moment to the quaternion fields and the spin affine connection fields in a Riemannian space. The exact mass operator is constructed from these fields, and is then approximated in 3 different ways in order to permit calculation. The expectation value of these approximations to the mass operator is then found, using the relativistic Coulomb wavefunctions. The choice of Coulomb states is due to the consideration that the pairs that comprise the vacuum in this field theory couple to the magnetic moment of the core electron in a manner resembling that of the electrons in the Hydrogen atom. As the coupling the author is considering in his model is that of magnetic dipole by design, an argument is presented in which the Coulombic coupling strength parameters of the Coulomb states are scaled in order to provide a suitable description of the magnetic states which the author is actually interested in. The resulting values for the mass of the tau lepton are then within half an order of magnitude of the experimental values.
Action principle combining electromagnetism and general relativity
Moyer, H.G.
1987-03-01
The stationary action problem for a single, classical, point particle in external gravitational and electromagnetic fields is written in optimal control format. The relativistic interval is the independent variable and time, space, and action are the five dependent variables. A general metric is used for the space-time manifold so that the equations are manifestly covariant. The form of the system equations guarantees that the particle moves with unit speed with respect to interval. The Lagrangian is a function of the metric tensor and the electromagnetic four-potential, but not of particle parameters such as electric charge q and mass m. The Hamiltonian is not identically zero, unlike those derived in many earlier analyses. A constant of the motion is found that is identified with q/mc/sup 2/. An explanation is presented for the classical inequality mgreater than or equal to0. The trajectories can reduce to geodesics and even further to those governed by Fermat's principle of stationary time.
Towards absorbing outer boundaries in general relativity
NASA Astrophysics Data System (ADS)
Buchman, Luisa T.; Sarbach, Olivier C. A.
2006-12-01
We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations on a subset of flat spacetime of the form [0, T] × BR, where BR is a ball of radius R, and analyse different kinds of boundary conditions on ∂BR. Our main results are as follows. (i) We give an explicit analytic example showing that boundary conditions obtained from freezing the incoming characteristic fields to their initial values are not compatible with the constraints. (ii) With the help of the exact solutions constructed, we determine the amount of artificial reflection of gravitational radiation from constraint-preserving boundary conditions which freeze the Weyl scalar Ψ0 to its initial value. For monochromatic radiation with wave number k and arbitrary angular momentum number ell >= 2, the amount of reflection decays as (kR)-4 for large kR. (iii) For each L >= 2, we construct new local constraint-preserving boundary conditions which perfectly absorb linearized radiation with ell <= L. (iv) We generalize our analysis to a weakly curved background of mass M and compute first-order corrections in M/R to the reflection coefficients for quadrupolar odd-parity radiation. For our new boundary condition with L = 2, the reflection coefficient is smaller than that for the freezing Ψ0 boundary condition by a factor of M/R for kR > 1.04. Implications of these results for numerical simulations of binary black holes on finite domains are discussed.
A semiclassical generalized quantum master equation for an arbitrary system-bath coupling
NASA Astrophysics Data System (ADS)
Shi, Qiang; Geva, Eitan
2004-06-01
The Nakajima-Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC-GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard-Jones atoms.
Relativeness in quantum gravity: limitations and frame dependence of semiclassical descriptions
NASA Astrophysics Data System (ADS)
Nomura, Yasunori; Sanches, Fabio; Weinberg, Sean J.
2015-04-01
Consistency between quantum mechanical and general relativistic views of the world is a longstanding problem, which becomes particularly prominent in black hole physics. We develop a coherent picture addressing this issue by studying the quantum mechanics of an evolving black hole. After interpreting the Bekenstein-Hawking entropy as the entropy representing the degrees of freedom that are coarse-grained to obtain a semiclassical description from the microscopic theory of quantum gravity, we discuss the properties these degrees of freedom exhibit when viewed from the semiclassical standpoint. We are led to the conclusion that they show features which we call extreme relativeness and spacetime-matter duality — a nontrivial reference frame dependence of their spacetime distribution and the dual roles they play as the "constituents" of spacetime and as thermal radiation. We describe black hole formation and evaporation processes in distant and infalling reference frames, showing that these two properties allow us to avoid the arguments for firewalls and to make the existence of the black hole interior consistent with unitary evolution in the sense of complementarity. Our analysis provides a concrete answer to how information can be preserved at the quantum level throughout the evolution of a black hole, and gives a basic picture of how general coordinate transformations may work at the level of full quantum gravity beyond the approximation of semiclassical theory.
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.
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. PMID:23242738
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
Quantum correlations and distinguishability of quantum states
Spehner, Dominique
2014-07-15
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: Decoy State Quantum Key Distribution with Odd Coherent State
NASA Astrophysics Data System (ADS)
Sun, Shi-Hai; Gao, Ming; Dai, Hong-Yi; Chen, Ping-Xing; Li, Cheng-Zu
2008-07-01
We propose a decoy state quantum key distribution scheme with odd coherent state which follows sub-Poissonian distributed photon count and has low probability of the multi-photon event and vacuum event in each pulse. The numerical calculations show that our scheme can improve efficiently the key generation rate and secure communication distance. Furthermore, only one decoy state is necessary to approach to the perfect asymptotic limit with infinite decoy states in our scheme, but at least two decoy states are needed in other scheme.
Walach, H
2003-08-01
Homeopathy is scientifically banned, both for lack of consistent empirical findings, but more so for lack of a sound theoretical model to explain its purported effects. This paper makes an attempt to introduce an explanatory idea based on a generalized version of quantum mechanics (QM), the weak quantum theory (WQT). WQT uses the algebraic formalism of QM proper, but drops some restrictions and definitions typical for QM. This results in a general axiomatic framework similar to QM, but more generalized and applicable to all possible systems. Most notably, WQT predicts entanglement, which in QM is known as Einstein-Podolsky-Rosen (EPR) correlatedness within quantum systems. According to WQT, this entanglement is not only tied to quantum systems, but is to be expected whenever a global and a local variable describing a system are complementary. This idea is used here to reconstruct homeopathy as an exemplification of generalized entanglement as predicted by WQT. It transpires that homeopathy uses two instances of generalized entanglement: one between the remedy and the original substance (potentiation principle) and one between the individual symptoms of a patient and the general symptoms of a remedy picture (similarity principle). By bringing these two elements together, double entanglement ensues, which is reminiscent of cryptographic and teleportation applications of entanglement in QM proper. Homeopathy could be a macroscopic analogue to quantum teleportation. This model is exemplified and some predictions are derived, which make it possible to test the model. PMID:12972724
Continuous-variable dense coding via a general Gaussian state: Monogamy relation
NASA Astrophysics Data System (ADS)
Lee, Jaehak; Ji, Se-Wan; Park, Jiyong; Nha, Hyunchul
2014-08-01
We study a continuous-variable dense coding protocol, originally proposed to employ a two-mode squeezed state, using a general two-mode Gaussian state as a quantum channel. We particularly obtain conditions to manifest quantum advantage by beating two well-known single-mode schemes, namely, the squeezed-state scheme (best Gaussian scheme) and the number-state scheme (optimal scheme achieving the Holevo bound). We then extend our study to a multipartite Gaussian state and investigate the monogamy of operational entanglement measured by the communication capacity under the dense coding protocol. We show that this operational entanglement represents a strict monogamy relation, by means of Heisenberg's uncertainty principle among different parties; i.e., the quantum advantage for communication can be possible for only one pair of two-mode systems among many parties.
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
NASA Astrophysics Data System (ADS)
Sun, Guo-Hua; Dong, Shi-Hai
2015-06-01
Based on a Hamiltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchard-like (non-diagonal case) and Kramers' (diagonal case) recurrence relations for arbitrary xκ which is independent of the central potential V(x). Some significant results in diagonal case are obtained for special κ in xκ (κ ≥ 2). In particular, we find the orthogonal relation
The Quantum Superalgebra ospq(1|2)} and a q-Generalization of the Bannai-Ito Polynomials
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
2016-05-01
The Racah problem for the quantum superalgebra ospq(1|2)} is considered. The intermediate Casimir operators are shown to realize a q-deformation of the Bannai-Ito algebra. The Racah coefficients of osp_q(1|2)} are calculated explicitly in terms of basic orthogonal polynomials that q-generalize the Bannai-Ito polynomials. The relation between these q-deformed Bannai-Ito polynomials and the q-Racah/Askey-Wilson polynomials is discussed.
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.
On a quantum algebraic approach to a generalized phase space
NASA Astrophysics Data System (ADS)
Bohm, D.; Hiley, B. J.
1981-04-01
We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms of a matrix algebra in a phase space. This makes clear not only the similarities of the two theories, but also certain essential differences, and lays a foundation for understanding their relationship. We use the Wigner-Moyal transformation as a change of representation in phase space, and we avoid the problem of “negative probabilities” by regarding the solutions of our equations as constants of the motion, rather than as statistical weight factors. We show a close relationship of our work to that of Prigogine and his group. We bring in a new nonnegative probability function, and we propose extensions of the theory to cover thermodynamic processes involving entropy changes, as well as the usual reversible processes.
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.
Outline of a Generalization and a Reinterpretation of Quantum Mechanics Recovering Objectivity
NASA Astrophysics Data System (ADS)
Garola, Claudio; Sozzo, Sandro; Wu, Junde
2016-05-01
The ESR model has been recently proposed in several papers to offer a possible solution to the problems raising from the nonobjectivity of physical properties in quantum mechanics (QM) (mainly the objectification problem of the quantum theory of measurement). This solution is obtained by embodying the mathematical formalism of QM into a broader mathematical framework and reinterpreting quantum probabilities as conditional on detection rather than absolute. We provide a new and more general formulation of the ESR model and discuss time evolution according to it, pointing out in particular that both linear and nonlinear evolution may occur, depending on the physical environment.
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.
Quantum Anomalies for Generalized Euclidean Taub-Newman Metrics
NASA Astrophysics Data System (ADS)
Visinescu, Mihai; Visinescu, Anca
2008-09-01
We investigate the gravitational and axial anomalies with regard to quadratic constants of motion for the Euclidean Taub-Newman-Unti-Tamburino (Taub-NUT) space and its generalizations as was done by Iwai and Katayama. The generalized Taub-NUT metrics exhibit in general gravitational anomalies. This is in contrast with the fact that the standard Taub-NUT metric does not exhibit gravitational anomalies, which is a consequence of the fact that it admits Killing-Yano tensors forming Stäckel-Killing tensors as products. For the axial anomaly, interpreted as the index of the Dirac operator, the role of Killing-Yano tensors is irrelevant. We compute the index of the Dirac operator for the generalized Taub-NUT metrics with the APS boundary conditions and find these metrics do not contribute to the axial anomaly for not too large deformations of the standard Taub-NUT metric.
Inhomogeneous transport and derivative relations in the quantum Hall regime
NASA Astrophysics Data System (ADS)
Simon, Steven H.
1998-12-01
Several derivative relations have been observed in the quantum Hall regime including a relation between elements of the macroscopic resistivity tensor Rxx= αB(d Rxy/d B), a relation between elements of the macroscopic thermopower tensor Syx= αB(d Sxx/d B), as well as a similar relation observed in acoustoelectric experiments (here B is the magnetic field and α is a constant). It has been proposed in a number of recent works by the author and collaborators that these relations can be explained with a model of classical transport in an inhomogeneous medium. We review these works and briefly discuss to what extent the models which predict these derivative relations are appropriate for describing the experimental systems.
Minimax Quantum Tomography: Estimators and Relative Entropy Bounds
NASA Astrophysics Data System (ADS)
Ferrie, Christopher; Blume-Kohout, Robin
2016-03-01
A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O (1 /√{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. 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.
Minimax Quantum Tomography: Estimators and Relative Entropy Bounds.
Ferrie, Christopher; Blume-Kohout, Robin
2016-03-01
A minimax estimator has the minimum possible error ("risk") in the worst case. 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. 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. PMID:26991163
Quantum diffusion with drift and the Einstein relation. II
De Roeck, Wojciech; Fröhlich, Jürg; Schnelli, Kevin
2014-07-15
This paper is a companion to Paper I [W. De Roeck, J. Fröhlich, and K. Schnelli, “Quantum diffusion with drift and the Einstein relation. I,” J. Math. Phys. 55, 075206 (2014)]. The purpose of this paper is to describe and prove a certain number of technical results used in Paper I, but not proven there. Both papers concern long-time properties (diffusion, drift) of the motion of a driven quantum particle coupled to an array of thermal reservoirs. The main technical results derived in the present paper are: (1) an asymptotic perturbation theory applicable for small driving force, and (2) the construction of time-dependent correlation functions of particle observables.
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 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.
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.
Generalized Kac lemma for recurrence time in iterated open quantum systems
NASA Astrophysics Data System (ADS)
Sinkovicz, P.; Kiss, T.; Asbóth, J. K.
2016-05-01
We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special case of unital channels, including unitary channels. We prove that for a more general class of quantum channels the expected return time can be given as the inverse of the weight of the initial state in the steady state. This statement is a generalization of the Kac lemma for classical Markov chains.
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 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.
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.
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.
Zhang, Jun; Zhang, Yang; Yu, Chang-shui
2015-01-01
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. PMID:26118488
Zhang, Jun; Zhang, Yang; Yu, Chang-shui
2015-01-01
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. PMID:26118488
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".
A general framework for the Quantum Zeno and anti-Zeno effects
NASA Astrophysics Data System (ADS)
Chaudhry, Adam Zaman
2016-07-01
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.
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
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
Teaching Relativity and Quantum Mechanics to Non-Science Majors
NASA Astrophysics Data System (ADS)
Galloway, Heather
2009-10-01
A course titled ``Relativity and Quantum Mechanics'' was offered to a group of honors students from a variety of majors. The curriculum will be described and compared to other class outlines for this type of course. This class included a laboratory component which is not often included in a non-majors course. The response of students from different disciplines gives insight into other ways the course could be improved. While some outcomes of the course were expected, such as the use of history to engage students, other successes and failures of the course were more surprising.
Trade-off relation between information and disturbance in quantum measurement
NASA Astrophysics Data System (ADS)
Shitara, Tomohiro; Kuramochi, Yui; Ueda, Masahito
2016-03-01
We formulate a trade-off relation between information and disturbance in quantum measurement from an estimation-theoretic point of view. The information and disturbance are characterized in terms of the classical Fisher information and the average loss of the quantum Fisher information, respectively. We identify the necessary condition for various divergences between two quantum states to satisfy similar relations.
Emergent General Relativity and Local Translation Symmetry in Tensor Model
NASA Astrophysics Data System (ADS)
Sasakura, Naoki
2009-12-01
The tensor model is discussed as theory of dynamical fuzzy spaces and as a way to formulate gravity on fuzzy spaces. From numerical analyses, it is shown that the low-lying long-wavelength fluctuation spectra around Gaussian background solutions in the tensor model are in agreement with the geometric fluctuations on flat spaces in the general relativity. It is also shown that part of the orthogonal symmetry of the tensor model spontaneously broken by the backgrounds correspond to the local translation symmetry of the general relativity. Thus the tensor model can provide an interesting model of simultaneous emergence of space and the general relativity including the local translation symmetry.
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.
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
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
Experimental verification of reciprocity relations in quantum thermoelectric transport
NASA Astrophysics Data System (ADS)
Matthews, J.; Battista, F.; Sánchez, D.; Samuelsson, P.; Linke, H.
2014-10-01
Fundamental symmetries in thermoelectric quantum transport, beyond Onsagers relations, were predicted two decades ago but have to date not been observed in experiments. Recent works have predicted the symmetries to be sensitive to energy-dependent, inelastic scattering, raising the question whether they exist in practice. Here, we answer this question affirmatively by experimentally verifying the thermoelectric reciprocity relations in a four-terminal mesoscopic device where each terminal can be electrically and thermally biased individually. The linear-response thermoelectric coefficients are found to be symmetric under simultaneous reversal of magnetic field and exchange of injection and emission contacts. We also demonstrate a controllable breakdown of the reciprocity relations by increasing thermal bias, putting in prospect enhanced thermoelectric performance.
Relation of quantum control mechanism to landscape structure
NASA Astrophysics Data System (ADS)
Nanduri, Arun; Donovan, Ashley; Ho, Tak-San; Rabitz, Herschel
2014-07-01
The control of quantum dynamics is generally accomplished by seeking a tailored electromagnetic field to meet a posed objective. A particular shaped field can be thought of as specifying a point on a quantum control landscape, which is the objective as a functional of the controls. Optimizing the pulse shape corresponds to climbing the landscape, and previous work showed that the paths taken up the landscapes, guided by a gradient algorithm, are surprisingly straight when projected into the space of control fields. The direct nature of these control trajectories can be quantified by the metric R ≥1, defined as the ratio of the length of the control trajectory to the Euclidean distance between its end points. The prior observation of often finding low values of R implies that the landscapes are structurally simple. In this work, we investigate whether there is a relationship between the intricacy of the control mechanism and the complexity of the trajectory taken through the control space reflected in the value of R. We use the Hamiltonian encoding procedure to identify the mechanism, and we examine control of the state-to-state transition probability. No significant correlation is found between the landscape structure, reflected in the value of R, and the control mechanism. This result has algorithmic implications, opening up the prospect of seeking fields producing particular mechanisms at little penalty in the search effort due to encountering complex landscape structure.
From massive gravity to modified general relativity II
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
2011-05-01
We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy-momentum tensor. On the classical level this leads to a further modification of general relativity.
2. GENERAL VIEW SHOWING RELATION OF BRIDGE TO THE TOPOGRAPHY ...
2. GENERAL VIEW SHOWING RELATION OF BRIDGE TO THE TOPOGRAPHY OF THE APPROACH ROAD. - Speicher Bridge, Church Road over Tulpehocken Creek between Penn & North Heidelberg Townships, Bernville, Berks County, PA
Galileons as the scalar analogue of general relativity
NASA Astrophysics Data System (ADS)
Klein, Remko; Ozkan, Mehmet; Roest, Diederik
2016-02-01
We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial alternative to gauge theories (including general relativity). Moreover, it is shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations, similar to the Lovelock gravity theories. Possible extensions are discussed.
A Recurrence Relation Approach to Higher Order Quantum Superintegrability
NASA Astrophysics Data System (ADS)
Kalnins, Ernie G.; Kress, Jonathan M.; Miller, Willard
2011-03-01
We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method provides rigorous proofs of superintegrability and explicit constructions of higher order generators for the symmetry algebra. We apply the method to 5 families of systems, each depending on a parameter k, including most notably the caged anisotropic oscillator, the Tremblay, Turbiner and Winternitz system and a deformed Kepler-Coulomb system, and we give proofs of quantum superintegrability for all rational values of k, new for 4 of these systems. In addition, we show that the explicit information supplied by the special function recurrence relations allows us to prove, for the first time in 4 cases, that the symmetry algebra generated by our lowest order symmetries closes and to determine the associated structure equations of the algebras for each k. We have no proof that our generating symmetries are of lowest possible order, but we have no counterexamples, and we are confident we can can always find any missing generators from our raising and lowering operator recurrences. We also get for free, one variable models of the action of the symmetry algebra in terms of difference operators. We describe how the Stäckel transform acts and show that it preserves the structure equations.
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)
Gerd, Niestegge
2010-12-01
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.
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)
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.
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2016-02-01
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.
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.
Introduction to General Relativity and John Archibald Wheeler
NASA Astrophysics Data System (ADS)
Ciufolini, Ignazio; Matzner, Richard
John Archibald Wheeler was born on July 9, 1911, in Jacksonville, Florida, and passed away on April 13, 2008, in Hightstown, New Jersey; his influence on gravitational physics and science in general will remain forever. Among his many and important contributions to physics, he was one of the fathers of the renaissance of General Relativity. After a golden starting age of General Relativity, a few years after the Einstein's papers of 1915-1916, Einstein's gravitational theory was for many years, to quote the preface of a 1960 book of General Relativity [1], confined to "an ivory tower…and no doubt many a relativist looks forward to the day when the governments will seek his opinion on important questions".
NASA Astrophysics Data System (ADS)
Castro, Carlos
2014-08-01
An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.
NASA Astrophysics Data System (ADS)
Castro, Carlos
2014-09-01
An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.
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.
A Quantum-Like View to a Generalized Two Players Game
NASA Astrophysics Data System (ADS)
Bagarello, F.
2015-10-01
This paper consider the possibility of using some quantum tools in decision making strategies. In particular, we consider here a dynamical open quantum system helping two players, and , to take their decisions in a specific context. We see that, within our approach, the final choices of the players do not depend in general on their initial mental states, but they are driven essentially by the environment which interacts with them. The model proposed here also considers interactions of different nature between the two players, and it is simple enough to allow for an analytical solution of the equations of motion.
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.
The general class of the vacuum spherically symmetric equations of the general relativity theory
Karbanovski, V. V. Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N. Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-08-15
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.
Clarifying possible misconceptions in the foundations of general relativity
NASA Astrophysics Data System (ADS)
Brown, Harvey R.; Read, James
2016-05-01
We discuss what we take to be three possible misconceptions in the foundations of general relativity, relating to: (a) the interpretation of the weak equivalence principle and the relationship between gravity and inertia; (b) the connection between gravitational redshift results and spacetime curvature; and (c) the Einstein equivalence principle and the ability to "transform away" gravity in local inertial coordinate systems.
Position-momentum uncertainty relations in the presence of quantum memory
NASA Astrophysics Data System (ADS)
Furrer, Fabian; Berta, Mario; Tomamichel, Marco; Scholz, Volkher B.; Christandl, Matthias
2014-12-01
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.
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.
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.
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.
Lipparini, Filippo; Scalmani, Giovanni; Lagardère, Louis; Stamm, Benjamin; Cancès, Eric; Maday, Yvon; Piquemal, Jean-Philip; Frisch, Michael J; 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. PMID:25399133
NASA Astrophysics Data System (ADS)
Banchi, Leonardo
2013-11-01
Ballistic quantum information transfer through spin chains is based on the idea of making the spin dynamics ruled by collective excitations with linear dispersion relation. Unlike perfect state transfer schemes, a ballistic transmission requires only a minimal engineering of the interactions; in fact, for most practical purposes, the optimization of the couplings to the ends of the chain is sufficient to obtain an almost perfect transmission. In this work we review different ballistic quantum state transfer protocols based on the dynamics of quasi-free spin chains, and further generalize them both at zero and finite temperature. In particular, besides presenting novel analytical results for XX, XY, and Ising spin models, it is shown how, via a complete control on the first and last two qubits of the chain, destructive thermal effects can be cancelled, leading to a high-quality state transmission irrespective of the temperature.
NASA Astrophysics Data System (ADS)
Zhang, Sheng; Wang, Jian; Tang, Chao-Jing
2012-06-01
Counterfactual quantum cryptography, recently proposed by Noh, is featured with no transmission of signal particles. This exhibits evident security advantages, such as its immunity to the well-known photon-number-splitting attack. In this paper, the theoretical security of counterfactual quantum cryptography protocol against the general intercept-resend attacks is proved by bounding the information of an eavesdropper Eve more tightly than in Yin's proposal [Phys. Rev. A 82 042335 (2010)]. It is also shown that practical counterfactual quantum cryptography implementations may be vulnerable when equipped with imperfect apparatuses, by proving that a negative key rate can be achieved when Eve launches a time-shift attack based on imperfect detector efficiency.
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)
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.
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
NASA Astrophysics Data System (ADS)
Yeh, L.
1993-06-01
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 are 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.
Quantum Harmonic Brownian Motion in a General Environment: a Modified Phase-Space Approach.
NASA Astrophysics Data System (ADS)
Yeh, Leehwa
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, I propose 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 are 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. With the help of this theorem, the mechanism of this model is examined and the
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.
Simulations of accretion disks in pseudo-complex General Relativity
NASA Astrophysics Data System (ADS)
Hess, P. O.; Algalán B., M.; Schönenbach, T.; Greiner, W.
2015-11-01
After a summary on pseudo-complex General Relativity (pc-GR), circular orbits and stable orbits in general are discussed, including predictions compared to observations. Using a modified version of a model for accretions disks, presented by Page and Thorne in 1974, we apply the raytracing technique in order to simulate the appearance of an accretion disk as it should be observed in a detector. In pc-GR we predict a dark ring near a very massive, rapidly rotating object.
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.
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.
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.
Theory and Experiment in the Quantum-Relativity Revolution (Pais History of Physics Prize 2009)
NASA Astrophysics Data System (ADS)
Brush, Stephen
2010-02-01
Does new scientific knowledge come from theory (whose predictions are confirmed by experiment) or from experiment (whose results are explained by theory)? Either can happen, depending on whether theory is ahead of experiment or experiment is ahead of theory at a particular time. In the first case, new theoretical hypotheses are made and their predictions are tested by experiments. But even when the predictions are successful, we can't be sure that some other hypothesis might not have produced the same prediction. In the second case, as in a detective story, there are already enough facts, but several theories have failed to explain them. When a new hypothesis plausibly explains all of the facts, it may be quickly accepted before any further experiments are done. In the quantum- relativity revolution there are examples of both situations. Because of the two-stage development of both relativity (``special,'' then ``general'') and quantum theory (``old,'' then ``quantum mechanics'') in the period 1905-1930, we can make a double comparison of acceptance by prediction and by explanation. A curious anti-symmetry is revealed and discussed. )
General Monogamy Relation for the Entanglement of Formation in Multiqubit Systems
NASA Astrophysics Data System (ADS)
Bai, Yan-Kui; Xu, Yuan-Fei; Wang, Z. D.
2014-09-01
We prove exactly that the squared entanglement of formation, which quantifies the bipartite entanglement, obeys a general monogamy inequality in an arbitrary multiqubit mixed state. Based on this kind of exotic monogamy relation, we are able to construct two sets of useful entanglement indicators: the first one can detect all genuine multiqubit entangled states even in the case of the two-qubit concurrence and n-tangles being zero, while the second one can be calculated via quantum discord and applied to multipartite entanglement dynamics. Moreover, we give a computable and nontrivial lower bound for multiqubit entanglement of formation.
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
On the mass-coupling relation of multi-scale quantum integrable models
NASA Astrophysics Data System (ADS)
Bajnok, Zoltán; Balog, János; Ito, Katsushi; Satoh, Yuji; Tóth, Gábor Zsolt
2016-06-01
We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of the perturbation of a projected product of minimal models. This representation enables us to identify conserved tensor currents on the UV side. These UV operators are then mapped via form factor perturbation theory to operators on the IR side, which are characterized by their form factors. The relation between the UV and IR operators is given in terms of the sought-for mass-coupling relation. By generalizing the Θ sum rule Ward identity we are able to derive differential equations for the mass-coupling relation, which we solve in terms of hypergeometric functions. We check these results against the data obtained by numerically solving the thermodynamic Bethe Ansatz equations, and find a complete agreement.
Doppler frequency in interplanetary radar and general relativity
NASA Technical Reports Server (NTRS)
Mcvittie, G. C.
1972-01-01
The change of frequency of an interplanetary radar signal sent from the earth to another planet or to a space probe is worked out according to general relativity. The Schwarzschild spacetime is employed and its null geodesics control the motion of the signals. Exact Doppler frequency formulas are derived for one-way and two-way radar in terms of an arbitrary Schwarzschild radial coordinate. A reduction to the special relativity case is used to interpret the formulas in terms of the relative radial velocity of emitter and target. The general relativity corrections are worked out approximately for each of three possible Schwarzschild radial coordinates, and a numerical example is given. The amount of the correction is different according as one or the other of the Schwarzschild coordinates is identified with the radius vector deduced from classical celestial mechanics. The identification problem is discussed.
A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
Qi, Xiao-Liang; Wu, Yong-Shi; Zhang, Shou-Cheng; /Stanford U., Phys. Dept. /Tsinghua U., Beijing
2010-01-15
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern number, even if it is defined for a non-conserved quantity such as spin in the case of the spin Hall effect, one can always infer the existence of gapless edge states under certain twisted boundary conditions that allow tunneling between edges. This relation is robust against disorder and interactions, and it provides a unified topological classification of both the quantum (charge) Hall effect and the quantum spin Hall effect. In addition, it reconciles the apparent conflict between the stability of bulk topological order and the instability of gapless edge states in systems with open boundaries (as known happening in the spin Hall case). The consequences of time reversal invariance for bulk topological order and edge state dynamics are further studied in the present framework.
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
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.
Constraint algebra of general relativity from a formal continuum limit of canonical tensor model
NASA Astrophysics Data System (ADS)
Sasakura, Naoki; Sato, Yuki
2015-10-01
Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.
Non-inertial Frames in Special and General Relativity
NASA Astrophysics Data System (ADS)
Lusanna, Luca
A theory of global non-inertial frames in special relativity is developed by taking into account relativistic metrology and by avoiding the coordinate singularities of the rotating disk and of Fermi coordinates. Then this theory is used in general relativity for the treatment of globally hyperbolic, asymptotically Minkowskian space-times solution of Einstein's equations. Also some comments on the problem of dark matter, connecting it to the relativistic metrology used in astrophysics, are made.
Testing the Foundations of the Foundations of General Relativity
NASA Astrophysics Data System (ADS)
Lämmerzahl, Claus
2010-07-01
General Relativity is based on the Einstein Equivalence Principle consisting of the Universality of Free Fall, the Universality of the Gravitational Redshift and Local Lorentz Invariance. Stating these principles already employs some further underlying assumptions. These assumptions are related to the famous Newton's axioms. Accordingly, the existence of inertial systems, the form of the equation of motion and of the law of reciprocal action will be discussed in this article. Conditions are given which allow to test these underlying assumptions.
Unimodular metagravity vs. general relativity with a scalar field
Pirogov, Yu. F.
2010-01-15
The unimodular metagravity, with the graviscalar as a dark matter, is compared with General Relativity (GR) in the presence of a scalar field. The effect of the graviscalar on the static spherically symmetric metric is studied. An exact limit solution representing a new cosmic object, the (harmonic) graviscalar black hole, is given. The relation with the black hole in the environment of a scalar field in GR is discussed.
The Complexity of Relating Quantum Channels to Master Equations
NASA Astrophysics Data System (ADS)
Cubitt, Toby S.; Eisert, Jens; Wolf, Michael M.
2012-03-01
Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski, Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find its form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P = NP: any efficiently computable criterion for Markovianity would imply P = NP; whereas a proof that P = NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory.
The generalized partial transposition criterion for separability of multipartite quantum states
NASA Astrophysics Data System (ADS)
Chen, Kai; Wu, Ling-An
2002-12-01
We present a generalized partial transposition separability criterion for the density matrix of a multipartite quantum system. This criterion comprises as special cases the famous Peres-Horodecki criterion and the recent realignment criterion in [O. Rudolph, quant-ph/0202121] and [K. Chen, L.A. Wu, quant-ph/0205017]. It involves only straightforward matrix manipulations and is easy to apply. A quantitative measure of entanglement based on this criterion is also obtained.
Generalized entropies and logarithms and their duality relations
Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray
2012-01-01
For statistical systems that violate one of the four Shannon–Khinchin axioms, entropy takes a more general form than the Boltzmann–Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with these generalized entropies, making them useful for understanding distribution functions of non-Markovian or nonergodic complex systems. For such systems where the composability axiom is violated there exist only two ways to implement the maximum entropy principle, one using escort probabilities, the other not. The two ways are connected through a duality. Here we show that this duality fixes a unique escort probability, which allows us to derive a complete theory of the generalized logarithms that naturally arise from the violation of this axiom. We then show how the functional forms of these generalized logarithms are related to the asymptotic scaling behavior of the entropy. PMID:23129618
Related General-Vocabulary Knowledge Transfers to Learning Technical Terms
ERIC Educational Resources Information Center
Balch, William R.
2015-01-01
In a classroom experiment during the first week of an introductory psychology course, randomly assigned students received a pretest and then a brief training on the definitions of general-vocabulary words either related (e.g., "facilitation") or unrelated (e.g., "rendition") to 16 technical terms (e.g., "social…
Generalization of Moll Ross relations for heterojunction bipolar transistors
NASA Astrophysics Data System (ADS)
Mohammad, S. Noor
2002-04-01
Moll-Ross relations for the current flow through the base region of a bipolar transistor, and for the base transit time, have been generalized for heterojunction bipolar transistors with a nonuniform energy bandgap in the base region. The effect of both heavy doping and carrier degeneracy has been taken into account.
Factors Affecting the Relative Efficiency of General Acid Catalysis
ERIC Educational Resources Information Center
Kwan, Eugene E.
2005-01-01
A simple framework for evaluating experimental kinetic data to provide support for Specific Acid Catalysis (SAC) and General Acid Catalysis (GAC) is described based on the factors affecting their relative efficiency. Observations reveal that increasing the SAC-to-GAC rate constant ratio reduces the effective pH range for GAC.
Spinning fluids in general relativity. II - Self-consistent formulation
NASA Technical Reports Server (NTRS)
Ray, John R.; Smalley, Larry, L.; Krisch, Jean P.
1987-01-01
Methods used earlier to derive the equations of motion for a spinning fluid in the Einstein-Cartan theory are specialized to the case of general relativity. The main idea is to include the spin as a thermodynamic variable in the theory.
Probing Students' Understanding of Some Conceptual Themes in General Relativity
ERIC Educational Resources Information Center
Bandyopadhyay, Atanu; Kumar, Arvind
2010-01-01
This work is an attempt to see how physics undergraduates view the basic ideas of general relativity when they are exposed to the topic in a standard introductory course. Since the subject is conceptually and technically difficult, we adopted a "case studies" approach, focusing in depth on about six students who had just finished a one semester…
Stationarity of extremum entropy fluid bodies in general relativity
NASA Astrophysics Data System (ADS)
Schiffrin, Joshua Seth
We consider perfect fluid bodies ("stars'') in general relativity that are axisymmetric, asymptotically flat, and that admit a maximal hypersurface. We show that configurations that extremize the total entropy at fixed ADM mass, ADM angular momentum, and total particle number are stationary with circular flow. For such stars, this establishes that thermodynamic equilibrium implies dynamic equilibrium.
Stationarity of extremum entropy fluid bodies in general relativity
NASA Astrophysics Data System (ADS)
Schiffrin, Joshua S.
2015-09-01
We consider perfect fluid bodies (‘stars’) in general relativity that are axisymmetric, asymptotically flat, and that admit a maximal hypersurface. We show that configurations that extremize the total entropy at fixed ADM mass, ADM angular momentum, and total particle number are stationary with circular flow. For such stars, this establishes that thermodynamic equilibrium implies dynamic equilibrium.
Chern-Simons modified general relativity: Conserved charges
Tekin, Bayram
2008-01-15
We construct the conserved charges (mass and angular momentum) of the Chern-Simons modified general relativity in asymptotically flat and anti-de Sitter (AdS) spacetimes. Our definition is based on background Killing symmetries and reduces to the known expressions in the proper limits.
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
General immunity and superadditivity of two-way Gaussian quantum cryptography
NASA Astrophysics Data System (ADS)
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
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.
Application of generalized operator representation in the time evolution of quantum systems
NASA Astrophysics Data System (ADS)
He, Rui; Liu, Xiangyuan; Song, Jun
2016-07-01
We have systematically explored the application of generalized operator representation including P-, W-, and Husimi representation in the time evolution of quantum systems. In particular, by using the method of differentiation within an ordered product of operators, we give the normally and antinormally ordered forms of the integral kernels of Husimi operator representations and its corresponding formulations. By making use of the generalized operator representation, we transform exponentially complex operator equations into tractable phase-space equations. As a simple application, the time evolution equation of Husimi function in the amplitude dissipative channel is clearly obtained.
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.
2015-01-01
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
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. PMID:26651662
A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Fujisaki, Hiroshi
2012-05-01
We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the "centroid IRC," corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. This approach is applied to NH3 molecule and N2H_5^- ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH3, the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N2H_5^-, the centroid IRC is largely deviated from the "classical" IRC, and the free energy barrier is reduced by the quantum effects even more drastically.
A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates
Shiga, Motoyuki; Fujisaki, Hiroshi
2012-05-14
We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the ''centroid IRC,'' corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. This approach is applied to NH{sub 3} molecule and N{sub 2}H{sub 5}{sup -} ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH{sub 3}, the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N{sub 2}H{sub 5}{sup -}, the centroid IRC is largely deviated from the ''classical'' IRC, and the free energy barrier is reduced by the quantum effects even more drastically.
An interesting consequence of the general principle of relativity
NASA Astrophysics Data System (ADS)
Grøn, Øyvind; Jemterud, Torkild
2016-04-01
We show that Einstein's general theory of relativity, together with the assumption that the principle of relativity encompasses rotational motion, predicts that in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe model with dust and Lorentz Invariant Vacuum Energy (LIVE), the density parameter of vacuum energy must have the value Ω_{Λ 0}=0.737. The physical mechanism connecting the relativity of rotational motion with the energy density of dark energy is the inertial dragging effect. The predicted value is necessary in order to have perfect inertial dragging, which is required for rotational motion to be relative. If one accepts that due to the impossibility of defining motion for a single particle in an otherwise empty universe, the universe must be constructed so that all types of motion are relative, then this solves the so-called cosmological constant problem.
Consistency of certain constitutive relations with quantum electromagnetism
Horsley, S. A. R.
2011-12-15
Recent work by Philbin [New J. Phys. 12, 123008 (2010)] has provided a Lagrangian theory that establishes a general method for the canonical quantization of the electromagnetic field in any dispersive, lossy, linear dielectric. Working from this theory, we extend the Lagrangian description to reciprocal and nonreciprocal magnetoelectric (bianisotropic) media, showing that some versions of the constitutive relations are inconsistent with a real Lagrangian, and hence with quantization. This amounts to a restriction on the magnitude of the magnetoelectric coupling. Moreover, from the point of view of quantization, moving media are shown to be fundamentally different from stationary magnetoelectrics, despite the formal similarity in the constitutive relations.
Towards the quasi-localization of canonical general relativity
NASA Astrophysics Data System (ADS)
Szabados, László B.
2009-06-01
A general framework for a systematic quasi-localization of canonical general relativity and a new ingredient, the requirement of the gauge invariance of the boundary terms appearing in the calculation of Poisson brackets, are given. As a consequence of this it is shown, in particular, that the generator vector fields (built from the lapse and shift) of the quasi-local quantities must be divergence free with respect to a Sen-type connection, and the volume form induced from the spatial metric on the boundary surface must be fixed. Talk given at the Conference on Recent Results in Mathematical Relativity, The Erwin Schrödinger Institute, Vienna, 20-21 August 2008, and dedicated to Bobby Beig on the occasion of his 60th birthday.
Testing General Relativity with the Shadow Size of Sgr A(*).
Johannsen, Tim; Broderick, Avery E; Plewa, Philipp M; Chatzopoulos, Sotiris; Doeleman, Sheperd S; Eisenhauer, Frank; Fish, Vincent L; Genzel, Reinhard; Gerhard, Ortwin; Johnson, Michael D
2016-01-22
In general relativity, the angular radius of the shadow of a black hole is primarily determined by its mass-to-distance ratio and depends only weakly on its spin and inclination. If general relativity is violated, however, the shadow size may also depend strongly on parametric deviations from the Kerr metric. Based on a reconstructed image of Sagittarius A^{*} (Sgr A^{*}) from a simulated one-day observing run of a seven-station Event Horizon Telescope (EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that such an observation can measure the angular radius of the shadow of Sgr A^{*} with an uncertainty of ∼1.5 μas (6%). We show that existing mass and distance measurements can be improved significantly when combined with upcoming EHT measurements of the shadow size and that tight constraints on potential deviations from the Kerr metric can be obtained. PMID:26849580
Testing General Relativity with the Shadow Size of Sgr A*
NASA Astrophysics Data System (ADS)
Johannsen, Tim; Broderick, Avery E.; Plewa, Philipp M.; Chatzopoulos, Sotiris; Doeleman, Sheperd S.; Eisenhauer, Frank; Fish, Vincent L.; Genzel, Reinhard; Gerhard, Ortwin; Johnson, Michael D.
2016-01-01
In general relativity, the angular radius of the shadow of a black hole is primarily determined by its mass-to-distance ratio and depends only weakly on its spin and inclination. If general relativity is violated, however, the shadow size may also depend strongly on parametric deviations from the Kerr metric. Based on a reconstructed image of Sagittarius A* (Sgr A* ) from a simulated one-day observing run of a seven-station Event Horizon Telescope (EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that such an observation can measure the angular radius of the shadow of Sgr A* with an uncertainty of ˜1.5 μ as (6%). We show that existing mass and distance measurements can be improved significantly when combined with upcoming EHT measurements of the shadow size and that tight constraints on potential deviations from the Kerr metric can be obtained.
Some Links Between General Relativity and Other Parts of Physics
NASA Astrophysics Data System (ADS)
Gibbons, Gary W.
Now that General Relativity has become such a central part of modern physics, its geometrical formalism being taught as part of almost all undergraduate physics courses, it is natural to ask: how can its basic concepts and techniques be used to illuminate areas of physics which have no connection with gravity? Another way of asking this question is: are the analogues situations to those occurring in General Relativity? The search for such analogues is of course an old one, but recently, because of advances in technology, these questions have become more topical. In this talk I will illustrate this theme by examples drawn from optics, acoustics, liquid crystals, graphene and the currently popular topic of cloaking.
A century of general relativity: astrophysics and cosmology.
Blandford, R D
2015-03-01
One hundred years after its birth, general relativity has become a highly successful physical theory in the sense that it has passed a large number of experimental and observational tests and finds extensive application to a wide variety of cosmic phenomena. It remains an active area of research as new tests are on the way, epitomized by the exciting prospect of detecting gravitational waves from merging black holes. General relativity is the essential foundation of the standard model of cosmology and underlies our description of the black holes and neutron stars that are ultimately responsible for the most powerful and dramatic cosmic sources. Its interface with physics on the smallest and largest scales will continue to provide fertile areas of investigation in its next century. PMID:25745165
General Theory of Relativity: Will It Survive the Next Decade?
NASA Technical Reports Server (NTRS)
Bertolami, Orfeu; Paramos, Jorge; Turyshev, Slava G.
2006-01-01
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety years to describe gravitational phenomena on these various scales. We review the foundations of general relativity, discuss the recent progress in the tests of relativistic gravity, and present motivations for high-accuracy gravitational experiments in space. We also summarize the science objectives and technology needs for the laboratory experiments in space with laboratory being the entire solar system. We discuss the advances in our understanding of fundamental physics anticipated in the near future and evaluate discovery potential for the recently proposed gravitational experiments.
A century of general relativity: Astrophysics and cosmology
NASA Astrophysics Data System (ADS)
Blandford, R. D.
2015-03-01
One hundred years after its birth, general relativity has become a highly successful physical theory in the sense that it has passed a large number of experimental and observational tests and finds extensive application to a wide variety of cosmic phenomena. It remains an active area of research as new tests are on the way, epitomized by the exciting prospect of detecting gravitational waves from merging black holes. General relativity is the essential foundation of the standard model of cosmology and underlies our description of the black holes and neutron stars that are ultimately responsible for the most powerful and dramatic cosmic sources. Its interface with physics on the smallest and largest scales will continue to provide fertile areas of investigation in its next century.
NASA Astrophysics Data System (ADS)
Shi, Qiang; Geva, Eitan
2003-12-01
The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics. The standard approach is based on using a perturbative treatment of the system-bath coupling for calculating this kernel, and is therefore restricted to systems weakly coupled to the bath. In this paper, we propose a new approach for calculating the memory kernel for an arbitrary system-bath coupling. The memory kernel is obtained by solving a set of two coupled integral equations that relate it to a new type of two-time system-dependent bath correlation functions. The feasibility of the method is demonstrated in the case of an asymetrical two-level system linearly coupled to a harmonic bath.
Sensor failure detection using generalized parity relations for flexible structures
NASA Technical Reports Server (NTRS)
Mercadal, Mathieu
1989-01-01
Analytical redundancy may be preferable to hardware redundancy in failure detection/isolation tasks for such large-scale systems as space structures. Generalized single-sensor parity relations are presently applied to this problem; they are noted to yield a very simple isolation logic, and their generation is found to be extremely rapid, even in the case of extremely complex systems, provided only that the eigenstructure of the system be known. Their implementation is, however, extremely sensitive to modeling errors and noise.
GENERAL RELATIVITY DERIVATION OF BEAM REST-FRAME HAMILTONIAN.
WEI,J.
2001-06-18
Analysis of particle interaction in the laboratory frame of storage rings is often complicated by the fact that particle motion is relativistic, and that reference particle trajectory is curved. Rest frame of the reference particle is a convenient coordinate system to work with, within which particle motion is non-relativistic. We have derived the equations of motion in the beam rest frame from the general relativity formalism, and have successfully applied them to the analysis of crystalline beams [1].
Exploring the transition from special to general relativity
NASA Astrophysics Data System (ADS)
Semon, Mark D.; Malin, Shimon; Wortel, Stephanie
2009-05-01
In a previous paper we discussed two examples of circular motion which are especially useful in relativity courses because they lead to predictions verified by experiments with macroscopic objects. We analyzed these examples by considering motion around an N-gon and then taking the limit as N →∞ and the N-gon becomes a circle. In this paper we use the same approach to illustrate how generalizing special relativity to a theory that includes non-inertial frames can lead to a non-Euclidean geometry. We also derive two properties of clocks at rest in a reference frame traveling on a circular path.
The effects of general relativity on near-earth satellites
NASA Technical Reports Server (NTRS)
Ries, J. C.; Watkins, M. M.; Tapley, B. D.; Huang, C.
1990-01-01
Whether one uses a solar system barycentric frame or a geocentric frame when including the general theory of relativity in orbit determination for near-earth satellites, the results should be equivalent to some limiting accuracy. The purpose of this paper is to clarify the effects of relativity in each frame and to demonstrate their equivalence through the analysis of three years of laser tracking data taken on the Lageos satellite. It is demonstrated that the simpler formulation in the geocentric frame is adequate for the purpose of near-earth satellite orbit determination. A correction to the conventional barycentric equations of motion is shown to be required.
Sagnac interferometry as a probe to the commutation relation of a macroscopic quantum mirror
Yang Ran; Gong Xuefei; Pei Shouyong; Luo Ziren; Lau, Y. K.
2010-09-15
Single photon Sagnac interferometry as a probe to macroscopic quantum mechanics is considered at the theoretical level. For a freely moving macroscopic quantum mirror susceptible to radiation pressure force inside a Sagnac interferometer, a careful analysis of the input-output relation reveals that the particle spectrum readout at the bright and dark ports encode information concerning the noncommutativity of position and momentum of the macroscopic mirror. A feasible experimental scheme to probe the commutation relation of a macroscopic quantum mirror is outlined to explore the possible frontier between classical and quantum regimes. In the Appendix, the case of Michelson interferometry as a feasible probe is also sketched.
Language Generativity, Response Generalization, and Derived Relational Responding
Stewart, Ian; McElwee, John; Ming, Siri
2013-01-01
Language generativity can be described as the ability to produce sentences never before said, and to understand sentences never before heard. One process often cited as underlying language generativity is response generalization. However, though the latter seems to promise a technical understanding of the former at a process level, an investigation of definitions and approaches to the term “response generalization” that appear in the literature suggests that it does not do so. We argue that a more promising candidate for the role of key process underlying language generativity is derived relational responding. We introduce the latter concept and describe empirical research showing its connection with language. We subsequently present a relational frame theory (RFT) conceptualization of derived relations as contextually controlled generalized relational responding. We then review a series of recent studies on derived manding in developmentally delayed children and adults that arguably demonstrate the applied utility of a derived relations-based approach with respect to the phenomenon of generative language. PMID:23814374
Tests of general relativity from timing the double pulsar.
Kramer, M; Stairs, I H; Manchester, R N; McLaughlin, M A; Lyne, A G; Ferdman, R D; Burgay, M; Lorimer, D R; Possenti, A; D'Amico, N; Sarkissian, J M; Hobbs, G B; Reynolds, J E; Freire, P C C; Camilo, F
2006-10-01
The double pulsar system PSR J0737-3039A/B is unique in that both neutron stars are detectable as radio pulsars. They are also known to have much higher mean orbital velocities and accelerations than those of other binary pulsars. The system is therefore a good candidate for testing Einstein's theory of general relativity and alternative theories of gravity in the strong-field regime. We report on precision timing observations taken over the 2.5 years since its discovery and present four independent strong-field tests of general relativity. These tests use the theory-independent mass ratio of the two stars. By measuring relativistic corrections to the Keplerian description of the orbital motion, we find that the "post-Keplerian" parameter s agrees with the value predicted by general relativity within an uncertainty of 0.05%, the most precise test yet obtained. We also show that the transverse velocity of the system's center of mass is extremely small. Combined with the system's location near the Sun, this result suggests that future tests of gravitational theories with the double pulsar will supersede the best current solar system tests. It also implies that the second-born pulsar may not have formed through the core collapse of a helium star, as is usually assumed. PMID:16973838
Explanatory and illustrative visualization of special and general relativity.
Weiskopf, Daniel; Borchers, Marc; Ertl, Thomas; Falk, Martin; Fechtig, Oliver; Frank, Regine; Grave, Frank; King, Andreas; Kraus, Ute; Müller, Thomas; Nollert, Hans-Peter; Rica Mendez, Isabel; Ruder, Hanns; Schafhitzel, Tobias; Schär, Sonja; Zahn, Corvin; Zatloukal, Michael
2006-01-01
This paper describes methods for explanatory and illustrative visualizations used to communicate aspects of Einstein's theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. Our illustrations target a general audience of laypersons interested in relativity. We discuss visualization strategies, motivated by physics education and the didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Our primary approach is to adopt an egocentric point of view: The recipients of a visualization participate in a visually enriched thought experiment that allows them to experience or explore a relativistic scenario. In addition, we often combine egocentric visualizations with more abstract illustrations based on an outside view in order to provide several presentations of the same phenomenon. Although our visualization tools often build upon existing methods and implementations, the underlying techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, special relativistic 4D ray tracing for accelerating scene objects, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators. PMID:16805261
Gravitation experiments at Stanford. [using general relativity theory
NASA Technical Reports Server (NTRS)
Lipa, J. A.
1980-01-01
The experimental situation in post-Newtonian gravitation is briefly reviewed in order to reexamine the extent to which experiment supports or refutes general relativity. A description is given of the equivalence principle project, the gyroscope experiment, and the search for gravity waves. It is noted that even though some doubt has been cast on the value of the perihelion advance and the gravitational redshift as precise tests of general relativity in the past few years, many competing theories have been ruled out; in particular, the results from the Viking mission significantly reduce the credibility of the Brans-Dicke theory (Brans and Dicke, 1961). The dimensionless constant omega in this theory is now forced to exceed 50, while the value originally proposed was 6 (omega being infinity in general relativity). It is noted that the gyro experiment described is capable of putting much tighter limits on this parameter, and together with the other experiments in progress will help place gravitational theory on a firmer experimental footing.
Constraints on a new post-general relativity cosmological parameter
NASA Astrophysics Data System (ADS)
Caldwell, Robert; Cooray, Asantha; Melchiorri, Alessandro
2007-07-01
A new cosmological variable is introduced to characterize the degree of departure from Einstein’s general relativity with a cosmological constant. The new parameter, ϖ, is the cosmological analog of γ, the parametrized post-Newtonian variable which measures the amount of spacetime curvature per unit mass. In the cosmological context, ϖ measures the difference between the Newtonian and longitudinal potentials in response to the same matter sources, as occurs in certain scalar-tensor theories of gravity. Equivalently, ϖ measures the scalar shear fluctuation in a dark-energy component. In the context of a vanilla, cosmological constant-dominated universe, a nonzero ϖ signals a departure from general relativity or a fluctuating cosmological constant. Using a phenomenological model for the time evolution ϖ=ϖ0ρDE/ρM which depends on the ratio of energy density in the cosmological constant to the matter density at each epoch, it is shown that the observed cosmic microwave background temperature anisotropies limit the overall normalization constant to be -0.4<ϖ0<0.1 at the 95% confidence level. Existing measurements of the cross-correlations of the cosmic microwave background with large-scale structure further limit ϖ0>-0.2 at the 95% CL. In the future, integrated Sachs-Wolfe and weak lensing measurements can more tightly constrain ϖ0, providing a valuable clue to the nature of dark energy and the validity of general relativity.
Flaws in Black Hole Theory and General Relativity
NASA Astrophysics Data System (ADS)
Crothers, Stephen J.
2014-03-01
Alleged black hole models pertain to a universe that is spatially infinite, is eternal, contains only one mass, is not expanding, and is asymptotically flat or asymptotically not flat. But the alleged big bang cosmology pertains to a universe that is spatially finite (one case) or spatially infinite (two different cases), is of finite age, contains radiation and many masses including multiple black holes (some of which are primordial), is expanding, and is not asymptotically anything. Thus the black hole and the big bang contradict one another - they are mutually exclusive. It is surprisingly easy to prove that neither General Relativity nor Newton's theory predicts the black hole. Despite numerous claims for discovery of black holes in their millions, nobody has ever actually found one. It is also not difficult to prove that General Relativity violates the usual conservation of energy and momentum. Fundamentally there are contradictions contained in black hole theory, big bang cosmology, and General Relativity. Numerical methods are therefore to no avail.
Generalized microcanonical and Gibbs ensembles in classical and quantum integrable dynamics
NASA Astrophysics Data System (ADS)
Yuzbashyan, Emil A.
2016-04-01
We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it to the limit of infinite number of degrees of freedom. In quantum mechanics, we prove GGE for maximal Hamiltonians-a class of models stemming from a rigorous notion of quantum integrability understood as the existence of conserved charges with prescribed dependence on a system parameter, e.g. Hubbard U, anisotropy in the XXZ model etc. In analogy with classical integrability, the defining property of these models is that they have the maximum number of independent integrals. We contrast their dynamics induced by quenching the parameter to that of random matrix Hamiltonians.
Housing Electrons: Relating Quantum Numbers, Energy Levels, and Electron Configurations.
ERIC Educational Resources Information Center
Garofalo, Anthony
1997-01-01
Presents an activity that combines the concepts of quantum numbers and probability locations, energy levels, and electron configurations in a concrete, hands-on way. Uses model houses constructed out of foam board and colored beads to represent electrons. (JRH)
Yu, Xuezhi; Wen, Kai; Wang, Zhanhui; Zhang, Xiya; Li, Chenglong; Zhang, Suxia; Shen, Jianzhong
2016-04-01
Here, we describe a general bioluminescence resonance energy transfer (BRET) homogeneous immunoassay based on quantum dots (QDs) as the acceptor and Renilla luciferase (Rluc) as the donor (QD-BRET) for the determination of small molecules. The ratio of the donor-acceptor that could produce energy transfer varied in the presence of different concentrations of free enrofloxacin (ENR), an important small molecule in food safety. The calculated Förster distance (R0) was 7.86 nm. Under optimized conditions, the half-maximal inhibitory concentration (IC50) for ENR was less than 1 ng/mL and the linear range covered 4 orders of magnitude (0.023 to 25.60 ng/mL). The cross-reactivities (CRs) of seven representative fluoroquinolones (FQs) were similar to the data obtained by an enzyme-linked immunosorbent assay (ELISA). The average intra- and interassay recoveries from spiked milk of were 79.8-118.0%, and the relative standard deviations (RSDs) were less than 10%, meeting the requirement of residue detection, which was a satisfactory result. Furthermore, we compared the influence of different luciferase substrates on the performance of the assay. Considering sensitivity and stability, coelenterazine-h was the most appropriate substrate. The results from this study will enable better-informed decisions on the choice of Rluc substrate for QD-BRET systems. For the future, the QD-BRET immunosensor could easily be extended to other small molecules and thus represents a versatile strategy in food safety, the environment, clinical diagnosis, and other fields. PMID:26948147
The Energy-Momentum Problem in General Relativity
NASA Astrophysics Data System (ADS)
Xulu, S. S.
2003-08-01
Energy-momentum is an important conserved quantity whose definition has been a focus of many investigations in general relativity. Unfortunately, there is still no generally accepted definition of energy and momentum in general relativity. Attempts aimed at finding a quantity for describing distribution of energy-momentum due to matter, non-gravitational and gravitational fields resulted in various energy-momentum complexes whose physical meaning have been questioned. The problems associated with energy-momentum complexes resulted in some researchers even abandoning the concept of energy-momentum localization in favour of the alternative concept of quasi-localization. However, quasi-local masses have their inadequacies, while the remarkable work of Virbhadra and some others, and recent results of Cooperstock and Chang et al. have revived an interest in various energy-momentum complexes. Hence in this work we use energy-momentum complexes to obtain the energy distributions in various space-times. We elaborate on the problem of energy localization in general relativity and use energy-momentum prescriptions of Einstein, Landau and Lifshitz, Papapetrou, Weinberg, and Møller to investigate energy distributions in various space-times. It is shown that several of these energy-momentum complexes give the same and acceptable results for a given space-time. This shows the importance of these energy-momentum complexes. Our results agree with Virbhadra's conclusion that the Einstein's energy-momentum complex is still the best tool for obtaining energy distribution in a given space-time. The Cooperstock hypothesis for energy localization in GR is also supported.
PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma
NASA Astrophysics Data System (ADS)
Xie, Huasheng; Xiao, Yong
2016-02-01
A general, fast, and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations. The plasma dispersion function is approximated by J-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate; more strongly damped modes are less accurate, but are less likely to be of physical interest. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial guess. It is also free from convergence problems. The approach is demonstrated for electrostatic dispersion equations with one-dimensional and two-dimensional wavevectors, and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2015GB110003, 2011GB105001, 2013GB111000), National Natural Science Foundation of China (No. 91130031), the Recruitment Program of Global Youth Experts
Batalhão, Tiago B; Souza, Alexandre M; Mazzola, Laura; Auccaise, Ruben; Sarthour, Roberto S; Oliveira, Ivan S; Goold, John; De Chiara, Gabriele; Paternostro, Mauro; Serra, Roberto M
2014-10-01
We report the experimental reconstruction of the nonequilibrium work probability distribution in a closed quantum system, and the study of the corresponding quantum fluctuation relations. The experiment uses a liquid-state nuclear magnetic resonance platform that offers full control on the preparation and dynamics of the system. Our endeavors enable the characterization of the out-of-equilibrium dynamics of a quantum spin from a finite-time thermodynamics viewpoint. PMID:25325627
On the stability of Einstein static universe in doubly general relativity scenario
NASA Astrophysics Data System (ADS)
Khodadi, M.; Heydarzade, Y.; Nozari, K.; Darabi, F.
2015-12-01
By presenting a relation between the average energy of the ensemble of probe photons and the energy density of the universe, in the context of gravity's rainbow or the doubly general relativity scenario, we introduce a rainbow FRW universe model. By analyzing the fixed points in the flat FRW model modified by two well-known rainbow functions, we find that the finite time singularity avoidance (i.e. Big Bang) may still remain as a problem. Then we follow the "emergent universe" scenario in which there is no beginning of time and consequently there is no Big-Bang singularity. Moreover, we study the impact of high energy quantum gravity modifications related to the gravity's rainbow on the stability conditions of an "Einstein static universe" (ESU). We find that independent of the particular rainbow function, the positive energy condition dictates a positive spatial curvature for the universe. In fact, without raising a nonphysical energy condition in the quantum gravity regimes, we can observe agreement between gravity's rainbow scenario and the basic assumption of the modern version of the "emergent universe". We show that in the absence and presence of an energy-dependent cosmological constant Λ (ɛ ), a stable Einstein static solution is available versus the homogeneous and linear scalar perturbations under the variety of the obtained conditions. Also, we explore the stability of ESU against the vector and tensor perturbations.
Implementing general quantum measurements on linear optical and solid-state qubits
NASA Astrophysics Data System (ADS)
Ota, Yukihiro; Ashhab, Sahel; Nori, Franco
2013-03-01
We show a systematic construction for implementing general measurements on a single qubit, including both strong (or projection) and weak measurements. We mainly focus on linear optical qubits. The present approach is composed of simple and feasible elements, i.e., beam splitters, wave plates, and polarizing beam splitters. We show how the parameters characterizing the measurement operators are controlled by the linear optical elements. We also propose a method for the implementation of general measurements in solid-state qubits. Furthermore, we show an interesting application of the general measurements, i.e., entanglement amplification. YO is partially supported by the SPDR Program, RIKEN. SA and FN acknowledge ARO, NSF grant No. 0726909, JSPS-RFBR contract No. 12-02-92100, Grant-in-Aid for Scientific Research (S), MEXT Kakenhi on Quantum Cybernetics, and the JSPS via its FIRST program.
Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations
NASA Astrophysics Data System (ADS)
Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.
The Hamiltonian formulation of general relativity is considered in finite space-time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac-ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac-ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.
Testing general relativity using golden black-hole binaries
NASA Astrophysics Data System (ADS)
Ghosh, Abhirup; Ghosh, Archisman; Johnson-McDaniel, Nathan K.; Mishra, Chandra Kant; Ajith, Parameswaran; Del Pozzo, Walter; Nichols, David A.; Chen, Yanbei; Nielsen, Alex B.; Berry, Christopher P. L.; London, Lionel
2016-07-01
The coalescences of stellar-mass black-hole binaries through their inspiral, merger, and ringdown are among the most promising sources for ground-based gravitational-wave (GW) detectors. If a GW signal is observed with sufficient signal-to-noise ratio, the masses and spins of the black holes can be estimated from just the inspiral part of the signal. Using these estimates of the initial parameters of the binary, the mass and spin of the final black hole can be uniquely predicted making use of general-relativistic numerical simulations. In addition, the mass and spin of the final black hole can be independently estimated from the merger-ringdown part of the signal. If the binary black-hole dynamics is correctly described by general relativity (GR), these independent estimates have to be consistent with each other. We present a Bayesian implementation of such a test of general relativity, which allows us to combine the constraints from multiple observations. Using kludge modified GR waveforms, we demonstrate that this test can detect sufficiently large deviations from GR and outline the expected constraints from upcoming GW observations using the second-generation of ground-based GW detectors.
Hyperbolicity of physical theories with application to general relativity
NASA Astrophysics Data System (ADS)
Hilditch, David; Richter, Ronny
2016-08-01
We consider gauge theories from the free evolution point of view, in which initial data satisfying constraints of a theory are given, and because the constraints satisfy a closed evolution system, they remain so. We study a model constrained Hamiltonian theory and identify a particular structure in the equations of motion which we call the standard gauge freedom. The pure gauge subsystem of this model theory is identified, and the manner in which the gauge variables couple to the field equations is presented. We demonstrate that the set of gauge choices that can be coupled to the field equations to obtain a strongly hyperbolic formulation is exactly the set of strongly hyperbolic pure gauges. Consequently we analyze a parametrized family of formulations of general relativity. The generalization of the harmonic gauge formulation to a five parameter family of gauge conditions is obtained.
Structures of general relativity in dilaton-Maxwell electrodynamics
NASA Astrophysics Data System (ADS)
Kechkin, O. V.; Mosharev, P. A.
2016-08-01
It is shown that electro (magneto) static sector of Maxwell’s electrodynamics coupled to the dilaton field in a string theory form possesses the symmetry group of the stationary General Relativity in vacuum. Performing the Ernst formalism, we develope a technique for generation of exact solutions in this modified electrodynamics on the base of the normalized Ehlers symmetry transformation. In the electrostatic case, we construct and study a general class of spherically symmetric solutions that describes a pointlike source of the Coulomb type. It is demonstrated that this source is characterized by finite and singularity-free interaction at short distances. Also it is established that the total electrostatic energy of this source is finite and inversely proportional to the dilaton-Maxwell coupling constant.
Guidelines for composite materials research related to general aviation aircraft
NASA Technical Reports Server (NTRS)
Dow, N. F.; Humphreys, E. A.; Rosen, B. W.
1983-01-01
Guidelines for research on composite materials directed toward the improvement of all aspects of their applicability for general aviation aircraft were developed from extensive studies of their performance, manufacturability, and cost effectiveness. Specific areas for research and for manufacturing development were identified and evaluated. Inputs developed from visits to manufacturers were used in part to guide these evaluations, particularly in the area of cost effectiveness. Throughout the emphasis was to direct the research toward the requirements of general aviation aircraft, for which relatively low load intensities are encountered, economy of production is a prime requirement, and yet performance still commands a premium. A number of implications regarding further directions for developments in composites to meet these requirements also emerged from the studies. Chief among these is the need for an integrated (computer program) aerodynamic/structures approach to aircraft design.
A Generalized Relational Schema for an Integrated Clinical Patient Database
Friedman, Carol; Hripcsak, George; Johnson, Stephen B.; Cimino, James J.; Clayton, Paul D.
1990-01-01
Patient data is central to a Clinical Information System (CIS). The organization of the data in a patient database is essential to the functioning of the system. If the CIS contains a medical decision support component, further requirements are imposed on the database. It must be capable of accurately representing a broad range of clinical information in coded form, and be organized for efficient retrievals by patient, time, and type of clinical term. This paper presents a generalized schema for a clinical patient database within the relational database model. The general design makes it possible to represent diverse clinical data in a standard structure and to organize the data so that it is densely clustered by patient and time.
General Relativity and the Standard Model: Why evidence for one does not disconfirm the other
NASA Astrophysics Data System (ADS)
Jones, Nicholaos
General Relativity and the Standard Model often are touted as the most rigorously and extensively confirmed scientific hypotheses of all time. Nonetheless, these theories appear to have consequences that are inconsistent with evidence about phenomena for which, respectively, quantum effects and gravity matter. This paper suggests an explanation for why the theories are not disconfirmed by such evidence. The key to this explanation is an approach to scientific hypotheses that allows their actual content to differ from their apparent content. This approach does not appeal to ceteris-paribus qualifiers or counterfactuals or similarity relations. And it helps to explain why some highly idealized hypotheses are not treated in the way that a thoroughly refuted theory is treated but instead as hypotheses with limited domains of applicability.
Roura, Albert; Fleming, C H; Hu, B L
2008-01-01
We revisit the model of a system made up of a Brownian quantum oscillator linearly coupled to an environment made up of many quantum oscillators at finite temperature. We show that the HPZ master equation for the reduced density matrix derived earlier [B.L. Hu, J.P. Paz, Y. Zhang, Phys. Rev. D 45, 2843 (1992)] has incorrectly specified coefficients for the case of nonlocal dissipation. We rederive the QBM master equation, correctly specifying all coefficients, and determine the position uncertainty to be free of excessive cutoff sensitivity. Our coefficients and solutions are reduced entirely to contour integration for analytic spectra at arbitrary temperature, coupling strength, and cut-off. As an illustration we calculate the master equation coefficients and solve the master equation for ohmic coupling (with finite cutoff) and example supra-ohmic and sub-ohmic spectral densities. We determine the effect of an external force on the quantum oscillator and also show that our representation of the master equation and solutions naturally extends to a system of multiple oscillators bilinearly coupled to themselves and the bath in arbitrary fashion. This produces a formula for investigating the standard quantum limit which is central to addressing many theoretical issues in macroscopic quantum phenomena and experimental concerns related to low temperature precision measurements. We find that in a dissipative environment, all initial states settle down to a Gaussian density matrix whose covariance is determined by the thermal reservoir and whose mean is determined by the external force. We specify the thermal covariance for the spectral densities we explore.
A generalized quantum-inspired decision making model for intelligent agent.
Hu, Yuhuang; Loo, Chu Kiong
2014-01-01
A novel decision making for intelligent agent using quantum-inspired approach is proposed. A formal, generalized solution to the problem is given. Mathematically, the proposed model is capable of modeling higher dimensional decision problems than previous researches. Four experiments are conducted, and both empirical experiments results and proposed model's experiment results are given for each experiment. Experiments showed that the results of proposed model agree with empirical results perfectly. The proposed model provides a new direction for researcher to resolve cognitive basis in designing intelligent agent. PMID:24778580
Implications of the general constraints for single-qubit quantum process tomography
NASA Astrophysics Data System (ADS)
Bhandari, Ramesh; Peters, Nicholas
We revisit the general constraints of single qubit quantum process tomography and derive simplified forms in the Pauli basis. These forms give insight into the structure of the process matrix, which we examine in light of several examples. Specifically, we study some qubit leakage error models and show how different error models are manifest in the process matrix. NAP's research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy.
Generalized quantum master equations in and out of equilibrium: When can one win?
NASA Astrophysics Data System (ADS)
Kelly, Aaron; Montoya-Castillo, Andrés; Wang, Lu; Markland, Thomas E.
2016-05-01
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.
General Formalism of Decision Making Based on Theory of Open Quantum Systems
NASA Astrophysics Data System (ADS)
Asano, M.; Ohya, M.; Basieva, I.; Khrennikov, A.
2013-01-01
We present the general formalism of decision making which is based on the theory of open quantum systems. A person (decision maker), say Alice, is considered as a quantum-like system, i.e., a system which information processing follows the laws of quantum information theory. To make decision, Alice interacts with a huge mental bath. Depending on context of decision making this bath can include her social environment, mass media (TV, newspapers, INTERNET), and memory. Dynamics of an ensemble of such Alices is described by Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We speculate that in the processes of evolution biosystems (especially human beings) designed such "mental Hamiltonians" and GKSL-operators that any solution of the corresponding GKSL-equation stabilizes to a diagonal density operator (In the basis of decision making.) This limiting density operator describes population in which all superpositions of possible decisions has already been resolved. In principle, this approach can be used for the prediction of the distribution of possible decisions in human populations.
Generalized quantum master equations in and out of equilibrium: When can one win?
Kelly, Aaron; Montoya-Castillo, Andrés; Wang, Lu; Markland, Thomas E
2016-05-14
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations. PMID:27179469
NASA Astrophysics Data System (ADS)
Henriksen, Ellen K.; Bungum, Berit; Angell, Carl; Tellefsen, Cathrine W.; Frågåt, Thomas; Vetleseter Bøe, Maria
2014-11-01
In this article, we discuss how quantum physics and relativity can be taught in upper secondary school, in ways that promote conceptual understanding and philosophical reflections. We present the ReleQuant project, in which web-based teaching modules have been developed. The modules address competence aims in the Norwegian national curriculum for physics (final year of upper secondary education), which is unique in that it includes general relativity, entangled photons and the epistemological consequences of modern physics. These topics, with their high demands on students’ understanding of abstract and counter-intuitive concepts and principles, are challenging for teachers to teach and for students to learn. However, they also provide opportunities to present modern physics in innovative ways that students may find motivating and relevant both in terms of modern technological applications and in terms of contributions to students’ intellectual development. Beginning with these challenges and opportunities, we briefly present previous research and theoretical perspectives with relevance to student learning and motivation in modern physics. Based on this, we outline the ReleQuant teaching approach, where students use written and oral language and a collaborative exploration of animations and simulations as part of their learning process. Finally, we present some of the first experiences from classroom tests of the quantum physics modules.
Testing General Relativity and gravitational physics using the LARES satellite
NASA Astrophysics Data System (ADS)
Ciufolini, Ignazio; Paolozzi, Antonio; Pavlis, Erricos; Ries, John; Gurzadyan, Vahe; Koenig, Rolf; Matzner, Richard; Penrose, Roger; Sindoni, Giampiero
2012-11-01
The discovery of the accelerating expansion of the Universe, thought to be driven by a mysterious form of "dark energy" constituting most of the Universe, has further revived the interest in testing Einstein's theory of General Relativity. At the very foundation of Einstein's theory is the geodesic motion of a small, structureless test-particle. Depending on the physical context, a star, planet or satellite can behave very nearly like a test-particle, so geodesic motion is used to calculate the advance of the perihelion of a planet's orbit, the dynamics of a binary pulsar system and of an Earth-orbiting satellite. Verifying geodesic motion is then a test of paramount importance to General Relativity and other theories of fundamental physics. On the basis of the first few months of observations of the recently launched satellite LARES, its orbit shows the best agreement of any satellite with the test-particle motion predicted by General Relativity. That is, after modelling its known non-gravitational perturbations, the LARES orbit shows the smallest deviations from geodesic motion of any artificial satellite: its residual mean acceleration away from geodesic motion is less than 0.5×10^{-12} m/s^2. LARES-type satellites can thus be used for accurate measurements and for tests of gravitational and fundamental physics. Already with only a few months of observation, LARES provides smaller scatter in the determination of several low-degree geopotential coefficients (Earth gravitational deviations from sphericity) than available from observations of any other satellite or combination of satellites.
Quantum extended supersymmetries
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
2004-09-01
We analyse some quantum multiplets associated with extended supersymmetries. We study in detail the general form of the causal (anti)commutation relations. The condition of positivity of the scalar product imposes severe restrictions on the (quantum) model. It is problematic if one can find out quantum extensions of the standard model with extended supersymmetries.
FLRW non-singular cosmological model in general relativity
NASA Astrophysics Data System (ADS)
Jas Pacif, Shibesh Kumar; Mishra, Bivudutta
2015-12-01
A singularity free cosmological model is obtained in a homogeneous and isotropic background with a specific form of the Hubble parameter in the presence of an interacting dark energy represented by a time-varying cosmological constant in general relativity. Different cases that arose have been extensively studied for different values of the curvature parameter. Some interesting results have been found with this form of the Hubble parameter to meet the possible negative value of the deceleration parameter ≤ft({ - \\frac{1}{3} ≤slant q < 0} \\right) as the current observations reveal. For some particular values of these parameters, the model reduces to Berman's model.
Derivation of Einstein-Cartan theory from general relativity
NASA Astrophysics Data System (ADS)
Petti, Richard
2016-03-01
This article presents a derivation of Einstein-Cartan theory from general relativity with no additional assumptions or parameters. The derivation begins with distributions of Kerr masses that converge to a continuum with constant densities of mass, momentum, and angular momentum. The limit includes torsion and the spin-torsion relationship of Einstein-Cartan theory. The construction of curvature and torsion is equivalent to definition of curvature with Cartan forms on fiber bundles. Advantages of Einstein-Cartan theory include accommodating exchange of classical intrinsic and orbital angular momentum and generation of inflation-like expansion in high density cosmological models.
Vector order parameter in general relativity: Covariant equations
Meierovich, Boris E.
2010-07-15
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are derived. The topological defects are classified in accordance with the symmetry of the covariant derivative of the vector order parameter. The abilities of the derived equations are demonstrated in application to the braneworld concept. New solutions of the Einstein equations with a transverse vector order parameter are presented. In the vicinity of phase transition, the solutions are found analytically.
Rotating black holes in the teleparallel equivalent of general relativity
NASA Astrophysics Data System (ADS)
Nashed, Gamal G. L.
2016-05-01
We derive set of solutions with flat transverse sections in the framework of a teleparallel equivalent of general relativity which describes rotating black holes. The singularities supported from the invariants of torsion and curvature are explained. We investigate that there appear more singularities in the torsion scalars than in the curvature ones. The conserved quantities are discussed using Einstein-Cartan geometry. The physics of the constants of integration is explained through the calculations of conserved quantities. These calculations show that there is a unique solution that may describe true physical black hole.
Tests of general relativity using Starprobe radio metric tracking data
NASA Technical Reports Server (NTRS)
Mease, K. D.; Anderson, J. D.; Wood, L. J.; White, L. K.
1982-01-01
The potential of a proposed spacecraft mission, called Starprobe, for testing general relativity and providing information on the interior structure and dynamics of the sun is investigated. Parametric, gravitational perturbation terms are derived which represent relativistic effects and effects due to spatial and temporal variations in the solar potential at a given radial distance. A covariance analysis based on Kalman filtering theory predicts the accuracies with which the free parameters in the perturbation terms can be estimated with radio metric tracking data through the process of trajectory reconstruction. It is concluded that Starprobe can contribute significant information on both the nature of gravitation and the structure and dynamics of the solar interior.
A superconducting gyroscope to test Einstein's general theory of relativity
NASA Technical Reports Server (NTRS)
Everitt, C. W. F.
1978-01-01
Schiff (1960) proposed a new test of general relativity based on measuring the precessions of the spin axes of gyroscopes in earth orbit. Since 1963 a Stanford research team has been developing an experiment to measure the two effects calculated by Schiff. The gyroscope consists of a uniform sphere of fused quartz 38 mm in diameter, coated with superconductor, electrically suspended and spinning at about 170 Hz in vacuum. The paper describes the proposed flight apparatus and the current state of development of the gyroscope, including techniques for manufacturing and measuring the gyro rotor and housing, generating ultralow magnetic fields, and mechanizing the readout.
Testing general relativity in space-borne and astronomical laboratories
NASA Technical Reports Server (NTRS)
Will, Clifford M.
1989-01-01
The current status of space-based experiments and astronomical observations designed to test the theory of general relativity is surveyed. Consideration is given to tests of post-Newtonian gravity, searches for feeble short-range forces and gravitomagnetism, improved measurements of parameterized post-Newtonian parameter values, explorations of post-Newtonian physics, tests of the Einstein equivalence principle, observational tests of post-Newtonian orbital effects, and efforts to detect quadrupole and dipole radiation damping. Recent numerical results are presented in tables.
Testing General Relativity with Spherical Resonant Mass Detectors
NASA Astrophysics Data System (ADS)
Sylvester, Alex J.
Gravitational waves in f(R) gravity excite monopole and m = 0+/-2 quadrupole resonance modes of a spherical detector. This document reviews the basic ideas of general relativity and gravitational waves, and then applies those concepts to an f( R) gravitational wave. The acoustic response of a GW incident with a spherical detector is reviewed in detail, and the absorption cross section for an f(R) GW impinging on the spherical detector is calculated. Minimum detectable scalar wave amplitudes are explored for the Mario Schenberg detector. The mass of the scalar mode affects its detectability.
NASA Astrophysics Data System (ADS)
Dolce, Donatello; Perali, Andrea
2014-09-01
Pure quantum phenomena are characterized by intrinsic recurrences in space and time. We use this intrinsic periodicity as a quantization condition to derive a heuristic description of the essential quantum phenomenology of superconductivity. The resulting description is based on fundamental quantum dynamics and geometrical considerations, rather than on microscopical characteristics of the superconducting materials. This allows us to investigate the related gauge symmetry breaking in terms of the competition between quantum recurrence and thermal noise. We also test the validity of this approach to describe the case of carbon nanotubes.
NASA Astrophysics Data System (ADS)
Kuramochi, Yui; Ueda, Masahito
2015-03-01
We consider the information flow on a system observable X corresponding to a positive-operator-valued measure under a quantum measurement process Y described by a completely positive instrument from the viewpoint of the relative entropy. We establish a sufficient condition for the relative-entropy conservation law which states that the average decrease in the relative entropy of the system observable X equals the relative entropy of the measurement outcome of Y , i.e., the information gain due to measurement. This sufficient condition is interpreted as an assumption of classicality in the sense that there exists a sufficient statistic in a joint successive measurement of Y followed by X such that the probability distribution of the statistic coincides with that of a single measurement of X for the premeasurement state. We show that in the case when X is a discrete projection-valued measure and Y is discrete, the classicality condition is equivalent to the relative-entropy conservation for arbitrary states. The general theory on the relative-entropy conservation is applied to typical quantum measurement models, namely, quantum nondemolition measurement, destructive sharp measurements on two-level systems, a photon counting, a quantum counting, homodyne and heterodyne measurements. These examples except for the nondemolition and photon-counting measurements do not satisfy the known Shannon-entropy conservation law proposed by Ban [M. Ban, J. Phys. A: Math. Gen. 32, 1643 (1999), 10.1088/0305-4470/32/9/012], implying that our approach based on the relative entropy is applicable to a wider class of quantum measurements.
Testing general relativity with Landers on the Martian satellite Phobos
NASA Technical Reports Server (NTRS)
Anderson, J. D.; Borderies, N. J.; Campbell, J. K.; Dunne, J. A.; Ellis, J.
1989-01-01
A planned experiment to obtain range and Doppler data with the Phobos 2 Lander on the surface of the Martian satellite Phobos is described. With the successful insertion on January 29, 1989 of Phobos 2 into Mars orbit, it is anticipated that the Lander will be placed on the surface of Phobos in April 1989. Depending on the longevity of the Lander, range and Doppler data for a period of from one to several years are expected. Because these data are of value in performing solar-system tests of general relativity, the current accuracy of the relevant relativity tests using Deep Space Network data from the Mariner-9 orbiter of Mars in 1971 and from the Viking Landers in 1976-1982 is reviewed. The expected improvement from data anticipated during the Phobos 2 Lander Mission is also discussed; most important will be an improved sensitivity to any time variation in the gravitational 'constant' as measured in atomic units.
Cosmological Tests of General Relativity with tomographic surveys
NASA Astrophysics Data System (ADS)
Silvestri, Alessandra; Zhao, Gongbo; Pogosian, Levon; Zylberberg, Joel
2010-02-01
Future cosmological surveys, combining galaxy counts and weak lensing measurements, will map the evolution of matter perturbations and gravitational potentials from the matter dominated epoch until today. In addition to tightening the constraints on allowed expansion histories, the combination of these measurements will test the relationships between matter overdensities, local curvature, and the Newtonian potential. These relation- ships can be modi?ed in alternative theories of gravity and by exotic forms of Dark Energy. I will present a study of the potential of upcoming and future tomographic surveys, such as DES and LSST, with the aid of CMB and supernovae data, to detect departures from the growth of perturbations expected within General Relativity with a cosmological constant. )
Integrated measures for rough sets based on general binary relations.
Teng, Shuhua; Liao, Fan; He, Mi; Lu, Min; Nian, Yongjian
2016-01-01
Uncertainty measures are important for knowledge discovery and data mining. Rough set theory (RST) is an important tool for measuring and processing uncertain information. Although many RST-based methods for measuring system uncertainty have been investigated, the existing measures cannot adequately characterise the imprecision of a rough set. Moreover, these methods are suitable only for complete information systems, and it is difficult to generalise methods for complete information systems to incomplete information systems. To overcome these shortcomings, we present new uncertainty measures, integrated accuracy and integrated roughness, that are based on general binary relations, and we study important properties of these measures. A theoretical analysis and examples show that the proposed integrated measures are more precise than existing uncertainty measures, they are suitable for both complete and incomplete information systems, and they are logically consistent. Therefore, integrated accuracy and integrated roughness overcome the limitations of existing measures. This research not only develops the theory of uncertainty, it also expands the application domain of uncertainty measures and provides a theoretical basis for knowledge acquisition in information systems based on general binary relations. PMID:26900539
A Conceptual Physics Course in General Relativity and Cosmology
NASA Astrophysics Data System (ADS)
Zeilik, Michael; Markus, M. Jennifer
2005-04-01
We have designed, implemented, assessed, and revised a new conceptual physics course at the University of New Mexico. Using the NRC/NAS report ``Connecting Quarks with the Cosmos'' (2003) as a guide, we pared down the 11 questions to six based on a student poll. The instructor (MZ) reconceptualized these six into a one- semester course focused on general relativity and cosmology, while taking into account known misconceptions research. The full implementation of an active- learning version took place in Spring 2003. The classes contained about 2/3 males and 1/3 females, about 60% ``freshmen.'' Some 50% took the course to meet a requirement. Students entered with a wide variety of math backgrounds, with the men reporting more advanced courses. We report on assessments to probe the success of the course based on our learning outcomes. In math and science aptitude, females and males ranked themselves the same at the start of the course; men felt more confident at the end. Using a conceptual diagnostic test as a pre- and post assessment, we found that males outscored the females pre- and post, but the normalized gains were the same. The normalized gains on Force Concept Inventory items was 0.2; for general relativity and cosmology ones, 0.5.
Dealing with quantum weirdness: Holism and related issues
Elby, A.R.
1995-12-01
Various issues are discussed in interpretation of quantum mechanics. All these explorations point toward the same conclusion, that some systems are holistically connected, i.e., some composite systems have properties that cannot, even in principle, be reduced to the properties of its subsystems. This is argued to be the central metaphysical lesson of quantum theory; this will remain pertinent even if quantum mechanics gets replaced by a superior theory. Chap. 2 discusses nonlocality and rules out hidden-variable theories that approximately reproduce the perfect correlations of quantum mechanics, as well as theories that obey locality conditions weaker than those needed to derive Bell`s inequality. Chap. 3 shows that SQUID experiments can rule out non-invasive measurability if not macrorealism. Chap. 4 looks at interpretational issues surrounding decoherence, the dissipative interaction between a system and its environment. Decoherence klcan help ``modal`` interpretations pick out the desired ``preferred`` basis. Chap. 5 explores what varieties of causation can and cannot ``explain`` EPR correlations. Instead of relying on ``watered down`` causal explanations, we should instead develop new, holistic explanatory frameworks.
Tang, Zhoufei; Gong, Zhihao; Wu, Jianlan
2015-09-14
For a general two-cluster network, a new methodology of the cluster-based generalized quantum kinetic expansion (GQKE) is developed in the matrix formalism under two initial conditions: the local cluster equilibrium and system-bath factorized states. For each initial condition, the site population evolution follows exactly a distinct closed equation, where all the four terms involved are systematically expanded over inter-cluster couplings. For the system-bath factorized initial state, the numerical investigation of the two models, a biased (2, 1)-site system and an unbiased (2, 2)-site system, verifies the reliability of the GQKE and the relevance of higher-order corrections. The time-integrated site-to-site rates and the time evolution of site population reveal the time scale separation between intra-cluster and inter-cluster kinetics. The population evolution of aggregated clusters can be quantitatively described by the approximate cluster Markovian kinetics.
Generalized asymmetric phase-covariant quantum cloning within a nonextensive approach
NASA Astrophysics Data System (ADS)
Boudjema, R.; Hamici, A.-H.; Hachemane, M.; Smida, A.
2016-01-01
In this paper, we present a generalized transformation of the optimal asymmetric 1longrightarrow 2 phase-covariant quantum cloning. This generalization is based on the deformed forms of the exponential that emerge from nonextensive statistical mechanics. In particular, two distinct definitions of the q-exponential are discussed. The case where the cloning is symmetric is also studied. In order to highlight the influence of nonextensive treatment on the perfection of clones and entanglement, the effect of the q-index has been clearly illustrated in figures depicting the fidelities in terms of the entanglement parameter θ for different values of q. Our study shows that due to the intrinsic properties of the system, the entanglement is not preserved. Thus, entanglement can be controlled by the nonextensive parameter. As an illustration, the incoherent attack on the BB84 protocol has also been considered in the economical case.
Generalized quantum kinetic expansion: Higher-order corrections to multichromophoric Förster theory
Wu, Jianlan Gong, Zhihao; Tang, Zhoufei
2015-08-21
For a general two-cluster energy transfer network, a new methodology of the generalized quantum kinetic expansion (GQKE) method is developed, which predicts an exact time-convolution equation for the cluster population evolution under the initial condition of the local cluster equilibrium state. The cluster-to-cluster rate kernel is expanded over the inter-cluster couplings. The lowest second-order GQKE rate recovers the multichromophoric Förster theory (MCFT) rate. The higher-order corrections to the MCFT rate are systematically included using the continued fraction resummation form, resulting in the resummed GQKE method. The reliability of the GQKE methodology is verified in two model systems, revealing the relevance of higher-order corrections.
NASA Astrophysics Data System (ADS)
Hofmann, Holger F.
2014-04-01
Recent results obtained in quantum measurements indicate that the fundamental relations between three physical properties of a system can be represented by complex conditional probabilities. Here, it is shown that these relations provide a fully deterministic and universally valid framework on which all of quantum mechanics can be based. Specifically, quantum mechanics can be derived by combining the rules of Bayesian probability theory with only a single additional law that explains the phases of complex probabilities. This law, which I introduce here as the law of quantum ergodicity, is based on the observation that the reality of physical properties cannot be separated from the dynamics by which they emerge in measurement interactions. The complex phases are an expression of this inseparability and represent the dynamical structure of transformations between the different properties. In its quantitative form, the law of quantum ergodicity describes a fundamental relation between the ergodic probabilities obtained by dynamical averaging and the deterministic relations between three properties expressed by the complex conditional probabilities. The complete formalism of quantum mechanics can be derived from this one relation, without any axiomatic mathematical assumptions about state vectors or superpositions. It is therefore possible to explain all quantum phenomena as the consequence of a single fundamental law of physics.
NASA Astrophysics Data System (ADS)
Emelyanov, S. A.
2013-06-01
We have demonstrated spatially-discontinuous quantum jumps of electrons at a distance as long as about 1cm. The effect occurs in a modified integer quantum Hall system consisted of a great number of extended Laughlin-Halperin-type states. Our observations directly contradict the no-aether Einstein's interpretation of special relativity together with the Minkowski's model of spacetime. However they are consistent with the aether-related Lorentz-Poincare's interpretation that allows absolute simultaneity. We thus strongly challenge the fundamental status of Lorentz invariance and hence break the basic argument against de Broglie-Bohm realistic quantum theory. We argue that both de Broglie-Bohm and Lorentz-Poincare theories are capable of providing a real synthesis of quantum and relativity theories. This synthesis is of such kind that quantum theory appears the most fundamental physical theory for which relativity is only a limiting case. In accordance with this hierarchy, quantum theory naturally resolves the problem of aether in Lorentz-Poincare's relativity. The role of aether could be played by a deeper Bohm-type undivided quantum pre-space, the relevance of which at any lengthscale directly follows from our observations.
Xun, D.M.; Liu, Q.H.; Zhu, X.M.
2013-11-15
A generalization of Dirac’s canonical quantization scheme for a system with second-class constraints is proposed, in which the fundamental commutation relations are constituted by all commutators between positions, momenta and Hamiltonian, so they are simultaneously quantized in a self-consistent manner, rather than by those between merely positions and momenta which leads to ambiguous forms of the Hamiltonian and the momenta. The application of the generalized scheme to the quantum motion on a torus leads to a remarkable result: the quantum theory is inconsistent if built up in an intrinsic geometric manner, whereas it becomes consistent within an extrinsic examination of the torus as a submanifold in three dimensional flat space with the use of the Cartesian coordinate system. The geometric momentum and potential are then reasonably reproduced. -- Highlights: •A generalization of Dirac’s canonical quantization is proposed for a system with second-class constraints. •Quantum motion on torus surface is explicitly treated to show how Schrödinger formalism is complementary to the Dirac one. •The embedding effect in quantum mechanics is originated from the quantization.
Quantized shells as a tool for studying semiclassical effects in general relativity
NASA Astrophysics Data System (ADS)
Casadio, Roberto
2000-06-01
Thin shells in general relativity can be used both as models of collapsing objects and as probes in the space-time outside compact sources. Therefore they provide a useful tool for the analysis of the final fate of collapsing matter and of the effects induced in the matter by strong gravitational fields. We describe the radiating shell as a (second quantized) many-body system with one collective degree of freedom, the (average) radius, by means of an effective action which also entails a thermodynamic description. Then we study some of the quantum effects that occur in the matter when the shell evolves from an (essentially classical) large initial radius towards the singularity and compute the corresponding backreaction on its trajectory.
Electrodynamics of a generalized charged particle in doubly special relativity framework
Pramanik, Souvik; Ghosh, Subir; Pal, Probir
2014-07-15
In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative κ-Minkowski space–time, compatible with Doubly Special Relativity, that is motivated to describe Quantum Gravity effects. Furthermore we have also considered the electromagnetic field to be dynamical and have derived the modified forms of Lienard–Wiechert like potentials for these extended charged particle models. In all the above cases we exploit the new and extended form of κ-Minkowski algebra where electromagnetic effects are incorporated in the lowest order, in the Dirac framework of Hamiltonian constraint analysis.
A Generalized Brownian Motion Model for Turbulent Relative Particle Dispersion
NASA Astrophysics Data System (ADS)
Shivamoggi, Bhimsen
2015-11-01
A generalized Brownian motion model has been applied to the turbulent relative particle dispersion problem (Shivamoggi). The fluctuating pressure forces acting on a fluid particle are taken to follow an Uhlenbeck-Ornstein process while it appears plausible to take their correlation time to have a power-law dependence on the flow Reynolds number Re. This ansatz provides an insight into the result that the Richardson-Obukhov scaling holds only in the infinite-Re limit and disappears otherwise. It provides a determination of the Richardson-Obukhov constant g as a function of Re, with an asymptotic constant value in the infinite-Re limit. This ansatz is further shown to be in quantitative agreement, in the small-Re limit, with the Batchelor-Townsend ansatz for the rate of change of the mean square interparticle separation in 3D FDT. My thanks to The Netherlands Organization for Scientific Research for Support.
CPT symmetry and antimatter gravity in general relativity
NASA Astrophysics Data System (ADS)
Villata, M.
2011-04-01
The gravitational behavior of antimatter is still unknown. While we may be confident that antimatter is self-attractive, the interaction between matter and antimatter might be either attractive or repulsive. We investigate this issue on theoretical grounds. Starting from the CPT invariance of physical laws, we transform matter into antimatter in the equations of both electrodynamics and gravitation. In the former case, the result is the well-known change of sign of the electric charge. In the latter, we find that the gravitational interaction between matter and antimatter is a mutual repulsion, i.e. antigravity appears as a prediction of general relativity when CPT is applied. This result supports cosmological models attempting to explain the Universe accelerated expansion in terms of a matter-antimatter repulsive interaction.
General relativity as an attractor for scalar-torsion cosmology
NASA Astrophysics Data System (ADS)
Järv, Laur; Toporensky, Alexey
2016-01-01
We study flat Friedmann-Lemaître-Robertson-Walker cosmological models for a scalar field coupled nonminimally to teleparallel gravity with generic coupling and potential functions. The goal in this paper is to determine the conditions under which cosmological evolution tends to the limit where the variation of the gravitational "constant" ceases and the system evolves close to general relativity (GR). These conditions can be read off from the approximate analytical solutions describing the process in matter and potential domination eras. Only those models where the GR limit exists and is an attractor can be considered viable. We expect the results to hold in the original "pure tetrad" formulation as well as in the recently suggested covariant formulation of the teleparallel theory. In the former case the GR attractor simultaneously provides a mechanism for how cosmological evolution suppresses the problematic degrees of freedom stemming from the lack of local Lorentz invariance.
Proper Time Dynamics in General Relativity and Conformal Unified Theory
NASA Astrophysics Data System (ADS)
Gyngazov, L. N.; Pawlowski, M.; Pervushin, V. N.; Smirichinski, V. I.
1998-12-01
The paper is devoted to the description a measurable time-interval ("proper time") in the Hamiltonian version of general relativity with the Dirac-ADM metric. To separate the dynamical parameter of evolution from the space metric we use the Lichnerowicz conformally invariant variables. In terms of these variables GR is equivalent to the conformally invariant Penrose-Chernikov-Tagirov theory of a scalar field the role of which is played by the scale factor multiplied by the Planck constant. Identification of this scalar field with the modulus of the Higgs field in the standard model of electroweak and strong interactions allows us to formulate an example of conformally invariant unified theory where the vacuum averaging of the scalar field is determined by cosmological integrals of motion of the evolution of the universe.
Collapse of magnetized hypermassive neutron stars in general relativity.
Duez, Matthew D; Liu, Yuk Tung; Shapiro, Stuart L; Shibata, Masaru; Stephens, Branson C
2006-01-27
Hypermassive neutron stars (HMNSs)--equilibrium configurations supported against collapse by rapid differential rotation--are possible transient remnants of binary neutron-star mergers. Using newly developed codes for magnetohydrodynamic simulations in dynamical spacetimes, we are able to track the evolution of a magnetized HMNS in full general relativity for the first time. We find that secular angular momentum transport due to magnetic braking and the magnetorotational instability results in the collapse of an HMNS to a rotating black hole, accompanied by a gravitational wave burst. The nascent black hole is surrounded by a hot, massive torus undergoing quasistationary accretion and a collimated magnetic field. This scenario suggests that HMNS collapse is a possible candidate for the central engine of short gamma-ray bursts. PMID:16486677
The Gravity Probe B test of general relativity
NASA Astrophysics Data System (ADS)
Everitt, C. W. F.; Muhlfelder, B.; DeBra, D. B.; Parkinson, B. W.; Turneaure, J. P.; Silbergleit, A. S.; Acworth, E. B.; Adams, M.; Adler, R.; Bencze, W. J.; Berberian, J. E.; Bernier, R. J.; Bower, K. A.; Brumley, R. W.; Buchman, S.; Burns, K.; Clarke, B.; Conklin, J. W.; Eglington, M. L.; Green, G.; Gutt, G.; Gwo, D. H.; Hanuschak, G.; He, X.; Heifetz, M. I.; Hipkins, D. N.; Holmes, T. J.; Kahn, R. A.; Keiser, G. M.; Kozaczuk, J. A.; Langenstein, T.; Li, J.; Lipa, J. A.; Lockhart, J. M.; Luo, M.; Mandel, I.; Marcelja, F.; Mester, J. C.; Ndili, A.; Ohshima, Y.; Overduin, J.; Salomon, M.; Santiago, D. I.; Shestople, P.; Solomonik, V. G.; Stahl, K.; Taber, M.; Van Patten, R. A.; Wang, S.; Wade, J. R.; Worden, P. W., Jr.; Bartel, N.; Herman, L.; Lebach, D. E.; Ratner, M.; Ransom, R. R.; Shapiro, I. I.; Small, H.; Stroozas, B.; Geveden, R.; Goebel, J. H.; Horack, J.; Kolodziejczak, J.; Lyons, A. J.; Olivier, J.; Peters, P.; Smith, M.; Till, W.; Wooten, L.; Reeve, W.; Anderson, M.; Bennett, N. R.; Burns, K.; Dougherty, H.; Dulgov, P.; Frank, D.; Huff, L. W.; Katz, R.; Kirschenbaum, J.; Mason, G.; Murray, D.; Parmley, R.; Ratner, M. I.; Reynolds, G.; Rittmuller, P.; Schweiger, P. F.; Shehata, S.; Triebes, K.; VandenBeukel, J.; Vassar, R.; Al-Saud, T.; Al-Jadaan, A.; Al-Jibreen, H.; Al-Meshari, M.; Al-Suwaidan, B.
2015-11-01
The Gravity Probe B mission provided two new quantitative tests of Einstein’s theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earth’s orbit. Data from four gyroscopes gave a geodetic drift-rate of -6601.8 ± 18.3 marc-s yr-1 and a frame-dragging of -37.2 ± 7.2 marc-s yr-1, to be compared with GR predictions of -6606.1 and -39.2 marc-s yr-1 (1 marc-s = 4.848 × 10-9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.
Remarks on the consistency of minimal deviations from general relativity
Pons, Josep M.; Talavera, Pere
2010-08-15
We study the consequences of some possible modifications of the phase space structure of general relativity imposed by breaking, in the simplest manner, the full diffeomorphism invariance but retaining the time foliation preserving diffeomorphisms. We examine the different sectors in phase space that satisfy the new structure of constraints. For some sectors we find an infinite tower of constraints. In spite of that, we also show that these sectors allow for solutions, among them some well-known families of black hole and cosmologies which fulfill all the constraints. We raise some physical concerns on the consequences of an absolute Galilean time, on the thermodynamical pathologies of such models, and on their unusual vacuum structure.
Ambiguous tests of general relativity on cosmological scales
Zuntz, Joe; Baker, Tessa; Ferreira, Pedro G.; Skordis, Constantinos E-mail: tessa.baker@astro.ox.ac.uk E-mail: skordis@nottingham.ox.ac.uk
2012-06-01
There are a number of approaches to testing General Relativity (GR) on linear scales using parameterized frameworks for modifying cosmological perturbation theory. It is sometimes assumed that the details of any given parameterization are unimportant if one uses it as a diagnostic for deviations from GR. In this brief report we argue that this is not necessarily so. First we show that adopting alternative combinations of modifications to the field equations significantly changes the constraints that one obtains. In addition, we show that using a parameterization with insufficient freedom significantly tightens the apparent theoretical constraints. Fundamentally we argue that it is almost never appropriate to consider modifications to the perturbed Einstein equations as being constraints on the effective gravitational constant, for example, in the same sense that solar system constraints are. The only consistent modifications are either those that grant near-total freedom, as in decomposition methods, or ones which map directly to a particular part of theory space.
Relative states and the existential interpretation: einselection, envariance and quantum Darwinism
Zurek, Wojciech H
2008-01-01
This is a brief 'guide to ideas' aimed at illuminating various developments that are based on the recognition of the role of the environment in the transition from quantum to dassical, and that are relevant to Everett's 'Relative State Interpretation' .
NASA Astrophysics Data System (ADS)
Oriti, Daniele
2009-03-01
Preface; Part I. Fundamental Ideas and General Formalisms: 1. Unfinished revolution C. Rovelli; 2. The fundamental nature of space and time G. 't Hooft; 3. Does locality fail at intermediate length scales R. Sorkin; 4. Prolegomena to any future quantum gravity J. Stachel; 5. Spacetime symmetries in histories canonical gravity N. Savvidou; 6. Categorical geometry and the mathematical foundations of quantum gravity L. Crane; 7. Emergent relativity O. Dreyer; 8. Asymptotic safety R. Percacci; 9. New directions in background independent quantum gravity F. Markopoulou; Questions and answers; Part II: 10. Gauge/gravity duality G. Horowitz and J. Polchinski; 11. String theory, holography and quantum gravity T. Banks; 12. String field theory W. Taylor; Questions and answers; Part III: 13. Loop Quantum Gravity T. Thiemann; 14. Covariant loop quantum gravity? E. LIvine; 15. The spin foam representation of loop quantum gravity A. Perez; 16. 3-dimensional spin foam quantum gravity L. Freidel; 17. The group field theory approach to quantum gravity D. Oriti; Questions and answers; Part IV. Discrete Quantum Gravity: 18. Quantum gravity: the art of building spacetime J. Ambjørn, J. Jurkiewicz and R. Loll; 19. Quantum Regge calculations R. Williams; 20. Consistent discretizations as a road to quantum gravity R. Gambini and J. Pullin; 21. The causal set approach to quantum gravity J. Henson; Questions and answers; Part V. Effective Models and Quantum Gravity Phenomenology: 22. Quantum gravity phenomenology G. Amelino-Camelia; 23. Quantum gravity and precision tests C. Burgess; 24. Algebraic approach to quantum gravity II: non-commutative spacetime F. Girelli; 25. Doubly special relativity J. Kowalski-Glikman; 26. From quantum reference frames to deformed special relativity F. Girelli; 27. Lorentz invariance violation and its role in quantum gravity phenomenology J. Collins, A. Perez and D. Sudarsky; 28. Generic predictions of quantum theories of gravity L. Smolin; Questions and
Relating the Resource Theories of Entanglement and Quantum Coherence.
Chitambar, Eric; Hsieh, Min-Hsiu
2016-07-01
Quantum coherence and quantum entanglement represent two fundamental features of nonclassical systems that can each be characterized within an operational resource theory. In this Letter, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically, we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a given state, and we introduce a new LIOCC monotone that completely characterizes a state's optimal rate of bipartite coherence distillation. This result allows us to precisely quantify the difference in operational powers between global incoherent operations, LIOCC, and local incoherent operations without classical communication. Finally, a bipartite mixed state is shown to have distillable entanglement if and only if entanglement can be distilled by LIOCC, and we strengthen the well-known Horodecki criterion for distillability. PMID:27447493
Relating the Resource Theories of Entanglement and Quantum Coherence
NASA Astrophysics Data System (ADS)
Chitambar, Eric; Hsieh, Min-Hsiu
2016-07-01
Quantum coherence and quantum entanglement represent two fundamental features of nonclassical systems that can each be characterized within an operational resource theory. In this Letter, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically, we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a given state, and we introduce a new LIOCC monotone that completely characterizes a state's optimal rate of bipartite coherence distillation. This result allows us to precisely quantify the difference in operational powers between global incoherent operations, LIOCC, and local incoherent operations without classical communication. Finally, a bipartite mixed state is shown to have distillable entanglement if and only if entanglement can be distilled by LIOCC, and we strengthen the well-known Horodecki criterion for distillability.
Quantum walks, deformed relativity and Hopf algebra symmetries.
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-28
We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. PMID:27091171
Colored Extensions of GLq(2) Quantum Group and Related Noncommutative Planes
NASA Astrophysics Data System (ADS)
Basu-Mallick, B.
An infinite-dimensional quantum group, containing the standard GLq(2) and GLp,q(2) cases as different subalgebras, is constructed by using a colored braid group representation. It turns out that all algebraic relations occurring in this “colored” quantum group can be expressed in the Heisenberg-Weyl form, for a nontrivial choice of corresponding basis elements. Moreover a novel quadratic algebra, defined through Kac-Moody-like generators, is obtained by making some power series expansion of related monodromy matrix elements. The structure of invariant noncommutative planes associated with this “colored” quantum group has also been investigated.
NASA Astrophysics Data System (ADS)
Jang, Seogjoo
2016-06-01
This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.