Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Symmetry and Covariance of Non-relativistic Quantum Mechanics
Omote, Minoru; kamefuchi, Susumu
2000-01-01
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum mechanics.
Non-relativistic quantum mechanics
Puri, Ravinder R.
2017-01-01
This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...
A Signed Particle Formulation of Non-Relativistic Quantum Mechanics
Sellier, Jean Michel
2015-01-01
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schroedinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the val...
Effective approach to non-relativistic quantum mechanics
Jacobs, David M
2015-01-01
Boundary conditions on non-relativistic wavefunctions are generally not completely constrained by the basic precepts of quantum mechanics, so understanding the set of possible self-adjoint extensions of the Hamiltonian is required. For real physical systems, non-trivial self-adjoint extensions have been used to model contact potentials when those interactions are expected a priori. However, they must be incorporated into the effective description of any quantum mechanical system in order to capture possible short-distance physics that does not decouple in the low energy limit. Here, an approach is described wherein an artificial boundary is inserted at an intermediate scale on which boundary conditions may encode short-distance effects that are hidden behind the boundary. Using this approach, an analysis is performed of the free particle, harmonic oscillator, and Coulomb potential in three dimensions. Requiring measurable quantities, such as spectra and cross sections, to be independent of this artificial bou...
Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems
Ghosh, Pijush K
2011-01-01
A method to construct non-dissipative non-Dirac-hermitian relativistic quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving the Dirac matrices and the bosonic degrees of freedom in terms of non-Dirac-hermitian operators, which are hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. Several examples of exactly solvable non-dissipative non-Dirac-hermitian relativistic quantum systems are presented by establishing/employing a connection between Dirac equation and supersymmetry
Deconstructing non-dissipative non-Dirac-Hermitian relativistic quantum systems
Ghosh, Pijush K.
2011-08-01
A method to construct non-dissipative non-Dirac-Hermitian relativistic quantum system that is isospectral with a Dirac-Hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving the Dirac matrices and the bosonic degrees of freedom in terms of non-Dirac-Hermitian operators, which are Hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. Several examples of exactly solvable non-dissipative non-Dirac-Hermitian relativistic quantum systems are presented by establishing/employing a connection between Dirac equation and supersymmetry.
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called high energy substantially differ between non-relativistic and relativistic cases.
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems
2011-01-01
A method to construct non-dissipative non-Dirac-hermitian relativistic quantum system that is isospectral with a Dirac-hermitian Hamiltonian is presented. The general technique involves a realization of the basic canonical (anti-)commutation relations involving the Dirac matrices and the bosonic degrees of freedom in terms of non-Dirac-hermitian operators, which are hermitian in a Hilbert space that is endowed with a pre-determined positive-definite metric. Several examples of exactly solvabl...
Relativistic Quantum Communication
Hosler, Dominic
2013-01-01
In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tend...
A non-perturbative approach to relativistic quantum communication channels
Landulfo, Andre G S
2016-01-01
We investigate the transmission of both classical and quantum information between two arbitrary observers in globally hyperbolic spacetimes using a quantum field as a communication channel. The field is supposed to be in some arbitrary quasifree state and no choice of representation of its canonical commutation relations is made. Both sender and receiver posses some localized two-level quantum system with which they can interact with the quantum field to prepare the input and receive the output of the channel, respectively. The interaction between the two-level systems and the quantum field is such that one can trace out the field degrees of freedom exactly and thus obtain the quantum channel in a non-perturbative way. We end the paper determining the unassisted as well as the entanglement-assisted classical and quantum channel capacities.
Quantum Exact Non-Abelian Vortices in Non-relativistic Theories
Nitta, Muneto; Vinci, Walter
2014-01-01
Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex. In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap. We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level. We provide a concrete and experimentally realizable example of a three-component Bose-Einstein condensate with U(1) x U(2) symmetry. We first show, at the classical level, the existence of S^3 = S^1 |x S^2 (S^1 fibered over S^2) NG modes associated to the breaking U(2) -> U(1) on vortices, where S^1 and S^2 correspond to type I and II NG modes, respectively. We th...
Relativistic quantum mechanics; Mecanique quantique relativiste
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Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
Towards relativistic quantum geometry
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Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Huang, Chun Yu; Ma, Wenchao; Wang, Dong; Ye, Liu
2017-02-01
In this work, the quantum fisher information (QFI) and Bell non-locality of a multipartite fermionic system are investigated. Unlike the currently existing research of QFI, we focus our attention on the differences between quantum fisher information and Bell non-locality under the relativistic framework. The results show that although the relativistic motion affects the strength of the non-locality, it does not change the physical structure of non-locality. However, unlike the case of non-locality, the relativistic motion not only influence the precision of the QFI Fϕ but also broke the symmetry of the function Fϕ. The results also show that for a special multipartite system, , the number of particles of a initial state do not affect the Fθ. Furthermore, we also find that Fθ is completely unaffected in non-inertial frame if there are inertial observers. Finally, in view of the decay behavior of QFI and non-locality under the non-inertial frame, we proposed a effective scheme to battle against Unruh effect.
Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.
Relativistic quantum revivals.
Strange, P
2010-03-26
Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.
Optical realization of relativistic non-Hermitian quantum mechanics.
Longhi, Stefano
2010-07-02
Light propagation in distributed-feedback optical structures with gain or loss regions is shown to provide an accessible laboratory tool to visualize in optics the spectral properties of the one-dimensional Dirac equation with non-Hermitian interactions. Spectral singularities and PT symmetry breaking of the Dirac Hamiltonian are shown to correspond to simple observable physical quantities and are related to well-known physical phenomena such as resonance narrowing and laser oscillation.
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Handbook of relativistic quantum chemistry
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Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering
2017-03-01
This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
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.
Relativistic quantum information
Mann, R. B.; Ralph, T. C.
2012-11-01
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from
Relativistic Quantum Noninvasive Measurements
Bednorz, Adam
2014-01-01
Quantum weak, noninvasive measurements are defined in the framework of relativity. Invariance with respect to reference frame transformations of the results in different models is discussed. Surprisingly, the bare results of noninvasive measurements are invariant for certain class of models, but not the detection error. Consequently, any stationary quantum realism based on noninvasive measurements will break, at least spontaneously, relativistic invariance and correspondence principle at zero temperature.
Velocity operator and velocity field for spinning particles in (non-relativistic) quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Recami, E. [Bergamo Univ. (Italy). Facolta` di Ingegneria]|[INFN, Milan (Italy)]|[Campinas State Univ., SP (Brazil). Dept. of Applied Math.; Salesi, G. [Catania Univ. (Italy). Dip. di Fisica
1995-06-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, the paper introduces - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, a new (non-relativistic) velocity operator for a spin 1/2 particle is also proposed. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of- mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework, i.e. in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which the constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current.
A Structurally Relativistic Quantum Theory. Part 1: Foundations
Grgin, Emile
2012-01-01
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A new number system with the properties needed to support an inherently relativistic quantum theory is brought to light and investigated to a point sufficient for applications.
Non-Hermitian ${\\cal PT}$-symmetric relativistic quantum theory in an intensive magnetic field
Rodionov, V N
2016-01-01
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of physical parameters. This condition not only guarantees the reality of the eigenvalues of Hamiltonian operators, but also implies the preservation of the probabilities of the considered quantum processes. However as it was shown relatively recently (Bender, Boettcher 1998), Hermiticity is a sufficient but it is not a necessary condition. It turned out that among non-Hermitian Hamiltonians it is possible to allocate a number of such which have real energy spectra and can ensure the development of systems over time with preserving unitarity. This type of Hamiltonians includes so-called parity-time (${\\cal PT}$) symmetric models which is already used in various fields of modern physics. The most developed in this respect are models, which used in the field of ${\\cal PT}$-symmetric op...
Virial Theorem for Non-relativistic Quantum Fields in D Spatial Dimensions
Lin, Chris L
2015-01-01
The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in lower-dimensional systems. The potential appearance of a Jacobian $J$ due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the $J=1$ case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, $J=1$, is not natural, and the generalization to the case $J\
Non-relativistic Schroedinger theory on q-deformed quantum spaces III, Scattering theory
Wachter, H
2007-01-01
This is the third part of a paper about non-relativistic Schroedinger theory on q-deformed quantum spaces like the braided line or the three-dimensional q-deformed Euclidean space. Propagators for the free q-deformed particle are derived and their basic properties are discussed. A time-dependent formulation of scattering is proposed. In this respect, q-analogs of the Lippmann-Schwinger equation are given. Expressions for their iterative solutions are written down. It is shown how to calculate S-matrices and transition probabilities. Furthermore, attention is focused on the question what becomes of unitarity of S-matrices in a q-deformed setting. The examinations are concluded by a discussion of the interaction picture and its relation to scattering processes.
Bethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory
Kormos, M.; Mussardo, G.; Pozsgay, B.
2010-01-01
We show that the matrix elements of integrable models computed by the algebraic Bethe ansatz (BA) can be put in direct correspondence with the form factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe ansatz model can be regarded as a suitable non-relativistic
Relativistic and non-relativistic geodesic equations
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Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Wachter, H
2007-01-01
This is the second part of a paper about a q-deformed analog of non-relativistic Schroedinger theory. It applies the general ideas of part I and tries to give a description of one-particle states on q-deformed quantum spaces like the braided line or the q-deformed Euclidean space in three dimensions. Hamiltonian operators for the free q-deformed particle in one as well as three dimensions are introduced. Plane waves as solutions to the corresponding Schroedinger equations are considered. Their completeness and orthonormality relations are written down. Expectation values of position and momentum observables are taken with respect to one-particle states and their time-dependence is discussed. A potential is added to the free-particle Hamiltonians and q-analogs of the Ehrenfest theorem are derived from the Heisenberg equations of motion. The conservation of probability is proved.
Lock, Maximilian P E
2016-01-01
The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.
Numerical Relativistic Quantum Optics
2013-11-08
µm and a = 1. The condition for an atomic spectrum to be non-relativistic is Z α−1 ≈ 137, as follows from elementary Dirac theory. One concludes that...peculiar result that B0 = 1 TG is a weak field. At present, such fields are observed only in connection with astrophysical phenomena [14]. The highest...pulsars. The Astrophysical Journal, 541:367–373, Sep 2000. [15] M. Tatarakis, I. Watts, F.N. Beg, E.L. Clark, A.E. Dangor, A. Gopal, M.G. Haines, P.A
Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"
Yonaga, Kouki; Shibata, Naokazu
2016-01-01
We present a relativistic formulation of the quantum Hall effect on a Riemann sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term.We clarify particular features of the relativistic quantum Hall states with use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to relativistic quantum Hall states are investigated in detail.The mass term acts as an interporating parameter between the relativistic and non-relativistic quantum Hall effects. It is pointed out that the mass term inequivalently affects to many-body physics of the positive and negative Landau levels and brings instability of the Laughlin state of the positive first relativistic Landau level as a consequence of the "parity anomaly".
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory
Dolce, Donatello
2016-01-01
In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In thi...
Relativistic quantum chemistry on quantum computers
DEFF Research Database (Denmark)
Veis, L.; Visnak, J.; Fleig, T.
2012-01-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only...... the nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac......-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-NOT (CNOT) gates, which implement a proof...
Teleportation of the Relativistic Quantum Field
Laiho, R; Nazin, S S
2000-01-01
The process of teleportation of a completely unknown one-particle state of a free relativistic quantum field is considered. In contrast to the non-relativistic quantum mechanics, the teleportation of an unknown state of the quantum field cannot be in principle described in terms of a measurement in a tensor product of two Hilbert spaces to which the unknown state and the state of the EPR-pair belong. The reason is of the existence of a cyclic (vacuum) state common to both the unknown state and the EPR-pair. Due to the common vacuum vector and the microcausality principle (commutation relations for the field operators), the teleportation amplitude contains inevitably contributions which are irrelevant to the teleportation process. Hence in the relativistic theory the teleportation in the sense it is understood in the non-relativistic quantum mechanics proves to be impossible because of the impossibility of the realization of the appropriate measurement as a tensor product of the measurements related to the ind...
Postnikov, Sergey
2013-01-01
This work extends the seminal work of Gottfried on the two-body quantum physics of particles interacting through a delta-shell potential to many-body physics by studying a system of non-relativistic particles when the thermal De-Broglie wavelength of a particle is smaller than the range of the potential and the density is such that average distance between particles is smaller than the range. The ability of the delta-shell potential to reproduce some basic properties of the deuteron are examined. Relations for moments of bound states are derived. The virial expansion is used to calculate the first quantum correction to the ideal gas pressure in the form of the second virial coefficient. Additionally, all thermodynamic functions are calculated up to the first order quantum corrections. For small departures from equilibrium, the net flows of mass, energy and momentum, characterized by the coefficients of diffusion, thermal conductivity and shear viscosity, respectively, are calculated. Properties of the gas are...
Energy Technology Data Exchange (ETDEWEB)
Bodek, K.; Rozpędzik, D.; Zejma, J. [Jagiellonian University, Faculty of Physics, Astronomy and Applied Informatics, Reymonta 4, 30059 Kraków (Poland); Caban, P.; Rembieliński, J.; Włodarczyk, M. [University of Łódź, Faculty of Physics and Applied Informatics, Pomorska 149/153, 90236 Łódź (Poland); Ciborowski, J. [University of Warsaw, Faculty of Physics, Hoza 69, 00681 Warsaw (Poland); Enders, J.; Köhler, A. [Technische Universität Darmstadt, Institut für Kernphysik, Schlossgartenstraße 9, 64289 Darmstadt (Germany); Kozela, A. [Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31342 Kraków (Poland)
2013-11-07
The Polish-German project QUEST aims at studying relativistic quantum spin correlations of the Einstein-Rosen-Podolsky-Bohm type, through measurement of the correlation function and the corresponding probabilities for relativistic electron pairs. The results will be compared to theoretical predictions obtained by us within the framework of relativistic quantum mechanics, based on assumptions regarding the form of the relativistic spin operator. Agreement or divergence will be interpreted in the context of non-uniqueness of the relativistic spin operator in quantum mechanics as well as dependence of the correlation function on the choice of observables representing the spin. Pairs of correlated electrons will originate from the Mo/ller scattering of polarized 15 MeV electrons provided by the superconducting Darmstadt electron linear accelerator S-DALINAC, TU Darmstadt, incident on a Be target. Spin projections will be determined using the Mott polarimetry technique. Measurements (starting 2013) are planned for longitudinal and transverse beam polarizations and different orientations of the beam polarization vector w.r.t. the Mo/ller scattering plane. This is the first project to study relativistic spin correlations for particles with mass.
Directory of Open Access Journals (Sweden)
Abdelmadjid MAIRECHE
2015-09-01
Full Text Available We obtain here the modified bound-states solutions for central fraction power singular potential (C.F.P.S. in noncommutative 3-dimensional non relativistic quantum mechanics (NC-3D NRQM. It has been observed that the commutative energy spectra was changed, and replaced degenerate new states, depending on four quantum numbers: j, l and sz=±1/2 corresponding to the two spins states of electron by (up and down and the deformed Hamiltonian formed by two new operators: the first describes the spin-orbit interaction , while the second obtained Hamiltonian describes the modified Zeeman effect (containing ordinary Zeeman effect in addition to the usual commutative Hamiltonian. We showed that the isotropic commutative Hamiltonian HCFPS will be in non commutative space anisotropic Hamiltonian HNC-CFPS.
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Exotic Non-relativistic String
Casalbuoni, Roberto; Longhi, Giorgio
2007-01-01
We construct a classical non-relativistic string model in 3+1 dimensions. The model contains a spurion tensor field that is responsible for the non-commutative structure of the model. Under double dimensional reduction the model reduces to the exotic non-relativistic particle in 2+1 dimensions.
Point form relativistic quantum mechanics and relativistic SU(6)
Klink, W. H.
1993-01-01
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
Star Products for Relativistic Quantum Mechanics
Henselder, P.
2007-01-01
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
Critique of Conventional Relativistic Quantum Mechanics.
Fanchi, John R.
1981-01-01
Following an historical sketch of the development of relativistic quantum mechanics, a discussion of the still unresolved difficulties of the currently accepted theories is presented. This review is designed to complement and update the discussion of relativistic quantum mechanics presented in many texts used in college physics courses. (Author/SK)
Quantum information processing and relativistic quantum fields
Benincasa, Dionigi M. T.; Borsten, Leron; Buck, Michel; Dowker, Fay
2014-04-01
It is shown that an ideal measurement of a one-particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light-crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one-particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh-DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of field modes are shown to lead to superluminal signalling. Such detectors do, however, provide successful phenomenological models of atom-qubits interacting with quantum fields in a cavity but are valid only on time scales many orders of magnitude larger than the light-crossing time of the cavity.
Non-Hermitian interaction representation and its use in relativistic quantum mechanics
Znojil, Miloslav
2017-10-01
The textbook interaction-picture formulation of quantum mechanics is extended to cover the unitarily evolving systems in which the Hermiticity of the observables is guaranteed via an ad hoc amendment of the inner product in Hilbert space. These systems are sampled by the Klein-Gordon equation with a space- and time-dependent mass term.
Non relativistic diffeomorphism and the geometry of the fractional quantum Hall effect
Banerjee, Rabin
2015-01-01
We show that our recently proposed method\\cite{BMM1,BMM2,BMM3,BM4} of constructing nonrelativistic diffeomorphism invariant field theories by gauging the Galilean symmetry provides a natural connection with the geometry of the fractional quantum Hall effect (FQHE). Specifically, the covariant derivative that appears on gauging, exactly reproduces the form that yields the Hall viscosity and Wen-Zee shift \\cite{CYF}.
Quantum Information Processing and Relativistic Quantum Fields
Benincasa, Dionigi M T; Buck, Michel; Dowker, Fay
2014-01-01
It is shown that an ideal measurement of a one-particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light-crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one-particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh-DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of ...
Relativistic Quantum Teleportation with superconducting circuits
Friis, Nicolai; Truong, Kevin; Sabín, Carlos; Solano, Enrique; Johansson, Göran; Fuentes, Ivette
2012-01-01
We study the effects of relativistic motion on quantum teleportation and propose a realizable experiment where our results can be tested. We compute bounds on the optimal fidelity of teleportation when one of the observers undergoes non-uniform motion for a finite time. The upper bound to the optimal fidelity is degraded due to the observer's motion however, we discuss how this degradation can be corrected. These effects are observable for experimental parameters that are within reach of cutting-edge superconducting technology.
Directory of Open Access Journals (Sweden)
Marcos Moshinsky
2007-11-01
Full Text Available A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function is presented, and the propagator can be obtained later with an inverse Laplace transform. The method is illustrated through simple one dimensional examples and for time independent potentials, though it can be generalized to the derivation of more complicated propagators.
Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures
Longhi, Stefano
2011-01-01
Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.
Lattice Boltzmann equation for relativistic quantum mechanics.
Succi, Sauro
2002-03-15
Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation.
Renormalization group for non-relativistic fermions.
Shankar, R
2011-07-13
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.
The mathematical representation of physical objects and relativistic Quantum Mechanics
Romay, Enrique Ordaz
2004-01-01
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic physics, and quantum physics, especially in quantum field theory, is nothing else than the difference between the mathematics that is used on both branches of the physics. A common physical and mathematical origin for the analysis of the different systems brings b...
Covariant geometric quantization of non-relativistic Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the Schrodinger representation of V^*Q. We show that this quantization is equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R, that makes the quantum algebra of non-relativistic mechanics an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra, which provides quantum evolution in non-relativistic mechanics as a parallel transport along time.
The Calculation of Matrix Elements in Relativistic Quantum Mechanics
Ilarraza-Lomelí, A. C.; Valdés-Martínez, M. N.; Salas-Brito, A. L.; Martínez-y-Romero, R. P.; Núñez-Yépez, H. N
2001-01-01
Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring Professor L\\"owdin, we report on a new relation we have recently discovered between the matrix elements $$ and $$---where $\\beta$ is a Dirac matrix and the numbers distiguish between different radial eigenstates--- that allow for a simplification and hence f...
Tensor Fields in Relativistic Quantum Mechanics
Dvoeglazov, Valeriy V
2015-01-01
We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.
Alba, David; Lusanna, Luca
2009-01-01
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived non-canonical predictive coordinates. In it we quantize the frozen Jacobi data of the non-local 4-center of mass and the Wigner-covariant relative variables in an abstract (frame-independent) internal space whose existence is implied by Wigner-covariance. The formalism takes care of the properties of both relativistic bound states and scattering ones. There is a natural solution to the \\textit{relativistic localization problem}. The non-relativistic limit leads to standard quantum mechanics but with a frozen Hamilton-Jacobi description of the center of mass. Due to the \\textit{non-locality} of the Poincar\\'e generators the resulting theory of relativistic entanglement is both \\textit{kinematically non-local and spatially non-separable}: these properties, absent in the non-relat...
Effective photon mass and exact translating quantum relativistic structures
Haas, Fernando; Manrique, Marcos Antonio Albarracin
2016-04-01
Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density, and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spin effects are not decisive.
Towards universal quantum computation through relativistic motion
Bruschi, David Edward; Kok, Pieter; Johansson, Göran; Delsing, Per; Fuentes, Ivette
2013-01-01
We show how to use relativistic motion to generate continuous variable Gaussian cluster states within cavity modes. Our results can be demonstrated experimentally using superconducting circuits where tunable boundary conditions correspond to mirrors moving with velocities close to the speed of light. In particular, we propose the generation of a quadripartite square cluster state as a first example that can be readily implemented in the laboratory. Since cluster states are universal resources for universal one-way quantum computation, our results pave the way for relativistic quantum computation schemes.
Relativistic quantum metrology: exploiting relativity to improve quantum measurement technologies.
Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette
2014-05-22
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.
Relativistic classical integrable tops and quantum R-matrices
Levin, A.; Olshanetsky, M.; Zotov, A.
2014-07-01
We describe classical top-like integrable systems arising from the quantum exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in terms of the quantum non-dynamical R-matrix even at the classical level, where the Planck constant plays the role of the relativistic deformation parameter in the sense of Ruijsenaars and Schneider (RS). The integrable systems (relativistic tops) are described as multidimensional Euler tops, and the inertia tensors are written in terms of the quantum and classical R-matrices. A particular case of gl N system is gauge equivalent to the N-particle RS model while a generic top is related to the spin generalization of the RS model. The simple relation between quantum R-matrices and classical Lax operators is exploited in two ways. In the elliptic case we use the Belavin's quantum R-matrix to describe the relativistic classical tops. Also by the passage to the noncommutative torus we study the large N limit corresponding to the relativistic version of the nonlocal 2d elliptic hydrodynamics. Conversely, in the rational case we obtain a new gl N quantum rational non-dynamical R-matrix via the relativistic top, which we get in a different way — using the factorized form of the RS Lax operator and the classical Symplectic Hecke (gauge) transformation. In particular case of gl2 the quantum rational R-matrix is 11-vertex. It was previously found by Cherednik. At last, we describe the integrable spin chains and Gaudin models related to the obtained R-matrix.
Microscopic picture of non-relativistic classicalons
Energy Technology Data Exchange (ETDEWEB)
Berkhahn, Felix; Müller, Sophia; Niedermann, Florian; Schneider, Robert, E-mail: felix.berkhahn@physik.lmu.de, E-mail: sophia.x.mueller@physik.uni-muenchen.de, E-mail: florian.niedermann@physik.lmu.de, E-mail: robert.bob.schneider@physik.uni-muenchen.de [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 Munich (Germany)
2013-08-01
A theory of a non-relativistic, complex scalar field with derivatively coupled interaction terms is investigated. This toy model is considered as a prototype of a classicalizing theory and in particular of general relativity, for which the black hole constitutes a prominent example of a classicalon. Accordingly, the theory allows for a non-trivial solution of the stationary Gross-Pitaevskii equation corresponding to a black hole in the case of GR. Quantum fluctuations on this classical background are investigated within the Bogoliubov approximation. It turns out that the perturbative approach is invalidated by a high occupation of the Bogoliubov modes. Recently, it was proposed that a black hole is a Bose-Einstein condensate of gravitons that dynamically ensures to stay at the verge of a quantum phase transition. Our result is understood as an indication for that claim. Furthermore, it motivates a non-linear numerical analysis of the model.
Wachter, H
2007-01-01
The aim of these three papers (I, II, and III) is to develop a q-deformed version of non-relativistic Schroedinger theory. Paper I introduces the fundamental mathematical and physical concepts. The braided line and the three-dimensional q-deformed Euclidean space play the role of position space. For both cases the algebraic framework is extended by a time element. A short review of the elements of q-deformed analysis on the spaces under consideration is given. The time evolution operator is introduced in a consistent way and its basic properties are discussed. These reasonings are continued by proposing q-deformed analogs of the Schroedinger and the Heisenberg picture.
Relativistic quantum Darwinism in Dirac fermion and graphene systems
Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis
2012-02-01
We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.
A Quantum Relativistic Prisoner's Dilemma Cellular Automaton
Alonso-Sanz, Ramón; Carvalho, Márcio; Situ, Haozhen
2016-10-01
The effect of variable entangling on the dynamics of a spatial quantum relativistic formulation of the iterated prisoner's dilemma game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests.
Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.
2017-09-01
The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.
Non-Relativistic Spacetimes with Cosmological Constant
Aldrovandi, R.; Barbosa, A. L.; Crispino, L.C.B.; Pereira, J. G.
1998-01-01
Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible ...
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
Optimization of a relativistic quantum mechanical engine
Peña, Francisco J.; Ferré, Michel; Orellana, P. A.; Rojas, René G.; Vargas, P.
2016-08-01
We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.
Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies
Ahmadi, Mehdi; Friis, Nicolai; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette
2013-01-01
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 (QFT). QFT 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 QFT including proper times and acce...
Non-relativistic classical mechanics for spinning particles
Salesi, G
2004-01-01
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which suggests classical interpretations for tunnel effect and quantum potential.
Relativistic non-equilibrium thermodynamics revisited
García-Colin, L S
2006-01-01
Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting equations for the entropy production and the local internal energy have the same structure as the non-relativistic ones. Assuming linear constitutive laws, it is shown that consistency is obtained both with the laws of thermodynamics and causality.
Path integration in relativistic quantum mechanics
Redmount, I H; Redmount, Ian H.; Suen, Wai-Mo
1993-01-01
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.
Relativistic Classical Integrable Tops and Quantum R-matrices
Levin, A; Zotov, A
2014-01-01
We describe classical top-like integrable systems arising from the quantum exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in terms of the quantum non-dynamical $R$-matrix even at the classical level, where the Planck constant plays the role of the relativistic deformation parameter in the sense of Ruijsenaars and Schneider (RS). The integrable systems (relativistic tops) are described as multidimensional Euler tops, and the inertia tensors are written in terms of the quantum and classical $R$-matrices. A particular case of ${\\rm gl}_N$ system is gauge equivalent to the $N$-particle RS model while a generic top is related to the spin generalization of the RS model. The simple relation between quantum $R$-matrices and classical Lax operators is exploited in two ways. In the elliptic case we use the Belavin's quantum $R$-matrix to describe the relativistic classical tops. Also by the passage to the noncommutative torus we study the large $N$ limit corresponding to the relat...
Weibel instability in relativistic quantum plasmas
Mendonça, J. T.; Brodin, G.
2015-08-01
Generation of quasi-static magnetic fields, due to the Weibel instability is studied in a relativistic quantum plasma. This instability is induced by a temperature anisotropy. The dispersion relation and growth rates for low frequency electromagnetic perturbations are derived using a wave-kinetic equation which describes the evolution of the electron Wigner quasi-distribution. The influence of parallel kinetic effects is discussed in detail.
On the Velocity of Moving Relativistic Unstable Quantum Systems
Directory of Open Access Journals (Sweden)
K. Urbanowski
2015-01-01
Full Text Available We study properties of moving relativistic quantum unstable systems. We show that in contrast to the properties of classical particles and quantum stable objects the velocity of freely moving relativistic quantum unstable systems cannot be constant in time. We show that this new quantum effect results from the fundamental principles of the quantum theory and physics: it is a consequence of the principle of conservation of energy and of the fact that the mass of the quantum unstable system is not defined. This effect can affect the form of the decay law of moving relativistic quantum unstable systems.
Entropy current for non-relativistic fluid
Banerjee, Nabamita; Jain, Akash; Roychowdhury, Dibakar
2014-01-01
We study transport properties of a parity-odd, non-relativistic charged fluid in presence of background electric and magnetic fields. To obtain stress tensor and charged current for the non-relativistic system we start with the most generic relativistic fluid, living in one higher dimension and reduce the constituent equations along the light-cone direction. We also reduce the equation satisfied by the entropy current of the relativistic theory and obtain a consistent entropy current for the non-relativistic system (we call it "canonical form" of the entropy current). Demanding that the non-relativistic fluid satisfies the second law of thermodynamics we impose constraints on various first order transport coefficients. For parity even fluid, this is straight forward; it tells us positive definiteness of different transport coefficients like viscosity, thermal conductivity, electric conductivity etc. However for parity-odd fluid, canonical form of the entropy current fails to confirm the second law of thermody...
Do non-relativistic neutrinos oscillate?
Akhmedov, Evgeny
2017-07-01
We study the question of whether oscillations between non-relativistic neutrinos or between relativistic and non-relativistic neutrinos are possible. The issues of neutrino production and propagation coherence and their impact on the above question are discussed in detail. It is demonstrated that no neutrino oscillations can occur when neutrinos that are non-relativistic in the laboratory frame are involved, except in a strongly mass-degenerate case. We also discuss how this analysis depends on the choice of the Lorentz frame. Our results are for the most part in agreement with Hinchliffe's rule.
Geometric Models of the Quantum Relativistic Rotating Oscillator
Cotaescu, I I
1997-01-01
A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual isotropic harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is different. As in the case of the (1+1) models, these will have even countable energy spectra or mixed ones, with a finite discrete sequence and a continuous part. In addition, all these spectra, except that of the pure anti-de Sitter model, will have a fine-structure, given by a rotator-like term.
Non-Relativistic Limit of the Dirac Equation
Ajaib, Muhammad Adeel
2016-01-01
We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.
Relativistic quantum information theory and quantum reference frames
Palmer, Matthew C
2013-01-01
This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of localised qubits in curved spacetimes. For example, this concerns quantum experiments on free-space photons and electrons in the vicinity of the Earth. From field theory a description of localised qubits that traverse classical trajectories in curved spacetimes is obtained, for photons and massive spin-1/2 fermions. The equations governing the evolution of the two-dimensional quantum state and its absolute phase are determined. Quantum information theory of these qubits is then developed. The Stern-Gerlach measurement formalism for massive spin-1/2 fermions is also derived from field theory. In the latter category of research, the process of changing reference frames is considered for the case where the reference frames are quantum systems. As part of this process, it is shown that...
On the velocity of moving relativistic unstable quantum systems
Urbanowski, K
2015-01-01
We study properties of moving relativistic quantum unstable systems. We show that in contrast to the properties of classical particles and quantum stable objects the velocity of moving freely relativistic quantum unstable systems can not be constant in time. We show that this effect results from the fundamental principles of the quantum theory and physics: It is a consequence of the principle of conservation of energy and of the fact that the mass of the quantum unstable system is not definite.
Lorentz covariant reduced-density-operator theory for relativistic quantum information processing
Ahn, D; Hwang, S W; Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo
2003-01-01
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. The formulation presented in this work is general and might be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.
Balance equations in semi-relativistic quantum hydrodynamics
Ivanov, A Yu; Kuz'menkov, L S
2014-01-01
Method of the quantum hydrodynamics has been applied in quantum plasmas studies. As the first step in our consideration, derivation of classical semi-relativistic (i. e. described by the Darwin Lagrangian on microscopic level) hydrodynamical equations is given after a brief review of method development. It provides better distinguishing between classic and quantum semi-relativistic effects. Derivation of the classical equations is interesting since it is made by a natural, but not very widespread method. This derivation contains explicit averaging of the microscopic dynamics. Derivation of corresponding quantum hydrodynamic equations is presented further. Equations are obtained in the five-momentum approximation including the continuity equation, Euler and energy balance equations. It is shown that relativistic corrections lead to presence of new quantum terms in expressions for a force field, a work field etc. The semi-relativistic generalization of the quantum Bohm potential is obtained. Quantum part of the...
Quantum ion-acoustic solitary waves in weak relativistic plasma
Indian Academy of Sciences (India)
Biswajit Sahu
2011-06-01
Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized twospecies relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive perturbation method. A linear dispersion relation is also obtained taking into account the relativistic effect. The properties of quantum ion-acoustic solitary waves, obtained from the deformed KdV equation, are studied taking into account the quantum mechanical effects in the weak relativistic limit. It is found that relativistic effects signiﬁcantly modify the properties of quantum ion-acoustic waves. Also the effect of the quantum parameter on the nature of solitary wave solutions is studied in some detail.
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Radożycki, Tomasz
2016-11-01
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by incorporating into them the Heisenberg uncertainty relation between position and momentum. Even the crude form of this incorporation makes the agreement between classical and quantum distributions unexpectedly good, except for the small area, where classical momenta are large. It is demonstrated that the slight improvement of this form, makes the classical distribution very similar to the quantum one in the whole space. The obtained results are much better than those from the WKB method. The paper is devoted to ground states, but the method applies to excited states too.
Causal localizations in relativistic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Castrigiano, Domenico P. L., E-mail: castrig@ma.tum.de; Leiseifer, Andreas D., E-mail: andreas.leiseifer@tum.de [Fakultät für Mathematik, TU München, Boltzmannstraße 3, 85747 Garching (Germany)
2015-07-15
Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac’s localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.
The relativistic bound states of a non-central potential
Indian Academy of Sciences (India)
MAHDI ESHGHI; HOSSEIN MEHRABAN; SAMEER MIKHDAIR
2017-04-01
We investigate the relativistic effects of a moving particle in the field of a pseudoharmonic oscillatory ring-shaped potential under the spin and pseudospin symmetric Dirac wave equation. We obtain the bound-state energy eigenvalue equation and the corresponding two-components spinor wave functions by using the formalism of supersymmetric quantum mechanics (SUSYQM). Furthermore, the non-relativistic limits are obtained by simply making a proper replacement of parameters. The thermodynamic properties are also studied. Our numerical results for the energy eigenvalues are also presented.
Quasiparticle excitations in relativistic quantum field theory
Arteaga, Daniel
2008-01-01
We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.
General relativistic corrections and non-Gaussianity
Villa, Eleonora; Matarrese, Sabino
2014-01-01
General relativistic cosmology cannot be reduced to linear relativistic perturbations superposed on an isotropic and homogeneous (Friedmann-Robertson-Walker) background, even though such a simple scheme has been successfully applied to analyse a large variety of phenomena (such as Cosmic Microwave Background primary anisotropies, matter clustering on large scales, weak gravitational lensing, etc.). The general idea of going beyond this simple paradigm is what characterises most of the efforts made in recent years: the study of second and higher-order cosmological perturbations including all general relativistic contributions -- also in connection with primordial non-Gaussianities -- the idea of defining large-scale structure observables directly from a general relativistic perspective, the various attempts to go beyond the Newtonian approximation in the study of non-linear gravitational dynamics, by using e.g., Post-Newtonian treatments, are all examples of this general trend. Here we summarise some of these ...
Heisenberg scaling in relativistic quantum metrology
Friis, Nicolai; Fuentes, Ivette; Dür, Wolfgang
2015-01-01
We address the issue of precisely estimating small parameters encoded in a general linear transformation of the modes of a bosonic quantum field. Such Bogoliubov transformations frequently appear in the context of quantum optics. We provide a recipe for computing the quantum Fisher information for arbitrary pure initial states. We show that the maximally achievable precision of estimation is inversely proportional to the squared average particle number, and that such Heisenberg scaling requires non-classical, but not necessarily entangled states. Our method further allows to quantify losses in precision arising from being able to monitor only finitely many modes, for which we identify a lower bound.
Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems
Wang, Guanglei; Xu, Hongya; Huang, Liang; Lai, Ying-Cheng
2017-01-01
Zitterbewegung (ZB) is a phenomenon in relativistic quantum systems where the electron wave packet exhibits a trembling or oscillating behavior during its motion, caused by its interaction or coupling with the negative energy state. To directly observe ZB in electronic systems is difficult, due to the challenges associated with the small amplitude of the motion which is of the order of Compton wavelength. Photonic systems offer an alternative paradigm. We exploit the concept of pseudo parity-time (pseudo { P }{ T }) symmetry to study ZB in non-Hermitian quantum systems implemented as an experimentally feasible optical waveguide array. In particular, the non-Hermitian Hamiltonian is realized through evanescent coupling among the waveguides to form a one-dimensional lattice with periodic modulations in gain and loss along the guiding direction. As the modulation frequency is changed, we obtain a number of phenomena including periodically suppressed ZB trembling, spatial energy localization, and Hermitian-like ZB oscillations. We calculate phase diagrams indicating the emergence of different types of dynamical behaviors of the relativistic non-Hermitian quantum system in an experimentally justified parameter space. We provide numerical results and a physical analysis to explain the distinct dynamical behaviors revealed by the phase diagrams. Our findings provide a deeper understanding of both the relativistic ZB phenomenon and non-Hermitian pseudo-{ P }{ T } systems, with potential applications in controlling/harnessing light propagation in waveguide-based optical systems.
Relativistic quantum mechanics and introduction to field theory
Energy Technology Data Exchange (ETDEWEB)
Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1996-12-01
The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.
Isotropic Landau levels of relativistic and non-relativistic fermions in 3D flat space
Li, Yi; Wu, Congjun
2012-02-01
The usual Landau level quantization, as demonstrated in the 2D quantum Hall effect, is crucially based on the planar structure. In this talk, we explore its 3D counterpart possessing the full 3D rotational symmetry as well as the time reversal symmetry. We construct the Landau level Hamiltonians in 3 and higher dimensional flat space for both relativistic and non-relativistic fermions. The 3D cases with integer fillings are Z2 topological insulators. The non-relativistic version describes spin-1/2 fermions coupling to the Aharonov-Casher SU(2) gauge field. This system exhibits flat Landau levels in which the orbital angular momentum and the spin are coupled with a fixed helicity. Each filled Landau level contributes one 2D helical Dirac Fermi surface at an open boundary, which demonstrates the Z2 topological nature. A natural generalization to Dirac fermions is found as a square root problem of the above non-relativistic version, which can also be viewed as the Dirac equation defined on the phase space. All these Landau level problems can be generalized to arbitrary high dimensions systematically. [4pt] [1] Yi Li and Congjun Wu, arXiv:1103.5422.[0pt] [2] Yi Li, Ken Intriligator, Yue Yu and Congjun Wu, arXiv:1108.5650.
Non-Newtonian Properties of Relativistic Fluids
Koide, Tomoi
2010-01-01
We show that relativistic fluids behave as non-Newtonian fluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell-Cattaneo-Vernotte (MCV) equation. By using the modified MCV equation, we obtain the causal dissipative relativistic (CDR) fluid dynamics, where unphysical propagation with infinite velocity does not exist. We further show that the problems of the violation of causality and instability are intimately related, and the relativistic Navier-Stokes equation is inadequate as the theory of relativistic fluids. Finally, the new microscopic formula to calculate the transport coefficients of the CDR fluid dynamics is discussed. The result of the microscopic formula is consistent with that of the Boltzmann equation, i.e., Grad's moment method.
Relativistic systems and their evolution in quantum tomography
Arkhipov, AS; Man'ko, [No Value
2004-01-01
We propose a method of writing the relativistic equation for the probability-distribution function in the tomographic representation. The connection with the quantum-mechanical description of a zero-spin particle is discussed.
Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics
Bauer, M
2016-01-01
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1
On a Probabilistic Interpretation of Relativistic Quantum Mechanics
Gorobey, Natalia; Lukyanenko, Inna
2010-01-01
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After that, quantum dynamics of a particle in the 3D space obtains the ordinary probabilistic interpretation. In addition, the classical dynamics of the Minkowsky time variable may serve as a tool for "observation" of the quantum dynamics of a particle. A relativistic analog of the hydrogen atom energy spectrum is obtained.
Relativistic and non-relativistic solitons in plasmas
Barman, Satyendra Nath
This thesis entitled as "Relativistic and Non-relativistic Solitons in Plasmas" is the embodiment of a number of investigations related to the formation of ion-acoustic solitary waves in plasmas under various physical situations. The whole work of the thesis is devoted to the studies of solitary waves in cold and warm collisionless magnetized or unmagnetized plasmas with or without relativistic effect. To analyze the formation of solitary waves in all our models of plasmas, we have employed two established methods namely - reductive perturbation method to deduce the Korteweg-de Vries (KdV) equation, the solutions of which represent the important but near exact characteristic concepts of soliton-physics. Next, the pseudopotential method to deduce the energy integral with total nonlinearity in the coupling process for exact characteristic results of solitons has been incorporated. In Chapter 1, a brief description of plasma in nature and laboratory and its generation are outlined elegantly. The nonlinear differential equations to characterize solitary waves and the relevant but important methods of solutions have been mentioned in this chapter. The formation of solitary waves in unmagnetized and magnetized plasmas, and in relativistic plasmas has been described through mathematical entity. Applications of plasmas in different fields are also put forwarded briefly showing its importance. The study of plasmas as they naturally occur in the universe encompasses number of topics including sun's corona, solar wind, planetary magnetospheres, ionospheres, auroras, cosmic rays and radiation. The study of space weather to understand the universe, communications and the activities of weather satellites are some useful areas of space plasma physics. The surface cleaning, sterilization of food and medical appliances, killing of bacteria on various surfaces, destroying of viruses, fungi, spores and plasma coating in industrial instruments ( like computers) are some of the fields
Solved and unsolved problems in relativistic quantum chemistry
Energy Technology Data Exchange (ETDEWEB)
Kutzelnigg, Werner, E-mail: werner.kutzelnigg@rub.de [Lehrstuhl fuer Theoretische Chemie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
2012-02-20
Graphical abstract: The graphical abstract represents the Dirac-Coulomb Hamiltonian in Fock space in a diagrammatic notation. A line (vertical or slanted) with an upgoing arrow represents an eletron, with a downgoing arrow a positron. A cross in the first line means the potential created by a nucleus, a broken line represents the Coulomb interaction between electrons and positrons. Highlights: Black-Right-Pointing-Pointer Relativistic many-electron theory needs a Fock space and a field-dependent vacuum. Black-Right-Pointing-Pointer A good starting point is QED in Coulomb gauge without transversal photons. Black-Right-Pointing-Pointer The Dirac underworld picture is obsolete. Black-Right-Pointing-Pointer A kinetically balanced even-tempered Gaussian basis is complete. Black-Right-Pointing-Pointer 'Quantum chemistry in Fock space is preferable over QED. - Abstract: A hierarchy of approximations in relativistic many-electron theory is discussed that starts with the Dirac equation and its expansion in a kinetically balanced basis, via a formulation of non-interacting electrons in Fock space (which is the only consistent way to deal with negative-energy states). The most straightforward approximate Hamiltonian for interacting electrons is derived from quantum electrodynamics (QED) in Coulomb gauge with the neglect of transversal photons. This allows an exact (non-perturbative) decoupling of the electromagnetic field from the fermionic field. The electric interaction of the fermions is non-retarded and non-quantized. The quantization of the fermionic field leads to a polarizable vacuum. The simplest (but somewhat problematic) approximation is a no-pair projected theory with external-field projectors. The Dirac-Coulomb operator in configuration space (first quantization) is not acceptable, even if the Brown-Ravenhall disease is much less virulent than often claimed. Effects of transversal photons, such as the Breit interaction and renormalized self-interaction can be
Generalized quantum similarity in atomic systems: A quantifier of relativistic effects
Martín, A. L.; Angulo, J. C.; Antolín, J.; López-Rosa, S.
2017-02-01
Quantum similarity between Hartree-Fock and Dirac-Fock electron densities reveals the depth of relativistic effects on the core and valence regions in atomic systems. The results emphasize the relevance of differences in the outermost subshells, as pointed out in recent studies by means of Shannon-like functionals. In this work, a generalized similarity functional allows us to go far beyond the Shannon-based analyses. The numerical results for systems throughout the Periodic Table show that discrepancies between the relativistic and non-relativistic descriptions are patently governed by shell-filling patterns.
Noldus, Johan
2005-01-01
This paper can be seen as an exercise in how to adapt quantum mechanics from a strict relativistic perspective while being respectful and critical towards the experimental achievements of the contemporary theory. The result is a fully observer independent relativistic quantum mechanics for N particle systems without tachyonic solutions. A remaining worry for the moment is Bell's theorem.
Quantum mechanics with non-unitary symmetries
Bistrovic, B
2000-01-01
This article shows how to properly extend symmetries of non-relativistic quantum mechanics to include non-unitary representations of Lorentz group for all spins. It follows from this that (almost) all existing relativistic single particle Lagrangians and equations are incorrect. This is shown in particular for Dirac's equation and Proca equations. It is shown that properly constructed relativistic extensions have no negative energies, zitterbewegung effects and have proper symmetric energy-momentum tensor and angular momentum density tensor. The downside is that states with negative norm are inevitable in all representations.
Energy Technology Data Exchange (ETDEWEB)
Rehman, M. A.; Qureshi, M. N. S. [Department of Physics, GC University, Kachery Road, Lahore 54000 (Pakistan); Shah, H. A. [Department of Physics, Forman Christian College, Ferozepur Road, Lahore 54600 (Pakistan); Masood, W. [COMSATS, Institute of Information Technology, Park Road, Chak Shehzad, Islamabad 44000 (Pakistan); National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan)
2015-10-15
Nonlinear circularly polarized Alfvén waves are studied in magnetized nonrelativistic, relativistic, and ultrarelativistic degenerate Fermi plasmas. Using the quantum hydrodynamic model, Zakharov equations are derived and the Sagdeev potential approach is used to investigate the properties of the electromagnetic solitary structures. It is seen that the amplitude increases with the increase of electron density in the relativistic and ultrarelativistic cases but decreases in the nonrelativistic case. Both right and left handed waves are considered, and it is seen that supersonic, subsonic, and super- and sub-Alfvénic solitary structures are obtained for different polarizations and under different relativistic regimes.
Irreversible degradation of quantum coherence under relativistic motion
Wang, Jieci; Jing, Jiliang; Fan, Heng
2016-01-01
We study the dynamics of quantum coherence under Unruh thermal noise and seek under which condition the coherence can be frozen in a relativistic setting. We find that the quantum coherence can not be frozen for any acceleration due to the effect of Unruh thermal noise. We also find that quantum coherence is more robust than entanglement under the effect of Unruh thermal noise and therefore the coherence type quantum resources are more accessible for relativistic quantum information processing tasks. Besides, the dynamic of quantum coherence is found to be more sensitive than entanglement to the preparation of the detectors' initial state and the atom-field coupling strength, while it is less sensitive than entanglement to the acceleration of the detector.
Spacetime Dependence of Local Temperature in Relativistic Quantum Field Theory
Gransee, Michael
2016-01-01
The spacetime dependence of the inverse temperature four-vector $\\boldsymbol{\\beta}$ for certain states of the quantized Klein-Gordon field on (parts of) Minkowski spacetime is discussed. These states fulfill a recently proposed version of the Kubo-Martin-Schwinger (KMS) boundary value condition, the so-called "local KMS (LKMS) condition". It turns out that, depending on the mass parameter $m\\geq 0$, any such state can be extended either (i) to a LKMS state on some forward or backward lightcone, with $\\boldsymbol{\\beta}$ depending linearily on spacetime, or (ii) to a thermal equilibrium (KMS) state on all of Minkowski space with constant $\\boldsymbol{\\beta}$. This parallels previously known results for local thermal equilibrium (LTE) states of the quantized Klein-Gordon field. Furthermore, in the case of a massless field our results point to a discrepancy with some classic results in general approaches to (non-quantum) relativistic thermodynamics.
Quantum regime of a free-electron laser: relativistic approach
Kling, Peter; Sauerbrey, Roland; Preiss, Paul; Giese, Enno; Endrich, Rainer; Schleich, Wolfgang P.
2017-01-01
In the quantum regime of the free-electron laser, the dynamics of the electrons is not governed by continuous trajectories but by discrete jumps in momentum. In this article, we rederive the two crucial conditions to enter this quantum regime: (1) a large quantum mechanical recoil of the electron caused by the scattering with the laser and the wiggler field and (2) a small energy spread of the electron beam. In contrast to our recent approach based on nonrelativistic quantum mechanics in a co-moving frame of reference, we now pursue a model in the laboratory frame employing relativistic quantum electrodynamics.
On the Theory of Resonances in Non-Relativistic QED and Related Models
DEFF Research Database (Denmark)
Abou Salem, Walid K.; Faupin, Jeremy; Froehlich, Juerg;
We study the mathematical theory of quantum resonances in the standard model of non-relativistic QED and in Nelson's model. In particular, we estimate the survival probability of metastable states corresponding to quantum resonances and relate the resonances to poles of an analytic continuation...
Remark on charge conjugation in the non relativistic limit
Cabo-Montes de Oca, Alejandro; Rojas, H P; Socolovsky, M
2005-01-01
We study the non relativistic limit of the charge conjugation operation $\\cal C$ in the context of the Dirac equation coupled to an electromagnetic field. The limit is well defined and, as in the relativistic case, $\\cal C$, $\\cal P$ (parity) and $\\cal T$ (time reversal) are the generators of a matrix group isomorphic to a semidirect sum of the dihedral group of eight elements and $\\Z_2$. The existence of the limit is supported by an argument based in quantum field theory. Finally, if one complexifies the Lorentz group and therefore the galilean spacetime $x_\\mu$, then the explicit form of the matrix for $\\cal C$ allows to interpret it, in this context, as the complex conjugation of the spatial coordinates: $\\vec{x} \\to \\vec{x}^*$. This result is natural in a fiber bundle description.
Supersymmetric solutions for non-relativistic holography
Energy Technology Data Exchange (ETDEWEB)
Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Blackett Laboratory, Imperial College, London (United Kingdom)]|[Institute for Mathematical Sciences, Imperial College, London (United Kingdom)
2009-01-15
We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic conformal algebra for various values of dynamical exponent z{>=}4 and z{>=}3, respectively. The solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds and generalise the known solutions with dynamical exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively. (orig.)
Quadratic relativistic invariant and metric form in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Pissondes, Jean-Claude [DAEC, Observatoire de Paris-Meudon, Meudon (France)
1999-04-16
The Klein-Gordon equation is recovered in the framework of the theory of scale-relativity, first in the absence, then in the presence of an electromagnetic field. In this framework, spacetime at quantum scales is characterized by non-differentiability and continuity, which involves the introduction of explicit resolution-dependent fractal coordinates. Such a description leads to the notion of scale-covariance and its corresponding tool, a scale-covariant; derivative operator {theta}/ds. Due to it, the Klein-Gordon equation is written as an equation of free motion and interpreted as a geodesic equation in fractal spacetime. However, we obtain a new form for the corresponding relativistic invariant, which differs from that of special and general relativity. Characterizing quantum mechanics in the present approach, it is not simply quadratic in terms of velocities, but contains an extra term of divergence, which is intrinsically present in its expression. Moreover, in spite of the scale-covariance statements of the present theory, we find an extra term of current in addition to the Lorentz force, within the equations of motion with electromagnetic field written in this framework. Finally, we introduce another tool - a 'symmetric product' - from the requirement of recovering the usual form of the Leibniz rule written with the operator {theta}/ds. This tool allows us to write most equations in this framework in their usual classical form; in particular the simple rules of differentiation, the equations of motion with field and also our new relativistic invariant. (author)
Convex Decompositions of Thermal Equilibrium for Non-interacting Non-relativistic Particles
Chenu, Aurelia; Branczyk, Agata; Sipe, John
2016-05-01
We provide convex decompositions of thermal equilibrium for non-interacting non-relativistic particles in terms of localized wave packets. These quantum representations offer a new tool and provide insights that can help relate to the classical picture. Considering that thermal states are ubiquitous in a wide diversity of fields, studying different convex decompositions of the canonical ensemble is an interesting problem by itself. The usual classical and quantum pictures of thermal equilibrium of N non-interacting, non-relativistic particles in a box of volume V are quite different. The picture in classical statistical mechanics is about (localized) particles with a range of positions and velocities; in quantum statistical mechanics, one considers the particles (bosons or fermions) associated with energy eigenstates that are delocalized through the whole box. Here we provide a representation of thermal equilibrium in quantum statistical mechanics involving wave packets with a localized coordinate representation and an expectation value of velocity. In addition to derive a formalism that may help simplify particular calculations, our results can be expected to provide insights into the transition from quantum to classical features of the fully quantum thermal state.
On two misconceptions in current relativistic quantum information
Bradler, Kamil
2011-01-01
We describe two problems current relativistic quantum information suffers from. The first point is an explanation of an alleged ambiguity of entropic quantities detected in a number of publications and incorrectly resolved in [M. Montero and E. Mart{\\i}n-Mart{\\i}nez, Physical Review A 83, 062323 (2011)]. We found that the problem arises due to wrong algebraic manipulations with fermions and ignoring the superselection rule for bosons and fermions. This leads to a misinterpretation of certain entropic quantities when applied to fermion fields. The second discussed point is to alert to a conceptual misunderstanding of the role of entanglement (and quantum correlations in general) in some of the studied relativistic scenarios. Instead, we argue in favor of investigating capacities of quantum channels induced by the relevant physical processes as dictated by quantum Shannon theory.
A quantum relativistic battle of the sexes cellular automaton
Alonso-Sanz, Ramón; Situ, Haozhen
2017-02-01
The effect of variable entangling on the dynamics of a spatial quantum relativistic formulation of the iterated battle of the sexes game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests. Despite the full range of quantum parameters initially accessible, they promptly converge into fairly stable configurations, that often show rich spatial structures in simulations with no negligible entanglement.
Effect of relativistic motion on witnessing nonclassicality of quantum states
Checińska, Agata; Lorek, Krzysztof; Dragan, Andrzej
2017-01-01
We show that the operational definition of nonclassicality of a quantum state depends on the motion of the observer. We use the relativistic Unruh-DeWitt detector model to witness nonclassicality of the probed field state. It turns out that the witness based on the properties of the P representation of the quantum state depends on the trajectory of the detector. Inertial and noninertial motion of the device have qualitatively different impact on the performance of the witness.
Relativistic n-body wave equations in scalar quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Emami-Razavi, Mohsen [Centre for Research in Earth and Space Science, York University, Toronto, Ontario, M3J 1P3 (Canada)]. E-mail: mohsen@yorku.ca
2006-09-21
The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.
Exact solution of the relativistic quantum Toda chain
Zhang, Xin; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng
2016-01-01
The relativistic quantum Toda chain model is studied with the generalized algebraic Bethe Ansatz method. By employing a set of local gauge transformations, proper local vacuum states can be obtained for this model. The exact spectrum and eigenstates of the model are thus constructed simultaneously.
Bags in relativistic quantum field theory with spontaneously broken symmetry
Energy Technology Data Exchange (ETDEWEB)
Wadati, M.; Matsumoto, H.; Umezawa, H.
1978-08-15
Presented is a microscopic derivation of bags from a relativistic quantum theory with spontaneously broken symmetry. The static energy of a bag whose singularity is the surface of a sphere coincides with the volume tension in the MIT bag theory. A similarity between the bags and the point defects in crystals is pointed out.
Holographic thermalization from non relativistic branes
Roychowdhury, Dibakar
2016-01-01
In this paper, based on the fundamental principles of Gauge/gravity duality and considering a \\textit{global quench}, we probe the physics of thermalization for a special class of strongly coupled non relativistic QFTs by computing the entanglement entropy of the plasma. The isometry group of such QFTs is comprised of the generators of the Schr\\"odinger algebra which could be precisely realized as an isometry group of the killing generators of an asymptotically Schr\\"odinger $ Dp $ brane space time. In our analysis, we note that during the pre local stages of the thermal equilibrium the entanglement entropy has a faster growth in time compared to its relativistic cousin. However, it shows a linear growth during the post local stages of thermal equilibrium where the so called tsunami velocity associated with the linear growth of the entanglement entropy saturates to that of its value corresponding to the relativistic scenario. Finally, we explore the saturation region and it turns out that one must constraint ...
Nonperturbative approach to relativistic quantum communication channels
Landulfo, André G. S.
2016-05-01
We investigate the transmission of both classical and quantum information between two arbitrary observers in globally hyperbolic spacetimes using a quantum field as a communication channel. The field is supposed to be in some arbitrary quasifree state and no choice of representation of its canonical commutation relations is made. Both sender and receiver possess some localized two-level quantum system with which they can interact with the quantum field to prepare the input and receive the output of the channel, respectively. The interaction between the two-level systems and the quantum field is such that one can trace out the field degrees of freedom exactly and thus obtain the quantum channel in a nonperturbative way. We end the paper determining the unassisted as well as the entanglement-assisted classical and quantum channel capacities.
Relativistic quantum correlations in bipartite fermionic states
Indian Academy of Sciences (India)
S KHAN; N A KHAN
2016-10-01
The influences of relative motion, the size of the wave packet and the average momentum of the particles on different types of correlations present in bipartite quantum states are investigated. In particular, the dynamics of the quantum mutual information, the classical correlation and the quantum discord on the spincorrelations of entangled fermions are studied. In the limit of small average momentum, regardless of the size of the wave packet and the rapidity, the classical and the quantum correlations are equally weighted. On the otherhand, in the limit of large average momentum, the only correlations that exist in the system are the quantum correlations. For every value of the average momentum, the quantum correlations maximize at an optimal size of the wave packet. It is shown that after reaching a minimum value, the revival of quantum discord occurs with increasing rapidity.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Gomis, Joaquim; Not, Daniel
2017-02-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Not, Daniel
2016-01-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Free space relativistic quantum cryptography with faint laser pulses
Molotkov, S. N.; Potapova, T. A.
2013-07-01
A new protocol for quantum key distribution through empty space is proposed. Apart from the quantum mechanical restrictions on distinguishability of non-orthogonal states, the protocol employs additional restrictions imposed by special relativity. The protocol ensures generation of a secure key even for the source generating non-strictly single-photon quantum states and for arbitrary losses in quantum communication channel.
Open quantum dots in graphene: Scaling relativistic pointer states
Ferry, D. K.; Huang, L.; Yang, R.; Lai, Y.-C.; Akis, R.
2010-04-01
Open quantum dots provide a window into the connection between quantum and classical physics, particularly through the decoherence theory, in which an important set of quantum states are not "washed out" through interaction with the environment-the pointer states provide connection to trapped classical orbits which remain stable in the dots. Graphene is a recently discovered material with highly unusual properties. This single layer, one atom thick, sheet of carbon has a unique bandstructure, governed by the Dirac equation, in which charge carriers imitate relativistic particles with zero rest mass. Here, an atomic orbital-based recursive Green's function method is used for studying the quantum transport. We study quantum fluctuations in graphene and bilayer graphene quantum dots with this recursive Green's function method. Finally, we examine the scaling of the domiant fluctuation frequency with dot size.
Foundations for proper-time relativistic quantum theory
Gill, Tepper L.; Morris, Trey; Kurtz, Stewart K.
2015-05-01
This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of relativistic quantum theory, followed by a review of the Dirac equation, providing new insights into the physical properties of both. We then introduce the canonical proper-time theory. For completeness, we give a brief outline of the canonical proper-time approach to electrodynamics and mechanics, and then introduce the canonical proper-time approach to relativistic quantum theory. This theory leads to three new relativistic wave equations. In each case, the canonical generator of proper-time translations is strictly positive definite, so that it represents a particle. We show that the canonical proper-time extension of the Dirac equation for Hydrogen gives results that are consistently closer to the experimental data, when compared to the Dirac equation. However, these results are not sufficient to account for either the Lamb shift or the anomalous magnetic moment.
Relativistic Quantum Thermodynamics of Ideal Gases in 2 Dimensions
Blas, H.; Pimentel, B. M.; Tomazelli, J. L.
1999-01-01
In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.
Relativistic quantum thermodynamics of ideal gases in two dimensions.
Blas, H; Pimentel, B M; Tomazelli, J L
1999-11-01
In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.
Relativistic quantum metrology in open system dynamics.
Tian, Zehua; Wang, Jieci; Fan, Heng; Jing, Jiliang
2015-01-22
Quantum metrology studies the ultimate limit of precision in estimating a physical quantity if quantum strategies are exploited. Here we investigate the evolution of a two-level atom as a detector which interacts with a massless scalar field using the master equation approach for open quantum system. We employ local quantum estimation theory to estimate the Unruh temperature when probed by a uniformly accelerated detector in the Minkowski vacuum. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over all possible detector preparations and evolution times, and compare its behavior with that of the quantum Fisher information (QFI). We find that the optimal precision of estimation is achieved when the detector evolves for a long enough time. Furthermore, we find that in this case the FI for population measurement is independent of initial preparations of the detector and is exactly equal to the QFI, which means that population measurement is optimal. This result demonstrates that the achievement of the ultimate bound of precision imposed by quantum mechanics is possible. Finally, we note that the same configuration is also available to the maximum of the QFI itself.
On the Effect of Quantum Noise in a Quantum-Relativistic Prisoner's Dilemma Cellular Automaton
Alonso-Sanz, Ramón; Situ, Haozhen
2016-12-01
The disrupting effect of quantum noise on the dynamics of a spatial quantum relativistic formulation of the iterated prisoner's dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests.
Toward a fully relativistic theory of quantum information
Adami, Christoph
2011-01-01
Information theory is a statistical theory dealing with the relative state of detectors and physical systems. Because of this physicality of information, the classical framework of Shannon needs to be extended to deal with quantum detectors, perhaps moving at relativistic speeds, or even within curved space-time. Considerable progress toward such a theory has been achieved in the last fifteen years, while much is still not understood. This review recapitulates some milestones along this road, and speculates about future ones.
Relativistic quantum level-spacing statistics in chaotic graphene billiards.
Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2010-05-01
An outstanding problem in quantum nonlinear dynamics concerns about the energy-level statistics in experimentally accessible relativistic quantum systems. We demonstrate, using chaotic graphene confinements where electronic motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are those given by Gaussian orthogonal ensemble (GOE) random matrices. Weak magnetic field can change the level-spacing statistics to those of Gaussian unitary ensemble for electrons in graphene. For sufficiently strong magnetic field, the GOE statistics are restored due to the appearance of Landau levels.
From quantum to classical instability in relativistic stars
Landulfo, André G S; Matsas, George E A; Vanzella, Daniel A T
2014-01-01
It has been shown that gravitational fields produced by realistic classical-matter distributions can force quantum vacuum fluctuations of some nonminimally coupled free scalar fields to undergo a phase of exponential growth. The consequences of this unstable phase to the background spacetime have not been addressed so far due to known difficulties concerning backreaction in semiclassical gravity. It seems reasonable to believe, however, that the quantum fluctuations will "classicalize" when they become large enough, after which backreaction can be treated in the general-relativistic context. Here we investigate the emergence of a classical regime out of the quantum field evolution during the unstable phase. By studying the appearance of classical correlations and loss of quantum coherence, we show that by the time backreaction becomes important the system already behaves classically. Consequently, the gravity-induced vacuum instability will naturally lead to initial conditions for the eventual classical descr...
Thermodynamics of relativistic quantum fields: extracting energy from gravitational waves
Bruschi, David Edward
2016-01-01
We investigate the quantum thermodynamical properties of localised relativistic quantum fields that can be used as quantum thermal machines. We study the efficiency and power of energy transfer between the classical degrees of freedom, such as the energy input due to motion or to an impinging gravitational wave, and the excitations of the confined quantum field. We find that the efficiency of energy transfer depends dramatically on the input initial state of the system. Furthermore, we investigate the ability to extract the energy and to store it in a battery. This process is inefficient in optical cavities but is significantly enhanced when employing trapped Bose Einstein Condensates. Finally, we apply our techniques to a setup where an impinging gravitational wave excites the phononic modes of a Bose Einstein Condensate. We find that, in this case, the amount of energy transfer to the phonons increases with time and quickly approaches unity. These results suggest that, in the future, it might be possible to...
A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
Nicolis, Alberto
2012-01-01
We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theories at finite charge density. It is customary to treat systems at finite density via non-relativistic Hamiltonians. Here we highlight the importance of the underlying relativistic dynamics. This leads to seemingly new results whenever the charge in question is spontaneously broken and does not commute with other broken charges. These would normally be associated with gapless Goldstone excitations. We find that, in fact, their currents interpolate gapped excitations. We derive exact non-perturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.
Recurrence relation for relativistic atomic matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2000-01-01
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.
Relativistic effects on the modulational instability of electron plasma waves in quantum plasma
Indian Academy of Sciences (India)
Basudev Ghosh; Swarniv Chandra; Sailendra Nath Paul
2012-05-01
Relativistic effects on the linear and nonlinear properties of electron plasma waves are investigated using the one-dimensional quantum hydrodynamic (QHD) model for a twocomponent electron–ion dense quantum plasma. Using standard perturbation technique, a nonlinear Schrödinger equation (NLSE) containing both relativistic and quantum effects has been derived. This equation has been used to discuss the modulational instability of the wave. Through numerical calculations it is shown that relativistic effects signiﬁcantly change the linear dispersion character of the wave. Unlike quantum effects, relativistic effects are shown to reduce the instability growth rate of electron plasma waves.
Experimental considerations for quantum-entanglement studies with relativistic fermions
Energy Technology Data Exchange (ETDEWEB)
Schlemme, Steffen; Peck, Marius; Enders, Joachim [TU Darmstadt (Germany); Bodek, Kazimierz; Rozpedzik, Dagmara; Zejma, Jacek [Jagiellonian University, Cracow (Poland); Caban, Pawel; Rembielinski, Jakub [University of Lodz, Lodz (Poland); Ciborowski, Jacek; Dragowski, Michal; Wlodarczyk, Marta [Warsaw University, Warsaw (Poland); Kozela, Adam [Institute of Nuclear Physics, PAS, Cracow (Poland)
2015-07-01
The QUEST (Quantum entanglement of Ultra-relativistic Electrons in Singlet and Triplet states) project is aimed at the determination of the electron spin correlation function at relativistic energies. Electron pairs are created through Moeller scattering, and polarization observables are planned to be measured in Mott scattering. The predicted spin correlation function is energy dependent with values of several per cent at energies of 10-20 MeV. The results of a first test experiment at the S-DALINAC were not sensitive enough to detect entangled and Mott-scattered electron pairs at the expected energies. Further steps are either to improve the former setup or design a new polarimeter for lower energies to improve statistics due to the higher scattering cross sections. This contribution presents general considerations, test results, and an outlook.
Non relativistic limit of integrable QFT and Lieb-Liniger models
Bastianello, Alvise; De Luca, Andrea; Mussardo, Giuseppe
2016-12-01
In this paper we study a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda field theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.
Non Relativistic Limit of Integrable QFT and Lieb-Liniger Models
Bastianello, Alvise; Mussardo, Giuseppe
2016-01-01
In this paper we study a suitable limit of integrable QFT with the aim to identify non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda Field Theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.
Relativistic quantum transport theory for electrodynamics
Zhuang, P; Zhuang, P; Heinz, U
1995-01-01
We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant formulation. We illustrate this statement in scalar and spinor QED. For scalar QED we derive Lorentz covariant transport and constraint equations directly from the Klein-Gordon equation rather than through the previously used Feshbach-Villars representation. We then consider pair production in a spatially homogeneous but time-dependent electric field and show that the pair density is derived much more easily via the energy averaging method than in the equal-time representation. Proceeding to spinor QED, we derive the covariant version of the equal-time equation derived by Bialynicki-Birula et al. We show that it must be supplemented by another self-adjoint equation to obtain a complete description of the covariant spinor Wigner operator. After spinor decomposition and energy averag...
Non-relativistic particles in a thermal bath
Directory of Open Access Journals (Sweden)
Vairo Antonio
2014-04-01
Full Text Available Heavy particles are a window to new physics and new phenomena. Since the late eighties they are treated by means of effective field theories that fully exploit the symmetries and power counting typical of non-relativistic systems. More recently these effective field theories have been extended to describe non-relativistic particles propagating in a medium. After introducing some general features common to any non-relativistic effective field theory, we discuss two specific examples: heavy Majorana neutrinos colliding in a hot plasma of Standard Model particles in the early universe and quarkonia produced in heavy-ion collisions dissociating in a quark-gluon plasma.
Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection
Lazarian, A; Takamoto, M; Pino, E M de Gouveia Dal; Cho, J
2015-01-01
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, includi...
Superluminal Neutrinos and a Curious Phenomenon in the Relativistic Quantum Hamilton-Jacobi Equation
Matone, Marco
2011-01-01
OPERA's results, if confirmed, pose the question of superluminal neutrinos. We investigate the kinematics defined by the quantum version of the relativistic Hamilton-Jacobi equation, i.e. E^2=p^2c^2+m^2c^4+2mQc^2, with Q the quantum potential of the free particle. The key point is that the quantum version of the Hamilton-Jacobi equation is a third-order differential equation, so that it has integration constants which are missing in the Schr\\"odinger and Klein-Gordon equations. In particular, a non-vanishing imaginary part of an integration constant leads to a quantum correction to the expression of the velocity which is curiously in agreement with OPERA's results.
Strauss, Y
1999-01-01
We apply the quantum Lax-Phillips scattering theory to a relativistically covariant quantum field theoretical form of the (soluble) Lee model. We construct the translation representations with the help of the wave operators, and show that the resulting Lax-Phillips $S$-matrix is an inner function (the Lax-Phillips theory is essentially a theory of translation invariant subspaces). We then discuss the non-relativistic limit of this theory, and show that the resulting kinematic relations coincide with the conditions required for the Galilean description of a decaying system.
Quantum relativistic fluid at global thermodynamic equilibrium in curved spacetime
Becattini, F
2015-01-01
We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.
Relativistic quantum chemistry the fundamental theory of molecular science
Reiher, Markus
2014-01-01
Einstein proposed his theory of special relativity in 1905. For a long time it was believed that this theory has no significant impact on chemistry. This view changed in the 1970s when it was realized that (nonrelativistic) Schrödinger quantum mechanics yields results on molecular properties that depart significantly from experimental results. Especially when heavy elements are involved, these quantitative deviations can be so large that qualitative chemical reasoning and understanding is affected. For this to grasp the appropriate many-electron theory has rapidly evolved. Nowadays relativist
Poincaré covariance of relativistic quantum position
Farkas, S; Weiner, M D; Farkas, Sz.
2002-01-01
A great number of problems of relativistic position in quantum mechanics are due to the use of coordinates which are not inherent objects of spacetime, cause unnecessary complications and can lead to misconceptions. We apply a coordinate-free approach to rule out such problems. Thus it will be clear, for example, that the Lorentz covariance of position, required usually on the analogy of Lorentz covariance of spacetime coordinates, is not well posed and we show that in a right setting the Newton--Wigner position is Poincar\\'e covariant, in contradiction with the usual assertions.
Relativistic and quantum electrodynamics effects in the helium pair potential.
Przybytek, M; Cencek, W; Komasa, J; Łach, G; Jeziorski, B; Szalewicz, K
2010-05-01
The helium pair potential was computed including relativistic and quantum electrodynamics contributions as well as improved accuracy adiabatic ones. Accurate asymptotic expansions were used for large distances R. Error estimates show that the present potential is more accurate than any published to date. The computed dissociation energy and the average R for the (4)He(2) bound state are 1.62+/-0.03 mK and 47.1+/-0.5 A. These values can be compared with the measured ones: 1.1(-0.2)(+0.3) mK and 52+/-4 A [R. E. Grisenti, Phys. Rev. Lett. 85, 2284 (2000)].
A finite Zitterbewegung model for relativistic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1990-02-19
Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.
The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics
Liu, Li-Yan; Hao, Qing-Hai
2014-06-01
We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein—Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.
Energy Technology Data Exchange (ETDEWEB)
Hussain, S.; Mahmood, S.; Rehman, Aman-ur- [Theoretical Physics Division (TPD), PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan and Pakistan Institute of Engineering and Applied Sciences (PIEAS), P.O. Nilore, Islamabad 44000 (Pakistan)
2014-11-15
Linear and nonlinear propagation of magnetosonic waves in the perpendicular direction to the ambient magnetic field is studied in dense plasmas for non-relativistic and ultra-relativistic degenerate electrons pressure. The sources of nonlinearities are the divergence of the ions and electrons fluxes, Lorentz forces on ions and electrons fluids and the plasma current density in the system. The Korteweg-de Vries equation for magnetosonic waves propagating in the perpendicular direction of the magnetic field is derived by employing reductive perturbation method for non-relativistic as well as ultra-relativistic degenerate electrons pressure cases in dense plasmas. The plots of the magnetosonic wave solitons are also shown using numerical values of the plasma parameters such a plasma density and magnetic field intensity of the white dwarfs from literature. The dependence of plasma density and magnetic field intensity on the magnetosonic wave propagation is also pointed out in dense plasmas for both non-relativistic and ultra-relativistic degenerate electrons pressure cases.
``Simplest Molecule'' Clarifies Modern Physics II. Relativistic Quantum Mechanics
Harter, William; Reimer, Tyle
2015-05-01
A ``simplest molecule'' consisting of CW- laser beam pairs helps to clarify relativity from poster board - I. In spite of a seemingly massless evanescence, an optical pair also clarifies classical and quantum mechanics of relativistic matter and antimatter. Logical extension of (x,ct) and (ω,ck) geometry gives relativistic action functions of Hamiltonian, Lagrangian, and Poincare that may be constructed in a few ruler-and-compass steps to relate relativistic parameters for group or phase velocity, momentum, energy, rapidity, stellar aberration, Doppler shifts, and DeBroglie wavelength. This exposes hyperbolic and circular trigonometry as two sides of one coin connected by Legendre contact transforms. One is Hamiltonian-like with a longitudinal rapidity parameter ρ (log of Doppler shift). The other is Lagrange-like with a transverse angle parameter σ (stellar aberration). Optical geometry gives recoil in absorption, emission, and resonant Raman-Compton acceleration and distinguishes Einstein rest mass, Galilean momentum mass, and Newtonian effective mass. (Molecular photons appear less bullet-like and more rocket-like.) In conclusion, modern space-time physics appears as a simple result of the more self-evident Evenson's axiom: ``All colors go c.''
"simplest Molecule" Clarifies Modern Physics II. Relativistic Quantum Mechanics
Reimer, T. C.; Harter, W. G.
2014-06-01
A "simplest molecule" consisting of CW-laser beam pairs helps to clarify relativity in Talk I. In spite of a seemingly massless evanescence, an optical pair also clarifies classical and quantum mechanics of relativistic matter and anti-matter. *Logical extension of (x,ct) and (ω,ck) geometry gives relativistic action functions of Hamiltonian, Lagrangian, and Poincare that may be constructed in a few ruler-and-compass steps to relate relativistic parameters for group or phase velocity, momentum, energy, rapidity, stellar aberration, Doppler shifts, and DeBroglie wavelength. This exposes hyperbolic and circular trigonometry as two sides of one coin connected by Legendre contact transforms. One is Hamiltonian-like with a longitudinal rapidity parameter ρ (log of Doppler shift). The other is Lagrange-like with a transverse angle parameter σ (stellar aberration). Optical geometry gives recoil in absorption, emission, and resonant Raman-Compton acceleration and distinguishes Einstein rest mass, Galilean momentum mass, and Newtonian effective mass. (Molecular photons appear less bullet-like and more rocket-like.) In conclusion, modern space-time physics appears as a simple result of the more self-evident Evenson's axiom: "All colors go c."
Objective realism and freedom of choice in relativistic quantum field theory
Bednorz, Adam
2016-01-01
An attempt to incorporate freedom of choice into relativistic quantum field theory is proposed. It is shown that it leads to breakdown of relativistic invariant properly defined objective realism. The argument does not rely on Bell theorem but direct analysis of invariance and positivity of objective correlations in quantum field theory.
Energy shift of interacting non-relativistic fermions in noncommutative space
Directory of Open Access Journals (Sweden)
A. Jahan
2005-06-01
Full Text Available A local interaction in noncommutative space modifies to a non-local one. For an assembly of particles interacting through the contact potential, formalism of the quantum field theory makes it possible to take into account the effect of modification of the potential on the energy of the system. In this paper we calculate the energy shift of an assembly of non-relativistic fermions, interacting through the contact potential in the presence of the two-dimensional noncommutativity.
Radiative transitions in mesons in a non relativistic quark model
Bonnaz, R.; Silvestre-Brac, B.; Gignoux, C.
2001-01-01
In the framework of the non relativistic quark model, an exhaustive study of radiative transitions in mesons is performed. The emphasis is put on several points. Some traditional approximations (long wave length limit, non relativistic phase space, dipole approximation for E1 transitions, gaussian wave functions) are analyzed in detail and their effects commented. A complete treatment using three different types of realistic quark-antiquark potential is made. The overall agreement with experi...
Radiative transitions in mesons in a non relativistic quark model
Bonnaz, R; Gignoux, C
2002-01-01
In the framework of the non relativistic quark model, an exhaustive study of radiative transitions in mesons is performed. The emphasis is put on several points. Some traditional approximations (long wave length limit, non relativistic phase space, dipole approximation for E1 transitions, gaussian wave functions) are analyzed in detail and their effects commented. A complete treatment using three different types of realistic quark-antiquark potential is made. The overall agreement with experimental data is quite good, but some improvements are suggested.
Investigation of Properties of Exotic Nuclei in Non-relativistic and Relativistic Models
Institute of Scientific and Technical Information of China (English)
2001-01-01
Properties of exotic nuclei are described by non-relativistic and relativistic models. The relativistic mean field theory predicts one proton halo in 26,27,28P and two proton halos in 27,28,29S, recently, one proton halo in 26,27,28P has been found experimentally in MSU lab. The relativistic Hartree-Fock theory has been used to investigate the contribution of Fock term and isovector mesons to the properties of exotic nuclei. It turns out that the influence of the Fock term and isovector mesons on the properties of neutron extremely rich nuclei is very different from that of near stable nuclei. Meanwhile, the deformed Hartree-Fock-Bogoliubov theory has been employed to describe the ground state properties of the isotopes for some light nuclei.
Relativistic three-partite non-locality
Montakhab, A
2015-01-01
Bell-like inequalities have been used in order to distinguish non-local quantum pure states by various authors. The behavior of such inequalities under Lorentz transformation has been a source of debate and controversies in the past. In this paper, we consider the two most commonly studied three-particle pure states, that of W and GHZ states which exhibit distinctly different type of entanglement. We discuss the various types of three-particle inequalities used in previous studies and point to their corresponding shortcomings and strengths. Our main result is that if one uses Svetlichny's inequality as the main measure of non-locality and uses the same angles in the rest frame ($S$) as well as the moving frame ($S^{\\prime}$), then maximally violated inequality in $S$ will decrease in the moving frame, and will eventually lead to lack of non-locality ( i.e. satisfaction of inequality) in the $v \\rightarrow c$ limit. This is shown for both GHZ and W states and in two different configurations which are commonly ...
Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter
Institute of Scientific and Technical Information of China (English)
ZHANG Qi-Ren; GAO Chun-Yuan
2011-01-01
We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field Φ is introduced.The equivalence of this procedure with the usual one is proven for any given value of Φ.By use of this procedure, the scalar meson field in the Walecka's MFA and in Chin's RHA are quantized around the mean field.Its corrections on these theories are considered by perturbation up to the second order.The arbitrariness of Φ makes us free to fix it at any stage in the calculation.When we fix it in the way of Walecka's MFA, the quantum corrections are big, and the result does not converge.When we fix it in the way of Chin's RHA, the quantum correction is negligibly small, and the convergence is excellent.It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka's MFA does not.We suggest to fix the parameter Φ at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory (QRMFT) a variational method.
Non-relativistic Bondi–Metzner–Sachs algebra
Batlle, Carles; Delmastro, Diego; Gomis, Joaquim
2017-09-01
We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein–Gordon field.
Going beyond "no-pair relativistic quantum chemistry".
Liu, Wenjian; Lindgren, Ingvar
2013-07-07
The current field of relativistic quantum chemistry (RQC) has been built upon the no-pair and no-retardation approximations. While retardation effects must be treated in a time-dependent manner through quantum electrodynamics (QED) and are hence outside RQC, the no-pair approximation (NPA) has to be removed from RQC for it has some fundamental defects. Both configuration space and Fock space formulations have been proposed in the literature to do this. However, the former is simply wrong, whereas the latter is still incomplete. To resolve the old problems pertinent to the NPA itself and new problems beyond the NPA, we propose here an effective many-body (EMB) QED approach that is in full accordance with standard methodologies of electronic structure. As a first application, the full second order energy E2 of a closed-shell many-electron system subject to the instantaneous Coulomb-Breit interaction is derived, both algebraically and diagrammatically. It is shown that the same E2 can be obtained by means of 3 Goldstone-like diagrams through the standard many-body perturbation theory or 28 Feynman diagrams through the S-matrix technique. The NPA arises naturally by retaining only the terms involving the positive energy states. The potential dependence of the NPA can be removed by adding in the QED one-body counter terms involving the negative energy states, thereby leading to a "potential-independent no-pair approximation" (PI-NPA). The NPA, PI-NPA, EMB-QED, and full QED then span a continuous spectrum of relativistic molecular quantum mechanics.
Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
Dandekar, Yogesh; Minwalla, Shiraz
2014-01-01
An all orders formula for the $S$-matrix for 2 $\\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this $S$-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the $S$-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic $S$-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory $S$-matrix.
Failure of relativistic codes in the non-relativistic limit: the role of Brillouin configurations
Indelicato, P J; Desclaux, J P
2004-01-01
In the present letter we solve a long standing problem with relativistic calculations done with the widely used Multi-Configuration Dirac-Fock Method. We show, using Relativistic Many-Body Perturbation Theory (RMBPT), how even for relatively high-$Z$, relaxation or correlation causes the non-relativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We identify the role of single excitations obeying to Brillouin's theorem in this problem. We show that with large scale calculations in which this problem is properly treated, we can reproduce very accurately recent high-precision measurements in F-like Ar, and turn then into precise test of QED
Non-Relativistic Anti-Snyder Model and Some Applications
Ching, Chee Leong; Ng, Wei Khim
2016-01-01
We examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the non-relativistic anti-Snyder model which is relevant to deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigen solutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states due to the orthogonality of the polynomials and the maximum energy is truncated at the maximum n. Similar to the minimal length case, the degeneracy of the Dirac-Landau levels in anti- Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit. By taking zero mass limit, we explore the motion of effective zero mass charged Fermions in Graphene like material and obtained a maximum bound of deformed parameter. Furthermore, we consider the modified energy dispersion relations and its...
Bartley, David L
2016-01-01
The Bohm/de Broglie theory of deterministic non-relativistic quantum mechanics is broadened to accommodate the free-particle Dirac equation. As with the spin-0 theory, an effective particle rest-mass scalar field in the presence of the spin-1/2 pilot wave is allowed, together with the assumption that the convective current component describes ensemble dynamics. Non-positive excursions of the ensemble density for extreme cases of positive-energy solutions of the Dirac equation are interpreted in terms of virtual-like pair creation and annihilation beneath the Compton wavelength. A specific second-rank tensor is defined in terms of the Dirac spinors for generalizing from simply a quantum potential to a stress tensor required to account for the force of pilot wave on particle. A simple dependence of the stress tensor on a two-component spin pseudovector field is determined. Consistency is found with an earlier non-relativistic theory of objects with spin.
Fields and fluids on curved non-relativistic spacetimes
Geracie, Michael; Roberts, Matthew M
2015-01-01
We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works. In this approach the derivative operator is defined by a Galilean spin connection valued in the Lie algebra of the Galilean group. This includes the usual spin connection plus an additional "boost connection" which parameterizes the freedom in the derivative operator not fixed by torsion or metric compatibility. As an example of this approach we develop the theory of non-relativistic dissipative fluids and find significant differences in both equations of motion and allowed transport coefficients from those found previously. Our approach also immediately generalizes to systems with independent mass and charge currents as would arise in multicomponent fluids. Along the way we also discuss how to write general locally Galilean invariant non-relativistic actions for multiple particle species at any order in derivatives. A detailed review of the geometry and its rela...
Semi-relativistic hydrodynamics of three-dimensional and low-dimensional quantum plasma
Andreev, Pavel; Kuz'menkov, Leonid
2014-01-01
Contributions of the current-current and Darwin interactions and weak-relativistic addition to kinetic energy in the quantum hydrodynamic equations are considered. Features of hydrodynamic equations for two-dimensional layer of plasma (two-dimensional electron gas for instance) are described. It is shown that the force fields caused by the Darwin interaction and weak-relativistic addition to kinetic energy are partially reduced. Dispersion of three- and two-dimensional semi-relativistic Langmuir waves is calculated.
Local thermodynamical equilibrium and the β frame for a quantum relativistic fluid
Becattini, Francesco; Bucciantini, Leda; Grossi, Eduardo; Tinti, Leonardo
2015-01-01
We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse tem...
Energy Technology Data Exchange (ETDEWEB)
Moussa, P. [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires
1968-06-01
This work describes the angular analysis of reactions between particles with spin in a fully relativistic fashion. One particle states are introduced, following Wigner's method, as representations of the inhomogeneous Lorentz group. In order to perform the angular analyses, the reduction of the product of two representations of the inhomogeneous Lorentz group is studied. Clebsch-Gordan coefficients are computed for the following couplings: l-s coupling, helicity coupling, multipolar coupling, and symmetric coupling for more than two particles. Massless and massive particles are handled simultaneously. On the way we construct spinorial amplitudes and free fields; we recall how to establish convergence theorems for angular expansions from analyticity hypothesis. Finally we substitute these hypotheses to the idea of 'potential radius', which gives at low energy the usual 'centrifugal barrier' factors. The presence of such factors had never been deduced from hypotheses compatible with relativistic invariance. (author) [French] On decrit un formalisme permettant de tenir compte de l'invariance relativiste, dans l'analyse angulaire des amplitudes de reaction entre particules de spin quelconque. Suivant Wigner, les etats a une particule sont introduits a l'aide des representations du groupe de Lorentz inhomogene. Pour effectuer les analyses angulaires, on etudie la reduction du produit de deux representations du groupe de Lorentz inhomogene. Les coefficients de Clebsch-Gordan correspondants sont calcules dans les couplages suivants: couplage l-s couplage d'helicite, couplage multipolaire, couplage symetrique pour plus de deux particules. Les particules de masse nulle et de masse non nulle sont traitees simultanement. Au passage, on introduit les amplitudes spinorielles et on construit les champs libres, on rappelle comment des hypotheses d'analyticite permettent d'etablir des theoremes de convergence pour les
Local Thermal Equilibrium States in Relativistic Quantum Field Theory
Gransee, Michael
2016-01-01
It is well-known that thermal equilibrium states in quantum statistical mechanics and quantum field theory can be described in a mathematically rigorous manner by means of the so-called Kubo-Martin-Schwinger (KMS) condition, which is based on certain analyticity and periodicity properties of correlation functions. On the other hand, the characterization of non-equilibrium states which only locally have thermal properties still constitutes a challenge in quantum field theory. We discuss a recent proposal for characterization of such states by a generalized KMS condition. The connection of this proposal to a proposal by D. Buchholz, I. Ojima and H.-J. Roos for characterizing local thermal equilibrium states in quantum field theory is discussed.
Construction of relativistic quantum theory: a progress report
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1986-06-01
We construct the particulate states of quantum physics using a recursive computer program that incorporates non-determinism by means of locally arbitrary choices. Quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G, connected to laboratory events via finite particle number scattering theory and the counter paradigm. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact.
Indian Academy of Sciences (India)
Rahmani Faramarz; Golshani Mehdi; Sarbishei Mohsen
2016-04-01
In this paper we shall argue that conformal transformations give some new aspects to a metric and changes the physics that arises from the classical metric. It is equivalent to adding a new potential to relativistic Hamilton–Jacobi equation. We start by using conformal transformations on a metric and obtain modified geodesics. Then, we try to show that extra terms in the modified geodesics are indications of a background force. We obtain this potential by using variational method. Then, we see that this background potential is the same as the Bohmian non-local quantum potential. This approach gives a method stronger than Bohm’s original method in deriving Bohmian quantumpotential. We do not use any quantum mechanical postulates in this approach.
Spin-flavor oscillations of Dirac neutrinos described by relativistic quantum mechanics
Dvornikov, Maxim
2010-01-01
We study spin-flavor oscillations of Dirac neutrinos in matter and magnetic field using the method of relativistic quantum mechanics. We start from the exact solution of the wave equation for a massive neutrino, taking into account external fields. Then we derive an effective Hamiltonian governing neutrino spin-flavor oscillations. We demonstrate the consistency of our approach with the commonly used quantum mechanical method. Our correction to the usual effective Hamiltonian results in the appearance of a new resonance in neutrino oscillations. We discuss applications to spin-flavor neutrino oscillations in the expanding envelope of a supernova. In particular, transitions between right-handed electron neutrinos and sterile neutrinos are studied for a realistic background matter and magnetic field distributions. We also analyze the influence of other factors such as a longitudinal magnetic field, matter polarization, and the non-standard contributions to the neutrino effective potential.
Introduction to relativistic statistical mechanics classical and quantum
Hakim, Rémi
2011-01-01
This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statisti
Non-Commutative Geometry, Categories and Quantum Physics
Bertozzini, Paolo; Lewkeeratiyutkul, Wicharn
2008-01-01
After an introduction to some basic issues in non-commutative geometry (Gel'fand duality, spectral triples), we present a "panoramic view" of the status of our current research program on the use of categorical methods in the setting of A.Connes' non-commutative geometry: morphisms/categories of spectral triples, categorification of Gel'fand duality. We conclude with a summary of the expected applications of "categorical non-commutative geometry" to structural questions in relativistic quantum physics: (hyper)covariance, quantum space-time, (algebraic) quantum gravity.
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary coordinat
A brief introduction to non-relativistic supergravity
Energy Technology Data Exchange (ETDEWEB)
Zojer, Thomas [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen (Netherlands)
2016-04-15
Non-relativistic geometries have received more attention lately. We review our attempts to construct supersymmetric extensions of this so-called Newton-Cartan geometry in three space-time dimensions. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary
Theory of non-relativistic three-particle scattering
Malfliet, R.; Ruijgrok, Th.
1967-01-01
A new method, using asymptotically stationary states, is developed to calculate the S-matrix for the scattering of a non-relativistic particle by the bound state of two other particles. For the scattering with breakup of this bound state, we obtain a simplified form of the Faddeev integral
Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces
Energy Technology Data Exchange (ETDEWEB)
Klink, W.H., E-mail: william-klink@uiowa.edu [Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242 (United States); Wickramasekara, S., E-mail: wickrama@grinnell.edu [Department of Physics, Grinnell College, Grinnell, IA 50112 (United States)
2016-06-15
One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner–Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated in quantum theory.
Palge, Veiko; Dunningham, Jacob; Hasegawa, Yuji
2016-01-01
In quantum physics Wigner's rotation is commonly regarded as confirmed by the Thomas precession in a hydrogen like atom. In this paper we show that a direct experimental verification of Wigner's rotation is in principle accessible in the regime of non-relativistic velocities at $2 \\cdot 10^3\\,$m/s and propose an experiment using thermal neutrons. The experiment can be carried out in a laboratory and it provides a test of relativity in the quantum domain.
Strong Coulomb Coupling in Relativistic Quantum Constraint Dynamics
Bawin, M.; Cugnon, J.; Sazdjian, H.
We study, in the framework of relativistic quantum constraint dynamics, the bound state problem of two oppositely charged spin 1/2 particles, with masses m1 and m2, in mutual electromagnetic interaction. We search for the critical value of the coupling constant α for which the bound state energy reaches the lower continuum, thus indicating the instability of the heavier particle or of the strongly coupled QED vacuum in the equal mass case. Two different choices of the electromagnetic potential are considered, corresponding to different extensions of the substitution rule into the nonperturbative region of α: (i) the Todorov potential, already introduced in the quasipotential approach and used by Crater and Van Alstine in Constraint Dynamics; (ii) a second potential (potential II), characterized by a regular behavior at short distances. For the Todorov potential we find that for m2>m1 there is always a critical value αc of α, depending on m2/m1, for which instability occurs. In the equal mass case, instability is reached at αc=1/2 with a vanishing value of the cutoff radius, generally needed for this potential at short distances. For potential II, on the other hand, we find that instability occurs only for m2>2.16 m1.
On kaonic deuterium. Quantum field theoretic and relativistic covariant approach
Ivanov, A N; Faber, M; Fuhrmann, H; Ivanova, V A; Marton, J; Troitskaya, N I; Zmeskal, J
2004-01-01
We study kaonic deuterium, the bound K^-d state A_{K d}. Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K^-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering near threshold is defined by the resonances Lambda(1405), Sigma(1750) and a smooth elastic background, and the inelastic channels K^- d -> NY and K^- d -> NY pion, with Y = Sigma^{+/-}, Sigma^0 and Lambda^0, where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K^-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A_{Kd} -> NY and experimental data on the rates of the NY-pair production in the reactions K^-d -> NY. We obt...
On kaonic hydrogen. Quantum field theoretic and relativistic covariant approach
Ivanov, A N; Faber, M; Marton, J; Troitskaya, N I; Zmeskal, J
2003-01-01
We study kaonic hydrogen, the bound K^-p state A_(Kp). Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K^-p scattering for arbitrary energies. The amplitude of low-energy K^-p scattering near threshold is defined by the contributions of three resonances Lambda(1405), Lambda(1800) and Sigma^0(1750) and a smooth elastic background. The amplitudes of inelastic channels of low-energy K^-p scattering fit experimental data on near threshold behaviour of the cross sections and the experimental data by the DEAR Collaboration. We use the soft-pion technique (leading order in Chiral Perturbation Theory) for the calculate of the partial width of the radiative decay of pionic hydrogen A_(pi p) -> n + gamma and the Panofsky ratio. The theoretical prediction for the Panofsky ratio agrees well with experimental data. We apply the soft-kaon technique (leading order in Chiral Perturbation Theory) to...
On kaonic hydrogen. Quantum field theoretic and relativistic covariant approach
Ivanov, A. N.; Cargnelli, M.; Faber, M.; Marton, J.; Troitskaya, N. I.; Zmeskal, J.
2004-07-01
We study kaonic hydrogen, the bound K - p state A K p . Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K - p scattering for arbitrary relative momenta. The amplitude of low-energy K - p scattering near threshold is defined by the contributions of three resonances Λ(1405), Λ(1800) and Σ^0(1750) and a smooth elastic background. The amplitudes of inelastic channels of low-energy K - p scattering fit experimental data on the near-threshold behaviour of the cross-sections and the experimental data by the DEAR Collaboration. We use the soft-pion technique (leading order in Chiral Perturbation Theory) for the calculation of the partial width of the radiative decay of pionic hydrogen A_{π p} to n + γ and the Panofsky ratio. The theoretical prediction for the Panofsky ratio agrees well with experimental data. We apply the soft-kaon technique (leading order in Chiral Perturbation Theory) to the calculation of the partial widths of radiative decays of kaonic hydrogen A_{Kp} to Λ^0 + γ and A_{K p} to Σ^0 + γ. We show that the contribution of these decays to the width of the energy level of the ground state of kaonic hydrogen is less than 1%.
Institute of Scientific and Technical Information of China (English)
董宇兵; 王翼展
2011-01-01
The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark i
Non-relativistic twistor theory and Newton--Cartan geometry
Dunajski, Maciej
2015-01-01
We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle ${\\mathcal O}\\oplus{\\mathcal O}(2)$. We show that the Newton--Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton--Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non--trivial on twistor lines. The resulting geometries agree with non--relativistic limits of anti-self-dual gravitational instantons.
Acceleration of positrons by a relativistic electron beam in the presence of quantum effects
Energy Technology Data Exchange (ETDEWEB)
Niknam, A. R. [Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Tehran (Iran, Islamic Republic of); Aki, H.; Khorashadizadeh, S. M. [Physics Department, Birjand University, Birjand (Iran, Islamic Republic of)
2013-09-15
Using the quantum magnetohydrodynamic model and obtaining the dispersion relation of the Cherenkov and cyclotron waves, the acceleration of positrons by a relativistic electron beam is investigated. The Cherenkov and cyclotron acceleration mechanisms of positrons are compared together. It is shown that growth rate and, therefore, the acceleration of positrons can be increased in the presence of quantum effects.
Path integral polymer propagator of relativistic and non-relativistic particles
Morales-Técotl, Hugo A; Ruelas, Juan C
2016-01-01
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The mechanical models we consider are deparametrized and thus the group averaging technique is used to deal with the corresponding constraints. The transition amplitudes are written in a vertex expansion form used in the spin foam models, where here a vertex is actually a jump in position. Polymer Propagators previously obtained by spectral methods for a nonrelativistic polymer particle, both free and in a box, are regained with this method. Remarkably, the approach is also shown to yield the polymer propagator of the relativistic particle. This reduces to the standard form in the continuum limit for which the length scale parameter of the polymer quantization is taken to be small. Some possible future developments are commented upon.
Quantum objects. Non-local correlation, causality and objective indefiniteness in the quantum world
Energy Technology Data Exchange (ETDEWEB)
Jaeger, Gregg [Boston Univ., MA (United States). Natural Sciences and Mathematics
2014-07-01
Presents interpretation of quantum mechanics, advances in quantum foundations and philosophy of quantum mechanics. Explains non-locality and its relationship to causality and probability in quantum theory. Displays foundational characteristics of quantum physic to understand conceptual origins of the unusual nature of quantum phenomena. Describes relationship of subsystems and space-time. Gives a careful review of existing views. Confronts the old approaches with recent results and approaches from quantum information theory. Delivers a clear and thorough analysis of the quantum events in the context of relativistic space-time, which impacts the problem of creating a theory of quantum gravity. Supplies a detailed discussion of non-local correlation within and beyond the bounds set by standard quantum mechanics, which impacts the foundations of information theory. Gives a detailed discussion of probabilistic causation (central to contemporary accounts of causation) in quantum mechanics and relativity. Leads a thorough discussion of the nature of ''quantum potentiality,'' the novel form of existence arising for the first time in quantum mechanics. This monograph identifies the essential characteristics of the objects described by current quantum theory and considers their relationship to space-time. In the process, it explicates the senses in which quantum objects may be consistently considered to have parts of which they may be composed or into which they may be decomposed. The book also demonstrates the degree to which reduction is possible in quantum mechanics, showing it to be related to the objective indefiniteness of quantum properties and the strong non-local correlations that can occur between the physical quantities of quantum subsystems. Careful attention is paid to the relationships among such property correlations, physical causation, probability, and symmetry in quantum theory. In this way, the text identifies and clarifies the
Do non-relativistic neutrinos constitute the dark matter?
Nieuwenhuizen, T.M.
2009-01-01
The dark matter of the Abell 1689 Galaxy Cluster is modeled by thermal, non-relativistic gravitating fermions and its galaxies and X-ray gas by isothermal distributions. A fit yields a mass of h(70)(1/2) (12/(g) over bar)(1)/(4) 1.445(30) eV. A dark-matter fraction Omega(nu) = h(70)(-3/2) 0.1893(39)
Newton-Cartan (super)gravity as a non-relativistic limit
Bergshoeff, Eric; Rosseel, Jan; Zojer, Thomas
2015-01-01
We define a procedure that, starting from a relativistic theory of supergravity, leads to a consistent, non-relativistic version thereof. As a first application we use this limiting procedure to show how the Newton-Cartan formulation of non-relativistic gravity can be obtained from general relativit
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Energy Technology Data Exchange (ETDEWEB)
Geracie, Michael, E-mail: mgeracie@uchicago.edu; Prabhu, Kartik, E-mail: kartikp@uchicago.edu; Roberts, Matthew M., E-mail: matthewroberts@uchicago.edu [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-10-15
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print http://arxiv.org/abs/1503.02680 ], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
Symmetries and couplings of non-relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Festuccia, Guido [Department of Physics and Astronomy, Uppsala University,Lägerhyddsvägen 1, Uppsala (Sweden); Hansen, Dennis [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark); Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes,Université Libre de Bruxelles, C.P. 231, Brussels, 1050 (Belgium); Obers, Niels A. [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark)
2016-11-08
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell’s equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a U(1) current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galilei algebra plus two dilatations remain. Hence one can scale time and space independently, allowing Lifshitz scale symmetries for any value of the critical exponent z.
Symmetries and Couplings of Non-Relativistic Electrodynamics
Festuccia, Guido; Hartong, Jelle; Obers, Niels A
2016-01-01
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a $U(1)$ current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galile...
Quantum Geometry: Relativistic energy approach to cooperative electron-nucleary-transition spectrum
Directory of Open Access Journals (Sweden)
Ольга Юрьевна Хецелиус
2014-11-01
Full Text Available An advanced relativistic energy approach is presented and applied to calculating parameters of electron-nuclear 7-transition spectra of nucleus in the atom. The intensities of the spectral satellites are defined in the relativistic version of the energy approach (S-matrix formalism, and gauge-invariant quantum-electrodynamical perturbation theory with the Dirac-Kohn-Sham density-functional zeroth approximation.
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
2016-09-01
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds.
Salazar-Ramírez, M.; Ojeda-Guillén, D.; Mota, R. D.
2016-09-01
We study a relativistic quantum particle in cosmic string spacetime in the presence of a magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the su(1 , 1) symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schrödinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.
Quantum Monte Carlo studies of relativistic effects in light nuclei
Forest, J. L.; Pandharipande, V. R.; Arriaga, A.
1999-07-01
Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials, and their boost corrections. In this work we use the variational Monte Carlo method to study two kinds of relativistic effects in 3H and 4He, using relativistic Hamiltonians. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by ~15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of ~0.4 (1.9) MeV in 3H (4He) and account for ~37% of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians. The wave functions of nuclei are not significantly changed by these effects.
Angular momentum in non-relativistic QED and photon contribution to spin of hydrogen atom
Energy Technology Data Exchange (ETDEWEB)
Chen Panying, E-mail: pychen@umd.ed [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Ji Xiangdong [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Institute of Particle Physics and Cosmology, Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240 (China); Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China); Xu Yang [Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China); Zhang Yue [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China)
2010-04-26
We study angular momentum in non-relativistic quantum electrodynamics (NRQED). We construct the effective total angular momentum operator by applying Noether's theorem to the NRQED lagrangian. We calculate the NRQED matching for the individual components of the QED angular momentum up to one loop. We illustrate an application of our results by the first calculation of the angular momentum of the ground state hydrogen atom carried in radiative photons, alpha{sub em}{sup 3}/18pi, which might be measurable in future atomic experiments.
Relativistic (SR-ZORA) quantum theory of atoms in molecules properties.
Anderson, James S M; Rodríguez, Juan I; Ayers, Paul W; Götz, Andreas W
2017-01-15
The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Al-Hashimi, M H; Wiese, U -J
2014-01-01
We consider the Schr\\"odinger equation for a relativistic point particle in an external 1-dimensional $\\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudo-differential operator $H = \\sqrt{p^2 + m^2}$. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.
Quantum And Relativistic Protocols For Secure Multi-Party Computation
Colbeck, Roger
2009-01-01
After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner, but, also, to introduce a new protocol for non-relativistic strong coin tossing. This protocol matches the security of the best protocol known to date while using a conceptually different approach to achieve the task. In the second part variable bias coin tossing is introduced. This is a variant of coin tossing in which one party secretly chooses one of two biased coins to toss. It is shown that this can be achieved with unconditional security for a specified range of biases, and with cheat-evident security for any bias. We also discuss two further protocols which are conjectured to be unconditionally secure for any bias. The third section looks at other two-party secure computations for which, prior to our work, protocols and no-go theorems were unknown. We introduce a gene...
Relativistic Hydrodynamics and Non-Equilibrium Steady States
Spillane, Michael
2015-01-01
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The new double shock solutions are in contrast with older solutions that involve one shock and one rarefaction wave. We use numerical simulations to show that the older solutions are preferred. Briefly we discuss the effects of a conserved charge. Finally, we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids.
Quantum resonances in reflection of relativistic electrons and positrons
Energy Technology Data Exchange (ETDEWEB)
Eykhorn, Yu.L.; Korotchenko, K.B. [National Research Tomsk Polytechnic University, 30, Lenin Avenue, Tomsk 634050 (Russian Federation); Pivovarov, Yu.L. [National Research Tomsk Polytechnic University, 30, Lenin Avenue, Tomsk 634050 (Russian Federation); Tomsk State University, 36, Lenin Avenue, Tomsk 634050 (Russian Federation); Takabayashi, Y. [SAGA Light Source, 8-7 Yayoigaoka, Tosu, Saga 841-0005 (Japan)
2015-07-15
Calculations based on the use of realistic potential of the system of crystallographic planes confirm earlier results on existence of resonances in reflection of relativistic electrons and positrons by the crystal surface, if the crystallographic planes are parallel to the surface.The physical reason of predicted phenomena, similar to the band structure of transverse energy levels, is connected with the Bloch form of the wave functions of electrons (positrons) near the crystallographic planes, which appears both in the case of planar channeling of relativistic electrons (positrons) and in reflection by a crystal surface. Calculations show that positions of maxima in reflection of relativistic electrons and positrons by crystal surface specifically depend on the angle of incidence with respect to the crystal surface and relativistic factor of electrons/positrons. These maxima form the Darwin tables similar to that in ultra-cold neutron diffraction.
Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation
Tsai, Hung-Ming
2016-01-01
In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schr\\"odinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantum mechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature---suggesting a "many interacting worlds" interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive ...
Quantum Monte Carlo Studies of Relativistic Effects in Light Nuclei
Forest, J L; Arriaga, A
1999-01-01
Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials and their boost corrections. In this work we use the variational Monte Carlo method to study two kinds of relativistic effects in the binding energy of 3H and 4He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by about 15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of 0.4 (1.9) MeV in 3H (4He) and account for 37% of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.
Gharbi, A.; Touloum, S.; Bouda, A.
2015-04-01
We study the Klein-Gordon equation with noncentral and separable potential under the condition of equal scalar and vector potentials and we obtain the corresponding relativistic quantum Hamilton-Jacobi equation. The application of the quantum Hamilton-Jacobi formalism to the double ring-shaped Kratzer potential leads to its relativistic energy spectrum as well as the corresponding eigenfunctions.
LETTER TO THE EDITOR: Recurrence relations for relativistic atomic matrix elements
Martínez-y-Romero, R. P.; Núñez-Yépez, H. N.; Salas-Brito, A. L.
2000-05-01
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired by the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non-relativistic quantum mechanics. We first obtain the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use this relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.
Relativistic quantum effects of confining potentials on the Klein-Gordon oscillator
Vitória, R. L. L.; Bakke, K.
2016-02-01
The behaviour of the Klein-Gordon oscillator under the influence of linear and Coulomb-type potentials is investigated. The introduction of the scalar potentials is made by modifying the mass term of the Klein-Gordon equation, then, by searching for relativistic bound states, a particular quantum effect can be observed: a dependence of the angular frequency of the Klein-Gordon oscillator on the quantum numbers associated with the radial modes and the angular momentum. As an example, we analyse the angular frequency and the energy level associated with the ground state of the relativistic system.
Non-Perturbative Four-Point Scattering from First-Quantized Relativistic JWKB
Irizarry-Gelpí, M E
2016-01-01
We apply the quantum mechanical (first-quantized) JWKB approximation to a two-body path integral describing the near-forward scattering of two relativistic, heavy, non-identical, scalar particles in $D$ spacetime dimensions. In contrast to the loop expansion, in $D = 4$ this gives a strong-coupling expansion, and in $D = 3$ a non-perturbative weak-coupling expansion. When the interaction is mediated by massless quanta with spin $N$, we obtain explicit, relativistic results for the scattering amplitude when $N = 0$, $1$ and $2$. In $D = 4$ we find a Regge trajectory function that agrees with the usual quantum mechanical spectrum. We also find an exponentiated infrared divergence that becomes a pure phase factor when the Mandelstam invariants $s$ and $t$ are inside of the physical scattering region. In $D = 3$ we find a singularity whose position along the $s$ axis is dependent on $t$. When the interaction is mediated by a heavy scalar with mass $M$, in $D = 3$ we find an all-order scattering amplitude where th...
Role of causality in ensuring unconditional security of relativistic quantum cryptography
Molotkov, S N
2001-01-01
The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not employ collective measurements and quantum codes, the cryptosystem can be experimentally realized with the present state-of-art in fiber optics technologies. The proposed cryptosystem employs only the individual measurements and classical codes and, in addition, the key distribution problem allows to postpone the choice of the state encoding scheme until after the states are already received instead of choosing it before sending the states into the communication channel (i.e. to employ a sort of ``antedate'' coding).
Quantum-mechanical description of Lense-Thirring effect for relativistic scalar particles
Silenko, Alexander J
2014-01-01
Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field approximated by a spatially isotropic metric is found. The quantum-mechanical description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz vector is given in the nonrelativistic and weak-field approximation. Relativistic quantum-mechanical equations for the velocity and acceleration operators are obtained. The equation for the acceleration defines the Coriolis-like and centrifugal-like accelerations and presents the quantum-mechanical description of the frame-dragging effect.
Ideas of Space - Euclidean, Non-Euclidean, and Relativistic
Gray, Jeremy
1989-09-01
Now in a revised and expanded new edition, this volume chronologically traces the evolution of Euclidean, non-Euclidean, and relativistic theories regarding the shape of the universe. A unique, highly readable, and entertaining account, the book assumes no special mathematical knowledge. It reviews the failed classical attempts to prove the parallel postulate and provides coverage of the role of Gauss, Lobachevskii, and Bolyai in setting the foundations of modern differential geometry, which laid the groundwork for Einstein's theories of special and general relativity. This updated account includes a new chapter on Islamic contributions to this area, as well as additional information on gravitation, the nature of space and black holes.
Ds and relativistic quantum mechanics in one dimension
Ruijgrok, TW
2003-01-01
It is recalled that a ten year old calculation of all meson masses may explain the low value of the recently discovered Ds(2317) meson. This calculation was based on a fully relativistic quasiparticle theory, which has been applied to a large number of bound state problems and scattering processes.
Losing energy in classical, relativistic and quantum mechanics
Atkinson, David
2007-01-01
A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. In relativistic mechanics, however, neit
Montero, M
2011-01-01
We provide a simple argument showing that, in the limit of infinite acceleration, the entanglement in a fermionic field bipartite system must be independent of the choice of Unruh modes. This implies that most tensor product structures used previously to compute field entanglement in relativistic quantum information cannot give rise to physical results.
Harder, T Mark
2016-01-01
It is shown how Fermionic material particles can emerge from a covariant formulation of the de Broglie-Bohm theory. Material particles are continuous fields, formed as the eigenvalue of the Schrodinger field operator, evaluated along a Bohmian trajectory. The motivation for this work is due to a theorem proved by Malament that states there cannot be a relativistic quantum mechanics of localizable particles.
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data
Donker, H. C.; Katsnelson, M. I.; De Raedt, H.; Michielsen, K.
2016-01-01
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data colle
Energy Technology Data Exchange (ETDEWEB)
B. Julia-Diaz, H. Kamano, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki
2009-04-01
Within the relativistic quantum field theory, we analyze the differences between the $\\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
Are non-relativistic neutrinos the dark matter particles?
Nieuwenhuizen, Theo M.
2010-06-01
The dark matter of a spherical, relaxed galaxy cluster is modeled by isothermal, non-interacting fermions; the galaxies and X-ray gas by isothermal classical distributions. A fit to lensing data of the cluster Abell 1689 works well and yields a mass of a few eV. This low value casts doubt on the existence of a Cold Dark Matter particle. The best case is the neutrino, for which in the cluster all 12 left- and righthanded modes are available. The fit gives an average mass 1.45(h/0.70)1/2 eV, with 2% error, while neutrino oscillations bring deviations of order meV. A neutrino mass between 0.2 and 2 eV will be searched in the Katrin experiment in 2012. The ideal value is mν = Yeme = 1.4998 eV, where Ye = 23/4GF1/2me is the Yukawa coupling of the electron. It occurs for reduced Hubble constant h = 0.744 with 4% error, right on top of and slightly sharper than the presently best supernova value of Riess et al. 2009, h = 0.742 with 4.8% error. In the cluster the neutrinos have a temperature of 0.045 K and a de Broglie length of 0.20 mm. They establish a quantum structure of several million light years across, the largest known in the Universe. The virial α-particle temperature of 9.9+/-1.1 keV/kB coincides with the average one of X-rays, while also the gas profile comes out well. Active neutrinos alone with the 1.45 eV mass give some 9.5% dark matter, more than allowed by the cold dark matter papradigm. A dark matter fraction of some 19%, Ων = (h/0.70)-3/20.189 (4), occurs for 12 degrees of freedom, i. e., for 3 families of left plus right handed neutrinos. The sterile modes may be produced in the early universe if there is a small Majorana mass matrix of order meV, on top of the Dirac matrix with ~1.45 eV masses. The neutrinos are free-streaming in the early universe and play no role during the decoupling. But now they are not homogeneous anymore. They condense on the Abell 1689 cluster fairly late, at redshift z~6-8, a prediction testable in future observations
Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation
Tsai, Hung-Ming; Poirier, Bill
2016-03-01
In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schrödinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantum mechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature—suggesting a “many interacting worlds” interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive and well-localized everywhere, and its spatial integral is conserved over time—in any inertial frame. Finally, the ensemble-averaged wavepacket motion is along a straight line path through spacetime. In this manner, the pathologies of the wave-based relativistic quantum theory, as applied to wavepacket propagation, are avoided.
Relativistic Spectrum of Hydrogen Atom in Space-Time Non-Commutativity
Moumni, Mustafa; Zaim, Slimane; 10.1063/1.4715429
2012-01-01
We study space-time non-commutativity applied to the hydrogen atom via the Seiberg-Witten map and its phenomenological effects. We find that it modifies the Coulomb potential in the Hamiltonian and add an r-3 part. By calculating the energies from Dirac equation using perturbation theory, we study the modifications to the hydrogen spectrum. We find that it removes the degeneracy with respect to the total angular momentum quantum number and acts like a Lamb shift. Comparing the results with experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter. N.B: In precedent works (arXiv:0907.1904, arXiv:1003.5732 and arXiv:1006.4590), we have used the Bopp Shift formulation of non-commutativity but here use it \\`a la Seiberg-Witten in the Relativistic case.
Ion Injection at Non-relativistic Collisionless Shocks
Caprioli, Damiano; Spitkovsky, Anatoly
2014-01-01
We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for i...
General relativistic effects in quantum interference of "clocks"
Zych, Magdalena; Costa, Fabio; Brukner, Časlav
2016-01-01
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.
Whistler wave generation by non-gyrotropic, relativistic, electron beams
Skender, Marina
2014-01-01
Particle-in-cell code, EPOCH, is used for studying features of the wave component evident to propagate backwards from the front of the non-gyrotropic, relativistic beam of electrons injected in the Maxwellian, magnetised background plasma with decreasing density profile. According to recent findings presented in Tsiklauri (2011), Schmitz & Tsiklauri (2013) and Pechhacker & Tsiklauri (2012), in a 1.5-dimensional magnetised plasma system, the non-gyrotropic beam generates freely escaping electromagnetic radiation with properties similar to the Type-III solar radio bursts. In this study the backwards propagating wave component evident in the perpendicular components of the elecromagnetic field in such a system is presented for the first time. Background magnetic field strength in the system is varied in order to prove that the backwards propagating wave's frequency, prescribed by the whistler wave dispersion relation, is proportional to the specified magnetic field. Moreover, the identified whistlers are...
Interacting relativistic quantum dynamics for multi-time wave functions
Directory of Open Access Journals (Sweden)
Lienert Matthias
2016-01-01
Full Text Available In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
Interacting relativistic quantum dynamics for multi-time wave functions
Lienert, Matthias
2016-11-01
In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
Weakly nonlinear ion-acoustic excitations in a relativistic model for dense quantum plasma.
Behery, E E; Haas, F; Kourakis, I
2016-02-01
The dynamics of linear and nonlinear ionic-scale electrostatic excitations propagating in a magnetized relativistic quantum plasma is studied. A quantum-hydrodynamic model is adopted and degenerate statistics for the electrons is taken into account. The dispersion properties of linear ion acoustic waves are examined in detail. A modified characteristic charge screening length and "sound speed" are introduced, for relativistic quantum plasmas. By employing the reductive perturbation technique, a Zakharov-Kuznetzov-type equation is derived. Using the small-k expansion method, the stability profile of weakly nonlinear slightly supersonic electrostatic pulses is also discussed. The effect of electron degeneracy on the basic characteristics of electrostatic excitations is investigated. The entire analysis is valid in a three-dimensional as well as in two-dimensional geometry. A brief discussion of possible applications in laboratory and space plasmas is included.
Certified Randomness from a Two-Level System in a Relativistic Quantum Field
Thinh, Le Phuc; Martin-Martinez, Eduardo
2016-01-01
Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis complementary to its preparation. Towards realizing this goal one may consider using atoms or superconducting qubits, promising candidates for quantum information processing. However, their unavoidable interaction with the electromagnetic field affects their dynamics. At large time scales, this can result in decoherence. Smaller time scales in principle avoid this problem, but may not be well analysed under the usual rotating wave and single-mode approximation (RWA and SMA) which break the relativistic nature of quantum field theory. Here, we use a fully relativistic analysis to quantify the information that an adversary with access to the field could get on the result of an atomic measurement. Surprisingly, we find that the adversary's guessing probability is not minimized for ...
Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems.
Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2015-03-11
Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems.
Radiative decays $V\\rightarrow P\\gamma^{*}$ in the instant form of relativistic quantum mechanics
Krutov, Alexander; Troitsky, Vadim
2016-01-01
Calculations of form factor for the radiative decays $V\\rightarrow P\\gamma^{*}$ process are performed in the framework of an instant form of relativistic quantum mechanics. The electromagnetic current operator for this decay is constructed. The transition form factor is obtained in the so called relativistic modified impulse approximation (MIA). The current operator satisfies the conditions of Lorentz-covariance and current conservation in MIA. The results of the calculations are compared with the analogous results in the light-front dynamics and in the model of vector meson dominance
AdS and dS black hole solutions in analogue gravity: The relativistic and non-relativistic cases
Dey, Ramit; Turcati, Rodrigo
2016-01-01
We show that Schwarzschild black hole solutions in asymptotically Anti-de Sitter (AdS) and de Sitter (dS) spaces may, up to a conformal factor, be reproduced in the framework of analogue gravity. The aforementioned derivation is performed using relativistic and non-relativistic Bose-Einstein condensates. In addition, we demonstrate that the (2+1) planar AdS black hole can be mapped into the non-relativistic acoustic metric. Given that AdS black holes are extensively employed in the gauge/gravity duality, we then comment on the possibility to study the AdS/CFT correspondence and gravity/fluid duality from an analogue gravity perspective.
Non-Abelian 3d Bosonization and Quantum Hall States
Radicevic, Djordje; Turner, Carl
2016-01-01
Bosonization dualities relate two different Chern-Simons-matter theories, with bosonic matter on one side replaced by fermionic matter on the other. We first describe a more general class of non-Abelian bosonization dualities. We then explore the non-relativistic physics of these theories in the quantum Hall regime. The bosonic theory lies in a condensed phase and admits vortices which are known to form a non-Abelian quantum Hall state. We ask how this same physics arises in the fermionic theory. We find that a condensed boson corresponds to a fully filled Landau level of fermions, while bosonic vortices map to fermionic holes. We confirm that the ground state of the two theories is indeed described by the same quantum Hall wavefunction.
General relativistic effects in quantum interference of “clocks”
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.
The Thomas-Fermi Quark Model: Non-Relativistic Aspects
Liu, Quan
2012-01-01
Non-relativistic aspects of the Thomas-Fermi statistical quark model are developed. A review is given and our modified approach to spin in the model is explained. Our results are limited so far to two inequivalent simultaneous wave functions which can apply to multiple degenerate flavors. An explicit spin interaction is introduced, which requires the introduction of a generalized spin "flavor". Although the model is designed to be most reliable for many-quark states, we find surprisingly that it may be used to fit the low energy spectrum of octet and decouplet baryons. The low energy fit allows us to investigate the six-quark doubly strange H-dibaryon state, possible 6 quark nucleon-nucleon resonances and flavor symmetric strange states of higher quark content.
Differential Regularization of a Non-relativistic Anyon Model
Freedman, Daniel Z; Rius, N
1994-01-01
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\\phi$ with $\\lambda (\\phi {}^{*} \\phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the $\\phi {}^{*} \\phi {}^{*} \\phi \\phi$ 4-point function, which is the only primitively divergent Green's function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the $\\beta$-function is investigated. If the renormalization scheme is fixed to agree with a previous 1-loop calculation, the 2- and 3-loop contributions to $\\beta(\\lambda,e)$ vanish, and $\\beta(\\lambda,e)$ itself vanishes when the ``self-dual'' condition relating $\\lambda$ to the gauge coupling $e$ is imposed.
Quantum interferometric visibility as a witness of general relativistic proper time.
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Brukner, Časlav
2011-10-18
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.
Local thermodynamical equilibrium and the β frame for a quantum relativistic fluid
Energy Technology Data Exchange (ETDEWEB)
Becattini, Francesco; Grossi, Eduardo [Universita di Firenze, Florence (Italy); INFN, Florence (Italy); Bucciantini, Leda [Dipartimento di Fisica, Universita di Pisa (Italy); INFN, Pisa (Italy); Tinti, Leonardo [Jan Kochanowski University, Kielce (Poland)
2015-05-15
We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector β, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of the stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the β frame and Landau frame and present an instance where they differ. (orig.)
Local thermodynamical equilibrium and the β frame for a quantum relativistic fluid
Energy Technology Data Exchange (ETDEWEB)
Becattini, Francesco, E-mail: becattini@fi.infn.it [Università di Firenze and INFN Sezione di Firenze, Florence (Italy); Bucciantini, Leda, E-mail: leda.bucciantini@df.unipi.it [Dipartimento di Fisica dell’Università di Pisa and INFN, 56127, Pisa (Italy); Grossi, Eduardo, E-mail: grossi@fi.infn.it [Università di Firenze and INFN Sezione di Firenze, Florence (Italy); Tinti, Leonardo, E-mail: dr.leonardo.tinti@gmail.com [Jan Kochanowski University, Kielce (Poland)
2015-05-05
We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector β, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of the stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the β frame and Landau frame and present an instance where they differ.
Rideout, David; Amelino-Camelia, Giovanni; Demarie, Tommaso F; Higgins, Brendon L; Kempf, Achim; Kent, Adrian; Laflamme, Raymond; Ma, Xian; Mann, Robert B; Martin-Martinez, Eduardo; Menicucci, Nicolas C; Moffat, John; Simon, Christoph; Sorkin, Rafael; Smolin, Lee; Terno, Daniel R
2012-01-01
Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 meters. In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ${\\sim} 10^{-20}$ meters, up to that of hundreds of kilometers. Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide...
Non-hermitian quantum thermodynamics
Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh
2016-03-01
Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions, namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.
Non-hermitian quantum thermodynamics.
Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh
2016-03-22
Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the Jarzynski equality holds true for all non-hermitian quantum systems with real spectrum. This equality expresses the second law of thermodynamics for isothermal processes arbitrarily far from equilibrium. In the quasistatic limit however, the second law leads to the Carnot bound which is fulfilled even if some eigenenergies are complex provided they appear in conjugate pairs. Furthermore, we propose two setups to test our predictions, namely with strongly interacting excitons and photons in a semiconductor microcavity and in the non-hermitian tight-binding model.
Clarifying the covariant formalism for the SZ effect due to relativistic non-thermal electrons
Boehm, Celine
2008-01-01
We derive the covariant formalism associated with the relativistic Sunyaev-Zel'dovich effect due to a non-thermal population of high energy electrons in clusters of galaxies. More precisely, we show that the formalism proposed by Wright in 1979, based on an empirical approach (but widely used in the literature) to compute the inverse Compton scattering of a population of relativistic electrons on CMB photons, can actually be re-interpreted as a Boltzmann-like equation, in the single scattering approximation. Although this would tend to reconcile Wright's approach with the latest works on the relativistic corrections of the thermal SZ effect, we find that the squared matrix amplitude derived by Wright by applying a relativistic Lorentz boost on Chandrasekhar's non-relativistic formula is incorrect (it is not equivalent to the well-known Compton scattering squared matrix amplitude in the limit of relativistic incoming electrons and low energy photons). This has important consequences. In particular, this modifi...
Ding, Min; Li, Yachun
2017-04-01
We study the 1-D piston problem for the relativistic Euler equations under the assumption that the total variations of both the initial data and the velocity of the piston are sufficiently small. By a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Meanwhile, we consider the convergence of the entropy solutions to the corresponding entropy solutions of the classical non-relativistic Euler equations as the light speed c→ +∞.
Li, En-Kun; Geng, Jin-Ling
2014-01-01
The modified holographic Ricci dark energy coupled to interacting relativistic and non-relativistic dark matter is considered in the nonflat Friedmann-Robertson-Walker universe. Through examining the deceleration parameter, one can find that the transition time of the Universe from decelerating to accelerating phase in the interacting holographic Ricci dark energy model is close to that in the $\\Lambda$ cold dark matter model. The evolution of modified holographic Ricci dark energy's state parameter and the evolution of dark matter and dark energy's densities shows that the dark energy holds the dominant position from the near past to the future. By studying the statefinder diagnostic and the evolution of the total pressure, one can find that this model could explain the Universe's transition from the radiation to accelerating expansion stage through the dust stage. According to the $Om$ diagnostic, it is easy to find that when the interaction is weak and the proportion of relativistic dark matter in total da...
De Sanctis, M; Santopinto, E; Vassallo, A
2015-01-01
We briefly describe our relativistic quark-diquark model, developed within the framework of point form dynamics, which is the relativistic extension of the interacting quark-diquark model. In order to do that we have to show the main properties and quantum numbers of the effective degree of freedom of constituent diquark. Our results for the nonstrange baryon spectrum and for the nucleon electromagnetic form factors are discussed.
Non-adiabatic geometrical quantum gates in semiconductor quantum dots
Solinas, P; Zanghì, N; Rossi, F; Solinas, Paolo; Zanardi, Paolo; Zanghì, Nino; Rossi, Fausto
2003-01-01
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be in principle implemented
Spin, angular momentum and spin-statistics for a relativistic quantum many body system
Horwitz, Lawrence
2012-01-01
The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wavepackets and admitting covariant expectation values for the coordinate operator x^\\mu introduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within the identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed using the usual Clebsch-Gordon coefficients associated with angular momentum. Important consequences, such as entanglement for subsystems at unequal times, covariant statistical correlations in many body systems, and the construction of relativistic boson and fermion statistical ensembles, as well as implications for the foliation of the Fock space and for quantum field theory are discussed.
Semi-classical locality for the non-relativistic path integral in configuration space
Gomes, Henrique
2015-01-01
In an accompanying paper, we have put forward an interpretation of quantum mechanics grounded on a non-relativistic Lagrangian 3+1 formalism of a closed Universe, existing on timeless configuration space. However, not much was said there about the role of locality, which was not assumed. In this paper, I describe how subsystems existing in (spatial) regions with fixed boundary conditions can be represented as submanifolds of the complete configuration space. I show that if the action functional can be put in the form of Riemannian distance element, then dynamical independence of the subsystem implies that the respective submanifolds are totally geodesic. When two regions are mutually independent the semi-classical path integral kernel factorizes, showing cluster decomposition. To exemplify these constructions I then construct a specific gravitational system with two propagating physical degrees of freedom and no refoliation-invariance. Finally, considering the path integral in this 3+1 context, I implement an...
Quantum correlation with moving beamsplitters in relativistic conﬁguration
Indian Academy of Sciences (India)
André Stefanov; Hugo Zbinden; Nicolas Gisin; Antoine Suarez
2002-08-01
We present a recent experiment [1] using space-like beamsplitters in motion revealing a new feature of quantum nonlocality: The correlations caused by two-particle quantum entanglement are not only independent of distance (as we already know from the conventional Bell-type experiments) but also independent of the time-ordering between the two single-photon measurements. Hence, it seems impossible to cast them in any real time ordering and maintain a causal explanation in which an earlier event inﬂuences a later one by arbitrarily fast communication.
Relativistic corrections and non-Gaussianity in radio continuum surveys
Energy Technology Data Exchange (ETDEWEB)
Maartens, Roy [Physics Department, University of the Western Cape, Cape Town 7535 (South Africa); Zhao, Gong-Bo; Bacon, David; Koyama, Kazuya [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom); Raccanelli, Alvise, E-mail: Roy.Maartens@port.ac.uk, E-mail: Gong-bo.Zhao@port.ac.uk, E-mail: David.Bacon@port.ac.uk, E-mail: Kazuya.Koyama@port.ac.uk, E-mail: alvise@caltech.edu [Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA 91109 (United States)
2013-02-01
Forthcoming radio continuum surveys will cover large volumes of the observable Universe and will reach to high redshifts, making them potentially powerful probes of dark energy, modified gravity and non-Gaussianity. We consider the continuum surveys with LOFAR, WSRT and ASKAP, and examples of continuum surveys with the SKA. We extend recent work on these surveys by including redshift space distortions and lensing convergence in the radio source auto-correlation. In addition we compute the general relativistic (GR) corrections to the angular power spectrum. These GR corrections to the standard Newtonian analysis of the power spectrum become significant on scales near and beyond the Hubble scale at each redshift. We find that the GR corrections are at most percent-level in LOFAR, WODAN and EMU surveys, but they can produce O(10%) changes for high enough sensitivity SKA continuum surveys. The signal is however dominated by cosmic variance, and multiple-tracer techniques will be needed to overcome this problem. The GR corrections are suppressed in continuum surveys because of the integration over redshift — we expect that GR corrections will be enhanced for future SKA HI surveys in which the source redshifts will be known. We also provide predictions for the angular power spectra in the case where the primordial perturbations have local non-Gaussianity. We find that non-Gaussianity dominates over GR corrections, and rises above cosmic variance when f{sub NL}∼>5 for SKA continuum surveys.
On Relativistic Quantum Information Properties of Entangled Wave Vectors of Massive Fermions
Cafaro, C; Mancini, S
2011-01-01
We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin-1/2 massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative motion. For the case of indistinguishable particles, we consider a balanced scenario where the momenta of the pair are well-defined but not maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ($\\eta$) family of entangled bipartite states. For the case of distinguishable particles, we consider an unbalanced scenario where the momenta of the pair are well-defined and maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ($\\xi$) family of non-maximally entangled bipartite states. In both cases, we show that neither the spin-spin ($ss$) nor the momentum-momentum ($mm$) entanglements quantified by means of Wootters' concurrence are Lorentz invariant quantities: the total amount of entangl...
Relativistic quantum dynamics of scalar bosons under a full vector Coulomb interaction
Energy Technology Data Exchange (ETDEWEB)
Castro, Luis B. [Universidade Federal do Maranhao (UFMA), Departamento de Fisica, Sao Luis, MA (Brazil); Oliveira, Luiz P. de [Universidade de Sao Paulo (USP), Instituto de Fisica, Sao Paulo, SP (Brazil); Garcia, Marcelo G. [Instituto Tecnologico de Aeronautica (ITA), Departamento de Fisica, Sao Jose dos Campos, SP (Brazil); Universidade Estadual de Campinas (UNICAMP), IMECC, Departamento de Matematica Aplicada, Campinas, SP (Brazil); Castro, Antonio S. de [Universidade Estadual Paulista (UNESP), Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil)
2017-05-15
The relativistic quantum dynamics of scalar bosons in the background of a full vector coupling (minimal plus nonminimal vector couplings) is explored in the context of the Duffin-Kemmer-Petiau formalism. The Coulomb phase shift is determined for a general mixing of couplings and it is shown that the space component of the nonminimal coupling is a sine qua non condition for the exact closed-form scattering amplitude. It follows that the Rutherford cross section vanishes in the absence of the time component of the minimal coupling. Bound-state solutions obtained from the poles of the partial scattering amplitude show that the time component of the minimal coupling plays an essential role. The bound-state solutions depend on the nonminimal coupling and the spectrum consists of particles or antiparticles depending on the sign of the time component of the minimal coupling without chance for pair production even in the presence of strong couplings. It is also shown that an accidental degeneracy appears for a particular mixing of couplings. (orig.)
On the disorder-driven quantum transition in three-dimensional relativistic metals
Louvet, T.; Carpentier, D.; Fedorenko, A. A.
2016-12-01
The Weyl semimetals are topologically protected from a gap opening against weak disorder in three dimensions. However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in d =2 +ɛ of a U (N ) Gross-Neveu model in the limit N →0 . Unfortunately, this model is not multiplicatively renormalizable in 2 +ɛ dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high-energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a d =4 -ɛ expansion. We also discuss the characterization of the transition by the multifractal spectrum of wave functions.
Effect of relativistic acceleration on continuous variable quantum teleportation and dense coding
Grochowski, Piotr T.; Rajchel, Grzegorz; Kiałka, Filip; Dragan, Andrzej
2017-01-01
We investigate how relativistic acceleration of the observers can affect the performance of the quantum teleportation and dense coding for continuous variable states of localized wavepackets. Such protocols are typically optimized for symmetric resources prepared in an inertial frame of reference. A mismatch of the sender and the receiver's accelerations can introduce asymmetry to the shared entanglement, which has an effect on the efficiency of the protocol that goes beyond entanglement degr...
Geometric back-reaction in pre-inflation from relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Arcodia, Marcos R.A. [Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), Mar del Plata (Argentina); Bellini, Mauricio [Universidad Nacional de Mar del Plata, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Mar del Plata (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), Mar del Plata (Argentina)
2016-06-15
The pre-inflationary evolution of the universe describes the beginning of the expansion from a static initial state, such that the Hubble parameter is initially zero, but increases to an asymptotic constant value, in which it could achieve a de Sitter (inflationary) expansion. The expansion is driven by a background phantom field. The back-reaction effects at this moment should describe vacuum geometrical excitations, which are studied in detail in this work using relativistic quantum geometry. (orig.)
Pramono, Subur; Cari, Cari
2016-01-01
In this work, we study the exact solution of Dirac equation in the hyper-spherical coordinate under influence of separable q-Deformed quantum potentials. The q-deformed hyperbolic Rosen-Morse potential is perturbed by q-deformed non-central trigonometric Scarf potentials, where whole of them can be solved by using Asymptotic Iteration Method (AIM). This work is limited to spin symmetry case. The relativistic energy equation and orbital quantum number equation lD-1 have been obtained using Asymptotic Iteration Method. The upper radial wave function equations and angular wave function equations are also obtained by using this method. The relativistic energy levels are numerically calculated using Mat Lab, the increase of radial quantum number n causes the increase of bound state relativistic energy level both in dimension D = 5 and D = 3. The bound state relativistic energy level decreases with increasing of both deformation parameter q and orbital quantum number nl.
Model of Quantum Computing in the Cloud: The Relativistic Vision Applied in Corporate Networks
Directory of Open Access Journals (Sweden)
Chau Sen Shia
2016-08-01
Full Text Available Cloud computing has is one of the subjects of interest to information technology professionals and to organizations when the subject covers financial economics and return on investment for companies. This work aims to present as a contribution proposing a model of quantum computing in the cloud using the relativistic physics concepts and foundations of quantum mechanics to propose a new vision in the use of virtualization environment in corporate networks. The model was based on simulation and testing of connection with providers in virtualization environments with Datacenters and implementing the basics of relativity and quantum mechanics in communication with networks of companies, to establish alliances and resource sharing between the organizations. The data were collected and then were performed calculations that demonstrate and identify connections and integrations that establish relations of cloud computing with the relativistic vision, in such a way that complement the approaches of physics and computing with the theories of the magnetic field and the propagation of light. The research is characterized as exploratory, because searches check physical connections with cloud computing, the network of companies and the adhesion of the proposed model. Were presented the relationship between the proposal and the practical application that makes it possible to describe the results of the main features, demonstrating the relativistic model integration with new technologies of virtualization of Datacenters, and optimize the resource with the propagation of light, electromagnetic waves, simultaneity, length contraction and time dilation.
Comments on a Discrepancy Between the Relativistic and the Quantum Concepts of Light
Pombo, Claudia
2007-12-01
The realist point of view of a physical theory assumes that physical concepts must have a correspondent in the phenomenological world. We adopt a slightly modified form of realism, based on Carnap's separation of languages, in which only the observational concepts, belonging to the observational language, have a phenomenological correspondent. Other physical concepts, belonging to a theoretical language, do not correspond to entities in the physical world. This point of view is named observational realism. Based on these ideas, we review the notions of relativistic and quantum observation, independently from measurement, and show that there is a discrepancy between the concepts of wave light in relativity and in quantum mechanics.
Holographic energy loss in non-relativistic backgrounds
Atashi, Mahdi; Farahbodnia, Mitra
2016-01-01
In this paper, we study some aspects of energy loss in non-relativistic theories from holography. We analyze the energy lost by a rotating heavy point particle along a circle of radius $l$ with angular velocity $\\omega$ in theories with general dynamical exponent $z$ and hyperscaling violation exponent $\\theta$. It is shown that this problem provides a novel perspective on the energy loss in such theories. A general computation at zero and finite temperature is done and it is shown that how the total energy loss rate depends non-trivially on two characteristic exponents $(z,\\theta)$. We find that at zero temperature there is a special radius $l_c$ where the energy loss is independent of different values of $(z,\\theta)$. Also, there is a crossover between a regime in which the energy loss is dominated by the linear drag force and by the radiation because of the acceleration of the rotating particle. We discover different behaviors at finite temperature case.
Charged relativistic fluids and non-linear electrodynamics
Dereli, T.; Tucker, R. W.
2010-01-01
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.
Teh, Mei-Hui; LeBohec, Stephan
2016-01-01
This article is the first in a series of two presenting the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. In this first paper, we present the definition of a complex "scale-covariant time-differential operator" and show that mechanics of non-differentiable paths is implemented in the same way as classical mechanics but with the replacement of the time derivative and velocity with the time-differential operator and associated complex velocity. With this, the generalized form of Newton's fundamental relation of dynamics is shown to take the form of a Langevin equation in the case of stationary motion characterized by a null average classical velocity. The numerical integration of the Langevin equation in the case of a harmonic oscillator reveals the same statistics as the stationary solutions of the Schrodinger equation for the same problem. This motivates the second paper which makes the relation to quantum mechanics explicit by discussing the axioms o...
Horwitz, Lawrence; Hu, Bei-Lok; Lee, Da-Shin; Gill, Tepper; Land, Martin
2011-12-01
find a propagating 0+ mode that could account for accelerated expansion. They discuss, in particular, a model in the Bianchi class A, and present a Lagrangian and a typical dynamical evolution. J T Hsiang, C H Wu, L H Ford and K W Ng review investigations of the effects of a quantum stress tensor of a conformal field on inflationary cosmology. They find that the quantum stress tensor fluctuations lead to effects that can depend upon the total expansion factor during inflation, which may contribute to a non-scale invariant and non-Gaussian component to the primordial spectrum of perturbations,and may be observable. In the framework of quantum field theory, A N Kvinikhidze and B Blankleider show that a relativistic quantum mechanics emerges from light frame quantum field theory, and that in the case of baryon-like conservation, these theories are equivalent. With T Skawronski, they show in a second paper the power of gauging for several body problems, and demonstrate how this idea can be applied to the study of parton distributions, two nucleon currents in cutoff quantum field theory, and in a potential model for πN scattering. C M Chen and J R Sun study a holographic dual of the Reissner-Nordström black hole in a quantum gravity description from the perspective of the AdS/CFT correspondence. On a fundamental level, somewhat related to the ideas of Finkelstein, A Gersten and A Moalem discuss the factorization of the d'Alembertian in a 4×4 representation of 'relativistic quaternions' to find an interpretation of Maxwell's equations; with an 8×8 factorization, they obtain spin two fields as in gravitation. They discuss a general method for obtaining field equations for zero mass particles and arbitrary spin. M Pavsic has developed a generalization of the theory of Stueckelberg, mentioned above, applicable to general relativity. He finds a source of the world time τ in M2,4, achieving a 5D metric tensor and a resolution of the 'problem of time' in this framework. In a
Quantum corrections to the Relativistic mean-field theory
Maydanyuk, Sergei P; Bakry, Ahmed
2016-01-01
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{\\rm shell}$. But, a difference between $V_{RMF}$ and $V_{\\rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indica...
Quantum non-locality and relativity metaphysical intimations of modern physics
Maudlin, Tim
2011-01-01
The third edition of Quantum Non-Locality and Relativity has been carefully updated to reflect significant developments, including a new chapter covering important recent work in the foundations of physics. A new edition of the premier philosophical study of Bell's Theorem and its implication for the relativistic account of space and timeDiscusses Roderich Tumiulka's explicit, relativistic theory that can reproduce the quantum mechanical violation of Bell's inequality. Discusses the "Free Will Theorem" of John Conway and Simon KochenIntroduces philosophers to the relevant physics and demonstra
Relationship of quantum mechanics to classical electromagnetism and classical relativistic mechanics
Energy Technology Data Exchange (ETDEWEB)
Field, J H [Departement de Physique Nucleaire et Corpusculaire, Universite de Geneve, 24, quai Ernest-Ansermet CH-1211 Geneva 4 (Switzerland)
2004-05-14
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the canonical commutation relations and the Maxwell-Lorentz equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as 'inverse correspondence' since quantum phenomena become apparent on considering the low photon number density limit of classical electromagnetism. Generalization to massive particles leads to the Klein-Gordon and Schroedinger equations. The difference between the quantum wavefunction of the photon and a classical electromagnetic wave is discussed in some detail.
Relativistic longitudinal non-Abelian oscillations in quark–antiquark plasma
Indian Academy of Sciences (India)
Vishnu M Bannur
2002-10-01
We study the relativistic version of the non-Abelian, longitudinal wave in quark–antiquark plasma reported earlier by Bhat et al [Phys. Rev. D39, 649 (1989)]. We have also relaxed various approximations they made in their analysis. Both the quark and antiquark dynamics are taken in our analysis. The non-linearity arising from non-Abelian ﬁeld as well as from plasma are included. Hence it is an exact longitudinal mode in relativistic quark–antiquark plasma, relevant to the study of quark gluon plasma. We ﬁnd that earlier results are reproduced for non-relativistic and low amplitude oscillations, but are modiﬁed for relativistic or large amplitude waves. Further more, the above results are based on just four ﬁrst-order equations for gauge invariant quantities derived from gauge covariant twelve ﬁrst-order equations.
Radiation of non-relativistic particle on a conducting sphere and a string of spheres
Shul'ga, N F; Larikova, E A
2016-01-01
The radiation arising under uniform motion of non-relativistic charged particle by (or through) perfectly conducting sphere is considered. The rigorous results are obtained using the method of images known from electrostatics.
Non-unitary probabilistic quantum computing
Gingrich, Robert M.; Williams, Colin P.
2004-01-01
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.
On Relativistic Quantum Information Properties of Entangled Wave Vectors of Massive Fermions
Cafaro, Carlo; Capozziello, Salvatore; Mancini, Stefano
2012-08-01
We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin-1/2 massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative motion. For the case of indistinguishable particles, we consider a balanced scenario where the momenta of the pair are well-defined but not maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ( η) family of entangled bipartite states. For the case of distinguishable particles, we consider an unbalanced scenario where the momenta of the pair are well-defined and maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ( ξ) family of non-maximally entangled bipartite states. In both cases, we show that neither the spin-spin ( ss) nor the momentum-momentum ( mm) entanglements quantified by means of Wootters' concurrence are Lorentz invariant quantities: the total amount of entanglement regarded as the sum of these entanglements is not the same in different inertial moving frames. In particular, for any value of the entangling parameters, both ss and mm-entanglements are attenuated by Lorentz transformations and their parametric rates of change with respect to the entanglements observed in a rest frame have the same monotonic behavior. However, for indistinguishable (distinguishable) particles, the change in entanglement for the momenta is (is not) the same as the change in entanglement for spins. As a consequence, in both cases, no entanglement compensation between spin and momentum degrees of freedom occurs.
Certified randomness from a two-level system in a relativistic quantum field
Thinh, Le Phuc; Bancal, Jean-Daniel; Martín-Martínez, Eduardo
2016-08-01
Randomness is an indispensable resource in modern science and information technology. Fortunately, an experimentally simple procedure exists to generate randomness with well-characterized devices: measuring a quantum system in a basis complementary to its preparation. Towards realizing this goal one may consider using atoms or superconducting qubits, promising candidates for quantum information processing. However, their unavoidable interaction with the electromagnetic field affects their dynamics. At large time scales, this can result in decoherence. Smaller time scales in principle avoid this problem, but may not be well analyzed under the usual rotating wave and single mode approximation (RWA and SMA) which break the relativistic nature of quantum field theory. Here, we use a fully relativistic analysis to quantify the information that an adversary with access to the field could get on the result of an atomic measurement. Surprisingly, we find that the adversary's guessing probability is not minimized for atoms initially prepared in the ground state (an intuition derived from the RWA and SMA model).
Equilibrium and non-equilibrium properties of a relativistic gas at the transition temperature
Chacón-Acosta, Guillermo
2016-11-01
The Jüttner distribution function for equilibrium relativistic fluids has two well-known limits, the non-relativistic limit at low temperatures and ultra-relativistic limit for high temperatures. Recently, the description of this transition in velocity space in the system, from a gaussian to a bimodal distribution was made by Mendoza et al. Physically, it is a transition between a regime where the relativistic energy is dominated by kinetic to another where the rest energy dominates. It has been found that the critical temperature at which the relativistic corrections becomes relevant, depends just on the dimension of the system, this allowed a description in terms of the theory of critical points (Montakhab et al.). In this contribution a review of the thermodynamic quantities that are only dependent on the ratio between temperature and critical temperature, and the dimension is made. We will also analyze the effects of critical temperature on dissipative processes in simple special relativistic fluids. Particularly, purely relativistic terms that are usually proportional to the number density gradient are studied. The transport coefficients can be written in terms of the transition temperature, this will allow us to identify the lower order relativistic effects just in terms of the dimension of the system.
Relativistic stellar jets: dynamics and non-thermal radiation
Directory of Open Access Journals (Sweden)
Bosch-Ramon Valentí
2013-12-01
Full Text Available Relativistic stellar jets, produced in binary systems called microquasars, propagate through media with different spatial scales releasing their energy in the form of work and radiation from radio to gamma rays. There are several medium-interaction scenarios that these jets can face. In particular, in relativistic stellar jets the presence of a star is an unavoidable element whose importance deserves to be studied. In the case of highmass stars, their powerful winds are likely to interact dynamically with the jet, but also low-mass stars in the post-main sequence phase can present dense winds that will act as an obstacle for the jet propagation. In this work, we present a semi-qualitative discussion on the importance of the star for the evolution of relativistic stellar jets.
Physical stress, mass, and energy for non-relativistic spinful matter
Geracie, Michael; Roberts, Matthew M
2016-01-01
For theories of relativistic matter fields with spin there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for non-relativistic matter theories. We point out that while the physical non-relativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. We also provide computations of these quantities for some simple non-relativistic actions.
Hayata, Tomoya; Hongo, Masaru; Noumi, Toshifumi
2015-01-01
We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time-evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without choice of frame such as the Landau-Lifshitz or Eckart frame.
Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime
Dernek, Mustafa; Sucu, Yusuf; Unal, Nuri
2016-01-01
In the study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, in the rest frame and the spin-1 matrices satisfy $SO(2,1)$ spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we construct the current components of the spin-1 particle.
A study of transverse charge density of pions in relativistic quantum mechanics
Institute of Scientific and Technical Information of China (English)
DONG Yu-Bing; WANG Yi-Zhan
2011-01-01
The transverse charge density of pions is calculated based on relativistic quantum mechanics,where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.
Relativistic quantum transport coefficients for second-order viscous hydrodynamics
Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw; Strickland, Michael
2015-01-01
We express the transport coefficients appearing in the second-order evolution equations for bulk viscous pressure and shear stress tensor using Bose-Einstein, Boltzmann, and Fermi-Dirac statistics for the equilibrium distribution function and Grad's 14-moment approximation as well as the method of Chapman-Enskog expansion for the non-equilibrium part. Specializing to the case of boost-invariant and transversally homogeneous longitudinal expansion of the viscous medium, we compare the results obtained using the above methods with those obtained from the exact solution of massive 0+1d Boltzmann equation in the relaxation-time approximation. We show that compared to the 14-moment approximation, the hydrodynamic transport coefficients obtained using the Chapman-Enskog method result in better agreement with the exact solution of the Boltzmann equation in relaxation-time approximation.
The Schrödinger problem, Levy processes noise in relativistic quantum mechanics
Garbaczewski, P; Olkiewicz, R
1995-01-01
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schr\\"{o}dinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feyman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard "free" case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schr\\"{o}dinge...
Description of Unstable Systems in Relativistic Quantum Mechanics in the Lax-Phillips Theory
Horwitz, L P
1998-01-01
We discuss some of the experimental motivation for the need for semigroup decay laws, and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the parametrized relativistic quantum theory is a natural setting for the realization of the Lax-Phillips theory.
Whistler wave generation by non-gyrotropic, relativistic, electron beams
Skender, Marina; Tsiklauri, David
2014-05-01
]. In this study [5], for the first time, the backwards propagating wave component evident in the perpendicular components of the electromagnetic field in such a system is presented. Features of the wave component propagating backwards from the front of the non-gyrotropic, relativistic, beam of electrons injected in the Maxwellian, magnetised background plasma with decreasing density profile are studied by using the Particle-In-Cell code EPOCH. Magnetic field in the 1.5-dimensional system is varied in order to prove that the backwards propagating wave is harmonic of the electron cyclotron frequency. The analysis has lead to the identification of the backwards travelling waves as whistlers. Moreover, the whistlers are shown to be generated by the normal and anomalous Doppler resonance. Large fraction of the energy of the perpendicular electromagnetic field components is found to be carried away by the whistler waves. [1] D. Tsiklauri, Phys. Plasmas 18, 052903 (2011). [2] D. Tsiklauri, H. Schmitz, Geophys. Res. Abs. 15, EGU2013-5403 (2013). [3] H. Schmitz, D. Tsiklauri, Phys. Plasmas 20, 062903 (2013). [4] R. Pechhacker, D. Tsiklauri, Phys. Plasmas 19, 112903 (2012). [5] M. Skender, D. Tsiklauri, submitted to Phys. Plasmas (2013): http://astro.qmul.ac.uk/ tsiklauri/
Pseudo-unitary dynamics of free relativistic quantum mechanical twofold systems
Cardoso, J. G.
2012-05-01
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably normalized vectors belonging to the two-complex-dimensional spaces that occur in local orthogonal decompositions of isomorphic copies of Cartan's space. The corresponding dynamical variables thus show up as bounded pseudo-Hermitian operator restrictions that possess real discrete spectra. Any measurement processes have to be performed locally in orthocronous proper Lorentz frames, but typical observational correlations are expressed in terms of symbolic configurations which come from the covariant action on spaces of state vectors of the Poincaré subgroup of an adequate realization of SU(2,2). The overall approach turns out to supply a supposedly natural description of the dynamics of free twofold systems in flat spacetime. One of the main outlooks devised here brings forward the possibility of carrying out methodically the construction of a background to a new relativistic theory of quantum information.
de Martini, Francesco; Santamato, Enrico
2016-04-01
The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper [E. Santamato and F. D. De Martini, Found. Phys. 45 (2015) 858] we presented a complete proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics” (CQG). In this paper, by the same theory, the proof of the spin-statistics theorem (SST) is extended to the relativistic domain in the scenario of curved spacetime. No relativistic quantum field operators are used in the present proof and the particle exchange properties are drawn from rotational invariance rather than from Lorentz invariance. Our relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. As in the nonrelativistic case, we find once more that the “intrinsic helicity” of the elementary particles enters naturally into play. It is therefore this property, not considered in the standard quantum mechanics (SQM), which determines the correct spin-statistics connection observed in Nature.
Imari Walker, Sara; Davies, Paul C. W.; Samantray, Prasant; Aharonov, Yakir
2014-06-01
Quantum weak measurements with states both pre- and post-selected offer a window into a hitherto neglected sector of quantum mechanics. A class of such systems involves time dependent evolution with transitions possible. In this paper we explore two very simple systems in this class. The first is a toy model representing the decay of an excited atom. The second is the tunneling of a particle through a barrier. The post-selection criteria are chosen as follows: at the final time, the atom remains in its initial excited state for the first example and the particle remains behind the barrier for the second. We then ask what weak values are predicted in the physical environment of the atom (to which no net energy has been transferred) and in the region beyond the barrier (to which the particle has not tunneled). Thus, just as the dog that didn't bark in Arthur Conan Doyle's story Silver Blaze gave Sherlock Holmes meaningful information about the dog's non-canine environment, here we probe whether the particle that has not decayed or has not tunneled can provide measurable information about physical changes in the environment. Previous work suggests that very large weak values might arise in these regions for long durations between pre- and post-selection times. Our calculations reveal some distinct differences between the two model systems.
Abdikian, A.; Mahmood, S.
2016-12-01
The obliquely nonlinear acoustic solitary propagation in a relativistically quantum magnetized electron-positron (e-p) plasma in the presence of the external magnetic field as well as the stationary ions for neutralizing the plasma background was studied. By considering the dynamic of the fluid e-p quantum and by using the quantum hydrodynamics model and the standard reductive perturbation technique, the Zakharov-Kuznetsov (ZK) equation is derived for small but finite amplitude waves and the solitary wave solution for the parameters relevant to dense astrophysical objects such as white dwarf stars is obtained. The numerical results show that the relativistic effects lead to propagate the electrostatic bell shape structures in quantum e-p plasmas like those in classical pair-ion or pair species for relativistic plasmas. It is also observed that by increasing the relativistic effects, the amplitude and width of the e-p acoustic solitary wave will decrease. In addition, the wave amplitude increases as positron density decreases in magnetized e-p plasmas. It is indicated that by increasing the strength of the magnetic field, the width of the soliton reduces and it becomes sharper. At the end, we have analytically and numerically shown that the pulse soliton solution of the ZK equation is unstable and have traced the dependence of the instability growth rate on electron density. It is found that by considering the relativistic pressure, the instability of the soliton pulse can be reduced. The results can be useful to study the obliquely nonlinear propagation of small amplitude localized structures in magnetized quantum e-p plasmas and be applicable to understand the particle and energy transport mechanism in compact stars such as white dwarfs, where the effects of relativistic electron degeneracy become important.
Non-Boolean probabilities and quantum measurement
Energy Technology Data Exchange (ETDEWEB)
Niestegge, Gerd
2001-08-03
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum mechanical Hilbert space formalism and exhibits a particular phenomenon (state-independent conditional probabilities) which may provide new opportunities for an understanding of the quantum measurement process. Examples of the proposed model are provided, using Jordan operator algebras. (author)
Energy Technology Data Exchange (ETDEWEB)
Kent, Adrian; Munro, William J.; Spiller, Timothy P. [Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, Cambridge, United Kingdom and Perimeter Institute for Theoretical Physics, Waterloo, Ontario (Canada); NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198 (Japan); Quantum Information Science, School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT (United Kingdom)
2011-07-15
We define the task of quantum tagging, that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is unbounded. We define simple security models for this task and briefly discuss alternatives. We illustrate the pitfalls of naive quantum cryptographic reasoning in this context by describing several protocols which at first sight appear unconditionally secure but which, as we show, can in fact be broken by teleportation-based attacks. We also describe some protocols which cannot be broken by these specific attacks, but do not prove they are unconditionally secure. We review the history of quantum tagging protocols, and show that protocols previously proposed by Malaney and Chandran et al. are provably insecure.
Soliton propagation in relativistic hydrodynamics
Fogaça, D A; 10.1016/j.nuclphysa.2007.03.104
2013-01-01
We study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. In a previous work we have derived a KdV equation from Euler and continuity equations in non-relativistic hydrodynamics. In the present contribution we extend our formalism to relativistic fluids. We present results for a given equation of state, which is based on quantum hadrodynamics (QHD).
Continuity properties of the semi-group and its integral kernel in non-relativistic QED
Matte, Oliver
2016-07-01
Employing recent results on stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics by B. Güneysu, J. S. Møller, and the present author, we study the continuity of the corresponding semi-group between weighted vector-valued Lp-spaces, continuity properties of elements in the range of the semi-group, and the pointwise continuity of an operator-valued semi-group kernel. We further discuss the continuous dependence of the semi-group and its integral kernel on model parameters. All these results are obtained for Kato decomposable electrostatic potentials and the actual assumptions on the model are general enough to cover the Nelson model as well. As a corollary, we obtain some new pointwise exponential decay and continuity results on elements of low-energetic spectral subspaces of atoms or molecules that also take spin into account. In a simpler situation where spin is neglected, we explain how to verify the joint continuity of positive ground state eigenvectors with respect to spatial coordinates and model parameters. There are no smallness assumptions imposed on any model parameter.
Stefanov, Stefan Z
2011-01-01
The realization of Daily Artificial Dispatcher as a quantum/relativistic computation consists of perturbative renormalization of the Electrical Power System (EPS), generating the flowcharts of computation, verification, validation, description and help. Perturbative renormalization of EPS energy and time has been carried out in this paper for a day ahead via virtual thermalization of the EPS for a day ahead.
Mohammadi, Vahid; Chenaghlou, Alireza
2017-09-01
The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum E3‧, anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang-Coulomb monopole (YCM) superintegrable system (a SU(2) non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.
Semi-classical Locality for the Non-relativistic Path Integral in Configuration Space
Gomes, Henrique
2017-09-01
In an accompanying paper Gomes (arXiv:1504.02818, 2015), we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space Q of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is based solely on the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, M-O, if the projection of extremal curves on Q onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to e^{i\\hat{H}t}circ prO= prOcirc e^{i\\hat{H}t}, where prO:Q→ Q_O^{partial O} is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality.
Persico, Franco; Power, Edwin A.
1988-01-01
The physics of the electromagnetic vacuum, its fluctuations and its role in spontaneous emission has been studied since the early days of the quantum theory of radiation. In recent years there has been a renewed interest in the nature of the vacuum state and its potency in giving rise to observable effects. For example the question of amplification of photon signals and the way vacuum fluctuations may provide inescapable noise is fundamental to the theory of measurement. Quantum electrodynamics in cavities has become a very active area of research both experimentally and theoretically and the way the radiation field, even in vacuo, is changed by confinement is of interest and importance. The effective Einstein A-coefficient can be much smaller than in free space because the available modes are sparser in a cavity. Radiative connections such as the Lamb shift energies are also changed as the virtual photon modes are varied by the confinement. The existence of electromagnetic field energy (from the vacuum fluctuations) in the neighbourhood of atoms/molecules in their ground state is demonstrated by its effect on test molecules brought into the vicinity of the original sources. All the forces analogous to that of Van der Waals, including of course their Casimir retardations at long range, are explicable in terms of these virtual cloud effects. The Adriatico Conference on "Vacuum in Non-Relativistic Matter-Radiation Systems" held in July 1987 brought together scientists in quantum optics, quantum field theorists and others interested in the electromagnetic vacuum. It was most successful in that the participants found enough mutual agreement but with clearly defined tensions between them to provide excitement and argument throughout the four days' meeting. This volume consists of most of the papers presented at the conference. It is clear that the collection ranges from the pedagogical and the review type article to research papers with original material. The
A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2001-05-11
We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.
Testing non-associative quantum mechanics
Bojowald, Martin; Buyukcam, Umut
2015-01-01
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to non-associative algebras. Their quantum physics has remained obscure. This letter presents the first derivation of potentially testable physical results in non-associative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.
Maxwell-Chern-Simons Models: Their Symmetries, Exact Solutions and Non-relativistic Limits
Directory of Open Access Journals (Sweden)
J. Niederle
2010-01-01
Full Text Available Two Maxwell-Chern-Simons (MCS models in the (1 + 3-dimensional space-space are discussed and families of their exact solutions are found. In contrast to the Carroll-Field-Jackiw (CFE model [2] these systems are relativistically invariant and include the CFJ model as a particular sector.Using the InNonNu-Wigner contraction a Galilei-invariant non-relativistic limit of the systems is found, which makes possible to find a Galilean formulation of the CFJ model.
On quantum effects in spontaneous emission by a relativistic electron beam in an undulator
Geloni, Gianluca; Saldin, Evgeni
2012-01-01
Robb and Bonifacio (2011) claimed that a previously neglected quantum effect results in noticeable changes in the evolution of the energy distribution associated with spontaneous emission in long undulators. They revisited theoretical models used to describe the emission of radiation by relativistic electrons as a continuous diffusive process, and claimed that in the asymptotic limit for a large number of undulator periods the evolution of the electron energy distribution occurs as discrete energy groups according to Poisson distribution. We show that these novel results have no physical sense, because they are based on a one-dimensional model of spontaneous emission and assume that electrons are sheets of charge. However, electrons are point-like particles and, as is well-known, the bandwidth of the angular-integrated spectrum of undulator radiation is independent of the number of undulator periods. If we determine the evolution of the energy distribution using a three-dimensional theory we find the well-kno...
Calculations of Bose-Einstein correlations from Relativistic Quantum Molecular Dynamics
Energy Technology Data Exchange (ETDEWEB)
Sullivan, J.P.; Berenguer, M.; Fields, D.E.; Jacak, B.V.; Sarabura, M.; Simon-Gillo, J.; Sorge, H.; van Hecke, H. [Los Alamos National Lab., NM (United States); Pratt, S. [Michigan State Univ., East Lansing, MI (United States)
1993-10-01
Bose-Einstein correlation functions which are in good agreement with pion data can be calculated from an event generator. Here pion and (preliminary) kaon data from CERN experiment NA44 are compared to the calculations. The dynamics of 200 GeV/nucleon {sup 32}S + Pb collisions are calculated, without correlations due to interference patterns of a many-body wavefunction for identical particles, using the Relativistic Quantum Molecular Dynamics model (RQMD). The model is used to generate the phase-space coordinates of the emitted hadrons at the time they suffer their last strong interaction (freeze-out). Using the freeze-out position and momentum of pairs of randomly selected identical particles, a two-particle symmetrized wave-function is calculated and used to add two-body correlations. Details of the technique have been described previously. The method is similar to that used in the Spacer program.
Brown, Natalie
In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infinite symmetric band-matrix structure. The corresponding representation of the Green's operator of such a matrix can be given as a matrix continued fraction. Furthermore, we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert space. Combining these two techniques, we are able to solve relativistic quantum mechanical problems of a spin-zero particle in a Coulomb-like potential with a high level of accuracy.
Non-Gaussianities due to Relativistic Corrections to the Observed Galaxy Bispectrum
Di Dio, E; Durrer, R; Marozzi, G; Dizgah, A Moradinezhad; Noreña, J; Riotto, A
2016-01-01
High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for relativistic corrections to the clustering statistics is particularly important for the upcoming galaxy surveys covering progressively larger fraction of the sky. We focus on relativistic projection effects due to the fact that we observe the galaxies through the light that reaches the telescope on perturbed geodesics. These projection effects can give rise to an effective $f_{\\rm NL}$ that can be misinterpreted as the primordial non-Gaussianity signal and hence is a systematic to be carefully computed and accounted for in modelling of the bispectrum. We develop the technique to properly account for relativistic effects in terms of purely observable quantities, namely angles and redshifts. We give some examples by applying this approach to a subset of the contributio...
Witnessing non-Markovianity of quantum evolution
Chruściński, Dariusz; Kossakowski, Andrzej
2014-01-01
We provide further characterization of non-Markovian quantum dynamics based on the concept of divisible dynamical maps. In analogy to entanglement witness we propose a non-Markovianity witness and introduce the corresponding measure of non-Markovianity. We also provide characterization of non-Markovianity in terms of Wigner-Yanase-Dyson skew information.
Origin of Dynamical Quantum Non-locality
Pachon, Cesar E.; Pachon, Leonardo A.
2014-03-01
Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two ``flavours'': a kinematic non-locality- arising from the structure of the Hilbert space- and a dynamical non-locality- arising from the quantum equations of motion-. Kinematic non-locality is unable to induce any change in the probability distributions, so that the ``action-at-a-distance'' cannot manifest. Conversely, dynamical non-locality does create explicit changes in probability, though in a ``causality-preserving'' manner. The origin of non-locality of quantum measurements and its relations to the fundamental postulates of quantum mechanics, such as the uncertainty principle, have been only recently elucidated. Here we trace the origin of dynamical non-locality to the superposition principle. This relation allows us to establish and identify how the uncertainty and the superposition principles determine the non-local character of the outcome of a quantum measurement. Being based on group theoretical and path integral formulations, our formulation admits immediate generalizations and extensions to to, e.g., quantum field theory. This work was supported by the Departamento Administrativo de Ciencia, Tecnologia e Innovacion -COLCIENCIAS- of Colombia under the grant number 111556934912.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
Relativistic regimes for dispersive shock-waves in non-paraxial nonlinear optics
Gentilini, Silvia; Conti, Claudio
2014-01-01
We investigate the effect of non-paraxiality in the dynamics of dispersive shock waves in the defocusing nonlinear Schroedinger equation. We show that the problem can be described in terms of a relativistic particle moving in a potential. Lowest order corrections enhance the wave-breaking and impose a limit to the highest achievable spectrum in an amount experimentally testable.
Light Fermion Finite Mass Effects in Non-relativistic Bound States
Eiras, D; Eiras, Dolors; Soto, Joan
2000-01-01
We present analytic expressions for the vacuum polarization effects due to a light fermion with finite mass in the binding energy and in the wave function at the origin of QED and (weak coupling) QCD non-relativistic bound states. Applications to exotic atoms, \\Upsilon (1s) and t\\bar{t} production near threshold are briefly discussed.
Entanglement in non-Hermitian quantum theory
Indian Academy of Sciences (India)
Arun K Pati
2009-09-01
Entanglement is one of the key features of quantum world that has no classical counterpart. This arises due to the linear superposition principle and the tensor product structure of the Hilbert space when we deal with multiparticle systems. In this paper, we will introduce the notion of entanglement for quantum systems that are governed by non-Hermitian yet $\\mathcal{PT}$ -symmetric Hamiltonians. We will show that maximally entangled states in usual quantum theory behave like non-maximally entangled states in $\\mathcal{PT}$ -symmetric quantum theory. Furthermore, we will show how to create entanglement between two $\\mathcal{PT}$ qubits using non-Hermitian Hamiltonians and discuss the entangling capability of such interaction Hamiltonians that are non-Hermitian in nature.
Non-linear (loop) quantum cosmology
Bojowald, Martin; Dantas, Christine C; Jaffe, Matthew; Simpson, David
2012-01-01
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a low-curvature universe can arise from tiny local contributions adding up coherently in large regions.
In search of a primitive ontology for relativistic quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Lam, Vincent [University of Lausanne, CH-1015 Lausanne (Switzerland)
2014-07-01
There is a recently much discussed approach to the ontology of quantum mechanics according to which the theory is ultimately about entities in 3-dimensional space and their temporal evolution. Such an ontology postulating from the start matter localized in usual physical space or spacetime, by contrast to an abstract high-dimensional space such as the configuration space of wave function realism, is called primitive ontology in the recent literature on the topic and finds its roots in Bell's notion of local beables. The main motivation for a primitive ontology lies in its explanatory power: the primitive ontology allows for a direct account of the behaviour and properties of familiar macroscopic objects. In this context, it is natural to look for a primitive ontology for relativistic quantum field theory (RQFT). The aim of this talk is to critically discuss this interpretative move within RQFT, in particular with respect to the foundational issue of the existence of unitarily inequivalent representations. Indeed the proposed primitive ontologies for RQFT rely either on a Fock space representation or a wave functional representation, which are strictly speaking only unambiguously available for free systems in flat spacetime. As a consequence, it is argued that these primitive ontologies constitute only effective ontologies and are hardly satisfying as a fundamental ontology for RQFT.
Seto, Keita; Nagatomo, Hideo; Koga, James; Mima, Kunioki
In the near future, the intensity of the ultra-short pulse laser will reach to 1022 W/cm2. When an electron is irradiated by this laser, the electron's behavior is relativistic with significant bremsstrahlung. This radiation from the electron is regarded as the energy loss of electron. Therefore, the electron's motion changes because of the kinetic energy changing. This radiation effect on the charged particle is the self-interaction, called the “radiation reaction” or the “radiation damping”. For this reason, the radiation reaction appears in laser electron interactions with an ultra-short pulse laser whose intensity becomes larger than 1022 W/cm2. In the classical theory, it is described by the Lorentz-Abraham-Dirac (LAD) equation. But, this equation has a mathematical difficulty, which we call the “run-away”. Therefore, there are many methods for avoiding this problem. However, Dirac's viewpoint is brilliant, based on the idea of quantum electrodynamics. We propose a new equation of motion in the quantum theory with radiation reaction in this paper.
On quantum effects in spontaneous emission by a relativistic electron beam in an undulator
Energy Technology Data Exchange (ETDEWEB)
Geloni, Gianluca [European XFEL GmbH, Hamburg (Germany); Kocharyan, Vitali; Saldin, Evgeni [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-02-15
Robb and Bonifacio (2011) claimed that a previously neglected quantum effect results in noticeable changes in the evolution of the energy distribution associated with spontaneous emission in long undulators. They revisited theoretical models used to describe the emission of radiation by relativistic electrons as a continuous diffusive process, and claimed that in the asymptotic limit for a large number of undulator periods the evolution of the electron energy distribution occurs as discrete energy groups according to Poisson distribution. We show that these novel results have no physical sense, because they are based on a one-dimensional model of spontaneous emission and assume that electrons are sheets of charge. However, electrons are point-like particles and, as is well-known, the bandwidth of the angular-integrated spectrum of undulator radiation is independent of the number of undulator periods. If we determine the evolution of the energy distribution using a three-dimensional theory we find the well-known results consistent with a continuous diffusive process. The additional pedagogical purpose of this paper is to review how quantum diffusion of electron energy in an undulator with small undulator parameter can be simply analyzed using the Thomson cross-section expression, unlike the conventional treatment based on the expression for the Lienard-Wiechert fields. (orig.)
Relativistic calculations of the non-resonant two-photon ionization of neutral atoms
Hofbrucker, Jiri; Fritzsche, Stephan
2016-01-01
The non-resonant two-photon one-electron ionization of neutral atoms is studied theoretically in the framework of relativistic second-order perturbation theory and independent particle approximation. In particular, the importance of relativistic and screening effects in the total two-photon ionization cross section is investigated. Detailed computations have been carried out for the K-shell ionization of neutral Ne, Ge, Xe, and U atoms. The relativistic effects significantly decrease the total cross section, for the case of U, for example, they reduce the total cross section by a factor of two. Moreover, we have found that the account for the screening effects of the remaining electrons leads to occurrence of an unexpected minimum in the total cross section at the total photon energies equal to the ionization threshold, for the case of Ne, for example, the cross section drops there by a factor of three.
Dimmelmeier, H; Font, J A; Dimmelmeier, Harald; Stergioulas, Nikolaos; Font, Jose A.
2005-01-01
We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an extended avoided crossing between the l = 0 and l = 4 first overtones, which is important for correctly identifying mode frequencies in case of detection. For uniformly rotating stars near the mass-shedding limit, we confirm the existence of the mass-shedding-induced damping of pulsations, though the effect is not as strong as i...
Condensation for non-relativistic matter in Hořava–Lifshitz gravity
Directory of Open Access Journals (Sweden)
Jiliang Jing
2015-10-01
Full Text Available We study condensation for non-relativistic matter in a Hořava–Lifshitz black hole without the condition of the detailed balance. We show that, for the fixed non-relativistic parameter α2 (or the detailed balance parameter ϵ, it is easier for the scalar hair to form as the parameter ϵ (or α2 becomes larger, but the condensation is not affected by the non-relativistic parameter β2. We also find that the ratio of the gap frequency in conductivity to the critical temperature decreases with the increase of ϵ and α2, but increases with the increase of β2. The ratio can reduce to the Horowitz–Roberts relation ωg/Tc≈8 obtained in the Einstein gravity and Cai's result ωg/Tc≈13 found in a Hořava–Lifshitz gravity with the condition of the detailed balance for the relativistic matter. Especially, we note that the ratio can arrive at the value of the BCS theory ωg/Tc≈3.5 by taking proper values of the parameters.
The confined hydrogenoid ion in non-relativistic quantum electrodynamics
Amour, L
2006-01-01
We consider a system of a nucleus with an electron together with the quantized electromagnetic field. Instead of fixing the nucleus, the system is confined by its center of mass. This model is used in theoretical physics to explain the Lamb-Dicke and the M\\"ossbauer effects (see [CTDRG]). When an ultraviolet cut-off is imposed we initiate the spectral analysis of the Hamiltonian describing the system and we derive the existence of a ground state. This is achieved without conditions on the fine structure constant. [CTDRG] C. Cohen-Tannoudji, J. Dupont-Roc and G. Grynberg. Processus d'interaction entre photons et atomes. Edition du CNRS, 2001.
Non-perturbative quantum geometry III
Krefl, Daniel
2016-08-01
The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stokes phenomena over the combined string coupling and quantized Kähler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local ℙ1 + ℙ1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stokes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local ℙ2 near the conifold point in moduli space is also provided.
Non-Perturbative Quantum Geometry III
Krefl, Daniel
2016-01-01
The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.
Modified stochastic variational approach to non-Hermitian quantum systems
Kraft, Daniel; Plessas, Willibald
2016-08-01
The stochastic variational method has proven to be a very efficient and accurate tool to calculate especially bound states of quantum-mechanical few-body systems. It relies on the Rayleigh-Ritz variational principle for minimizing real eigenenergies of Hermitian Hamiltonians. From molecular to atomic, nuclear, and particle physics there is actually a great demand of describing also resonant states to a high degree of reliance. This is especially true with regard to hadron resonances, which have to be treated in a relativistic framework. So far standard methods of dealing with quantum chromodynamics have not yet succeeded in describing hadron resonances in a realistic manner. Resonant states can be handled by non-Hermitian quantum Hamiltonians. These states correspond to poles in the lower half of the unphysical sheet of the complex energy plane and are therefore intimately connected with complex eigenvalues. Consequently the Rayleigh-Ritz variational principle cannot be employed in the usual manner. We have studied alternative selection principles for the choice of test functions to treat resonances along the stochastic variational method. We have found that a stationarity principle for the complex energy eigenvalues provides a viable method for selecting test functions for resonant states in a constructive manner. We discuss several variants thereof and exemplify their practical efficiencies.
Quantum Non-Objectivity from Performativity of Quantum Phenomena
Khrennikov, Andrei
2014-01-01
We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables and the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on the one hand, the formalism of QM constructed as a mathematical theory is self-consistent, but, on the other hand, quantum phenomena as results of experimenter's performances are not self-consistent. This self-inconsistency is an effect of that the language of QM differs much from the language of human performances. The first is the language of a mathematical theory which uses some Aristotelian and Russellian assumptions (e.g., the assumption that there are logical atoms). The second language consists of performative propositions which are self-consistent only from the viewpoint of conventional mathematical theory, but they satisfy another logic which is non-Aristotelian. Hence, the representation of quantum reality in linguistic terms may be different: from a mathematical theory to a logic of pe...
Non-perturbative description of quantum systems
Feranchuk, Ilya; Le, Van-Hoang; Ulyanenkov, Alexander
2015-01-01
This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
Non-Markovian Reactivation of Quantum Relays
Pirandola, Stefano; Jacobsen, Christian S; Spedalieri, Gaetana; Braunstein, Samuel L; Gehring, Tobias; Andersen, Ulrik L
2015-01-01
We consider a quantum relay which is used by two parties to perform several continuous-variable protocols: Entanglement swapping, distillation, quantum teleportation, and quantum key distribution. The theory of these protocols is extended to a non-Markovian model of decoherence characterized by correlated Gaussian noise. Even if bipartite entanglement is completely lost at the relay, we show that the various protocols can progressively be reactivated by the separable noise-correlations of the environment. In fact, above a critical amount, these correlations are able to restore the distribution of quadripartite entanglement, which can be localized into an exploitable bipartite form by the action of the relay. Our findings are confirmed by a proof-of-principle experiment and show the potential advantages of non-Markovian effects in a quantum network architecture.
Energy Technology Data Exchange (ETDEWEB)
Bakke, K., E-mail: kbakke@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa-PB (Brazil); Furtado, C., E-mail: furtado@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa-PB (Brazil); Belich, H., E-mail: belichjr@gmail.com [Departamento de Física e Química, Universidade Federal do Espírito Santo, Av. Fernando Ferrari, 514, Goiabeiras, 29060-900, Vitória, ES (Brazil)
2016-09-15
From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the violation of the Lorentz symmetry and write an effective metric for the cosmic string spacetime. Then, we investigate the arising of an analogue of the Anandan quantum phase for a relativistic Dirac neutral particle with a permanent magnetic dipole moment in the cosmic string spacetime under Lorentz symmetry breaking effects. Besides, we analyse the influence of the effects of the Lorentz symmetry violation and the topology of the defect on the Aharonov–Casher geometric quantum phase in the nonrelativistic limit.
Bakke, K.; Furtado, C.; Belich, H.
2016-09-01
From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the violation of the Lorentz symmetry and write an effective metric for the cosmic string spacetime. Then, we investigate the arising of an analogue of the Anandan quantum phase for a relativistic Dirac neutral particle with a permanent magnetic dipole moment in the cosmic string spacetime under Lorentz symmetry breaking effects. Besides, we analyse the influence of the effects of the Lorentz symmetry violation and the topology of the defect on the Aharonov-Casher geometric quantum phase in the nonrelativistic limit.
Non-Markovianity hinders Quantum Darwinism
Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina
2016-01-01
We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.
Non-Mechanism in Quantum Oracle Computing
Castagnoli, G C
1999-01-01
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As well known, some oracle problems are solved more efficiently by using quantum algorithms; this naturally implies changing the computer to quantum, while the choice of the software program remains sharp. In order to highlight the non-mechanistic origin of this higher efficiency, also the uncertainty about which program is installed must be represented in a quantum way.
Relativistic recursion relations for transition matrix elements
Martínez y Romero, R P; Salas-Brito, A L
2004-01-01
We review some recent results on recursion relations which help evaluating arbitrary non-diagonal, radial hydrogenic matrix elements of $r^\\lambda$ and of $\\beta r^\\lambda$ ($\\beta$ a Dirac matrix) derived in the context of Dirac relativistic quantum mechanics. Similar recursion relations were derived some years ago by Blanchard in the non relativistic limit. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\\"odinger case. An extension of the relations to the case of two potentials in the so-called unshifted case, but using an arbitrary radial function instead of a power one, is also given. Several important results are obtained as special instances of our recurrence relations, such as a generalization to the relativistic case of the Pasternack-Sternheimer rule. Our results are useful in any atomic or molecular calculation which take into account relativistic corrections.
Kovács, Attila
2017-03-17
Actinide trioxide (AnO3, An = U, Np, Pu, Am, Cm) molecules have been investigated by relativistic multireference quantum chemical calculations with the goal to elucidate their electronic structures. The molecular geometries of the ground and selected excited electronic states have been optimized at the spin-orbit-free complete active space second-order perturbation theory (SF-CASPT2) level. The low-lying vertical excitation states have been computed and characterized by CASPT2 calculations taking into account spin-orbit coupling. The reason for the considerable lengthening of the equatorial An-O bond in AmO3 and CmO3 with respect to the other trioxides has been analyzed on the basis of valence molecular orbitals of the SF ground electronic states. For the bond in question a singly occupied π orbital has been identified, this orbital is doubly occupied in the other (An = U, Np, Pu) trioxides. The clarified electronic structures of the investigated AnO3 molecules confirmed the pentavalent character of Am and Cm in their trioxides in contrast to the hexavalent character of U, Np, and Pu.
An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry
Shiozaki, Toru
2015-01-01
We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N > 10000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige-Van Loan algorithm [D. Kressner, BIT 43, 775 (2003)], which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of two than state-of-the-art implementations of complex Hermitian diagonalization; diagonalizing a 12800 x 12800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel MKL's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD license.
The quantum measurement of time
Shepard, Scott R.
1994-01-01
Traditionally, in non-relativistic Quantum Mechanics, time is considered to be a parameter, rather than an observable quantity like space. In relativistic Quantum Field Theory, space and time are treated equally by reducing space to also be a parameter. Herein, after a brief review of other measurements, we describe a third possibility, which is to treat time as a directly observable quantity.
Thermodynamics of Relativistic Fermions with Chern-Simons Coupling
Bralic, N; Schaposnik, F A
1994-01-01
We study the thermodynamics of the relativistic Quantum Field Theory of massive fermions in three space-time dimensions coupled to an Abelian Maxwell-Chern-Simons gauge field. We evaluate the specific heat at finite temperature and density and find that the variation with the statistical angle is consistent with the non-relativistic ideas on generalized statistics.
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Geracie, Michael; Roberts, Matthew M
2015-01-01
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativisitic symmetries which supports massive matter fields. In particular, one can not impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativis...
Non-thermal Radiation Processes in Relativistic Outflows from AGN
Lefa, Eva
2012-11-01
Non-thermal, leptonic radiation processes have been extensively studied for the interpretation of the observed radiation from jets of Active Galactic Nuclei (AGN). This work addresses the synchrotron and Inverse Compton scattering (ICS) mechanisms, and investigates the potential of a self-consistent, time-dependent approach to currently unsolved problems. Furthermore, it examines how deviations from standard, one-zone models can modify the radiated spectrum. A detailed analysis of the shape of the ICS spectrum is also performed. In the first part a possible interpretation of the hard γ-ray blazar spectra in the framework of leptonic models is investigated. It is demonstrated that hard γ-ray spectra can be generated and maintained in the presence of energy losses, under the basic assumption of a narrow electron energy distribution (EED). Broader spectra can also be modeled if multiple zones contribute to the emission. In such a scheme, hard flaring events, like the one in Mkn 501 in 2009, can be successfully interpreted within a "leading blob" scenario, when one or few zones of emission become dominant. In the second part the shape of the Compton spectrum close to the maximum cutoff is investigated. Analytical approximations for the spectral shape in the cutoff region are derived for various soft photon fields, providing a direct link between the parent EED and the upscattered spectrum. Additionally, a generalization of the beaming pattern for various processes is derived, which accounts for non-stationary, anisotropic and non-homogeneous EEDs. It is shown that anisotropic EEDs may lead to radiated spectra substantially different from the isotropic case. Finally, a self-consistent, non-homogeneous model describing the synchrotron emission from stratified jets is developed. It is found that transverse jet stratification leads to characteristic features in the emitted spectrum different to expectations in homogeneous models.
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
Németh, Z A
1997-01-01
The interaction of a spin 1/2 particle (described by the non-relativistic "Dirac" equation of Lévy-Leblond) with Chern-Simons gauge fields is studied. It is shown, that similarly to the four dimensional spinor models, there is a consistent possibility of coupling them also by axial or chiral type currents. Static self dual vortex solutions together with a vortex-lattice are found with the new couplings.
Hyperfine splitting of the dressed hydrogen atom ground state in non-relativistic QED
Amour, L
2010-01-01
We consider a spin-1/2 electron and a spin-1/2 nucleus interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. For a fixed total momentum sufficiently small, we study the multiplicity of the ground state of the reduced Hamiltonian. We prove that the coupling between the spins of the charged particles and the electromagnetic field splits the degeneracy of the ground state.
Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state
Amour, Laurent
2011-01-01
We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.
The task of the relativistic oscillator in a non-inertial frame of reference
Perepelkin, E. E.; Sadovnikov, B. I.; Inozemtseva, N. G.
2016-09-01
The relativistic theory is one of the most difficult parts of theoretical physics to understand by high school students and scientists alike. In this paper, the important aspects from this theory are considered. The case of the non-inertial reference frame in which the space-time interval was presented for the Lorentz-like transformations, and the condition by which the transition to the inertial reference frame takes place, is shown.
Quantization of Interacting Non-Relativistic Open Strings using Extended Objects
Arias, P J; Fuenmayor, E; Leal, L; Leal, Lorenzo
2005-01-01
Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model comprises open-strings interacting through a Kalb-Ramond field in four dimensions. It is shown that a consistent geometric-representation can be built using a scheme of ``surfaces and lines of Faraday'', provided that the coupling constant (the ``charge'' of the string) is quantized.
Walker, Sara Imari; Samantray, Prasant; Aharonov, Yakir
2016-01-01
Quantum weak measurements with states both pre- and postselected offer a window into a hitherto neglected sector of quantum mechanics. A class of such systems involves time dependent evolution with transitions possible. In this paper we explore two very simple systems in this class. The first is a toy model representing the decay of an excited atom. The second is the tunneling of a particle through a barrier. The postselection criteria are chosen as follows: at the final time, the "atom" remains in its initial excited state for the first example and the particle remains behind the barrier for the second. We then ask what weak values are predicted in the physical environment of the "atom" (to which no net energy has been transferred) and in the region beyond the barrier (to which the particle has not tunneled). Previous work suggests that very large weak values might arise in these regions for long durations between pre- and postselection times. Our calculations reveal some distinct differences between the two...
Relativistic Landau Models and Generation of Fuzzy Spheres
Hasebe, Kazuki
2015-01-01
Non-commutative geometry naturally emerges in low energy physics of Landau models as a consequence of level projection. In this work, we proactively utilize the level projection as an effective tool to generate fuzzy geometry. The level projection is specifically applied to the relativistic Landau models. In one-half of the paper, a detail analysis of the relativistic Landau problems on a sphere is presented, where a concise expression of the Dirac-Landau operator eigenstates is obtained based on algebraic methods. We establish $SU(2)$ "gauge" transformation between the relativistic Landau model and the Pauli-Schr\\"odinger non-relativistic quantum mechanics. In the other half, the fuzzy geometries generated from the relativistic Landau levels are elucidated, where unique properties of the relativistic fuzzy geometries are clarified. We consider mass deformation of the relativistic Landau models and demonstrate its geometrical effects to fuzzy geometry. Super fuzzy geometry is also constructed from a supersymm...
Institute of Scientific and Technical Information of China (English)
Kh. H. EL-SHORBAGY
2008-01-01
The effect of a high frequency (HF) electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid plasma model. An analytical study of the reflection of electro-static wave propagation along a magnetized non-uniform relativistic plasma slab subjected to an intense HF electric field is presented and compared with the case of a non relativistic plasma. It is found that, when the frequency of the incident wave is close to the relativistic electron plasma frequency, the plasma is less reflective due to the presence of both an HF field and the effect of rel-ativistic electrons. On the other hand, for a low-frequency incident wave the reflection coefficient is directly proportional to the amplitude of the HF field. Also, it is shown that the relativistic electron plasma leads to a decrease in the value of reflection coefficient in comparison with the case of the non relativistic plasma.
Quantum Monte Carlo studies of relativistic effects in 3H and 4He
Arriaga, A.
2000-03-01
Relativistic effects in 3H and 4He have been studied in the context of Relativistic Hamiltonian Dynamics, using Variational Monte Carlo Methods. Relativistic invariance is achieved through Poincaré group algebra, which introduces a boost interaction term defining the first relativistic effect considered. The second consists in the nonlocalities associated with the relativistic kinetic energy operator and with the relativistic one-pion exchange potential (OPEP). These nonlocalities tend to cancel, being the total effect on the binding energy attractive and very small, of the order of 1%. The dominant relativistic effect is due to the boost interaction, whose contribution is repulsive and of the order of 5%. The repulsive term of the nonrelativistic 3-body interaction has to be reduced by 37% so that the optimal triton binding energy is recovered, meaning that around 1/3 of this phenomenological term accounts for relativisitic effects. The changes induced on the wave functions of nuclei by these relativistic effetcs are very small and short ranged. Although the nonlocalities of OPEP, resulting in a reduction of 15%, are cancelled by other relativistic contributions, they may have significant effects on pion exchange currents in nuclei.
Relativistic Reconnection: an Efficient Source of Non-Thermal Particles
Sironi, Lorenzo
2014-01-01
In magnetized astrophysical outflows, the dissipation of field energy into particle energy via magnetic reconnection is often invoked to explain the observed non-thermal signatures. By means of two- and three-dimensional particle-in-cell simulations, we investigate anti-parallel reconnection in magnetically-dominated electron-positron plasmas. Our simulations extend to unprecedentedly long temporal and spatial scales, so we can capture the asymptotic state of the system beyond the initial transients, and without any artificial limitation by the boundary conditions. At late times, the reconnection layer is organized into a chain of large magnetic islands connected by thin X-lines. The plasmoid instability further fragments each X-line into a series of smaller islands, separated by X-points. At the X-points, the particles become unmagnetized and they get accelerated along the reconnection electric field. We provide definitive evidence that the late-time particle spectrum integrated over the whole reconnection r...
General Relativistic Non-radial Oscillations of Compact Stars
Hall, Zack, II; Jaikumar, Prashanth
2017-01-01
Currently, we lack a means of identifying the type of matter at the core of compact stars, but in the future, we may be able to use gravitational wave signals produced by fluid oscillations inside compact stars to discover new phases of dense matter. To this end, we study the fluid perturbations inside compact stars such as Neutron Stars and Strange Quark Stars, focusing on modes that couple to gravitational waves. Using a modern equation of state for quark matter that incorporates interactions at moderately high densities, we implement an efficient computational scheme to solve the oscillation equations in the framework of General Relativity, and determine the complex eigenfrequencies that describe the oscillation and damping of the non-radial fluid modes. We discuss the significance of our results for future detection of these modes through gravitational waves. This work is supported in part by the CSULB Graduate Research Fellowship and by the National Science Foundation NSF PHY-1608959.
Institute of Scientific and Technical Information of China (English)
Luo Shao-Kai
2007-01-01
For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables t, qs and (q)s. An example is given to illustrate the application of the results.
QUANTUM ELECTRODYNAMICS - AN INDIVIDUAL VIEW
1982-01-01
The aim of this report is to describe the development of the quantum electrodynamics in the years from the 1930's to the 1950's. It is based on the way the author saw and participate to this development. Four phases are discussed : preparation (1934 - 1946) ; non-covariant relativistic theory (1947) ; first covariant relativistic theory (1947 - 1948) ; second covariant relativistic theory (1949 - 1950). A detailed technical description is presented. The author shows the influence of quantum e...
Energy Technology Data Exchange (ETDEWEB)
Sahu, Biswajit, E-mail: biswajit-sahu@yahoo.co.in [Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126 (India); Sinha, Anjana, E-mail: sinha.anjana@gmail.com [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Department of Mathematics, Visva-Bharati, Santiniketan - 731 204, India and Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700 075 (India)
2015-09-15
A numerical study is presented of the nonlinear dynamics of a magnetized, cold, non-relativistic plasma, in the presence of electron-ion collisions. The ions are considered to be immobile while the electrons move with non-relativistic velocities. The primary interest is to study the effects of the collision parameter, external magnetic field strength, and the initial electromagnetic polarization on the evolution of the plasma system.
Quantum Mechanics and Quantum Field Theory
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
The lifespan of 3D radial solutions to the non-isentropic relativistic Euler equations
Wei, Changhua
2017-10-01
This paper investigates the lower bound of the lifespan of three-dimensional spherically symmetric solutions to the non-isentropic relativistic Euler equations, when the initial data are prescribed as a small perturbation with compact support to a constant state. Based on the structure of the hyperbolic system, we show the almost global existence of the smooth solutions to Eulerian flows (polytropic gases and generalized Chaplygin gases) with genuinely nonlinear characteristics. While for the Eulerian flows (Chaplygin gas and stiff matter) with mild linearly degenerate characteristics, we show the global existence of the radial solutions, moreover, for the non-strictly hyperbolic system (pressureless perfect fluid) satisfying the mild linearly degenerate condition, we prove the blowup phenomenon of the radial solutions and show that the lifespan of the solutions is of order O(ɛ ^{-1}), where ɛ denotes the width of the perturbation. This work can be seen as a complement of our work (Lei and Wei in Math Ann 367:1363-1401, 2017) for relativistic Chaplygin gas and can also be seen as a generalization of the classical Eulerian fluids (Godin in Arch Ration Mech Anal 177:497-511, 2005, J Math Pures Appl 87:91-117, 2007) to the relativistic Eulerian fluids.
Unification of Quantum and Gravity by Non Classical Information Entropy Space
Directory of Open Access Journals (Sweden)
Davide Fiscaletti
2013-09-01
Full Text Available A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy. Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity, the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement. In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum
On Non-Markovian Quantum Evolution
Chruściński, Dariusz; Kossakowski, Andrzej
2013-01-01
We analyze two measures of non-Markovianity: one based on the mathematical concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a simple example of qubit dynamic to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures.
Non-linear collisionless damping of Weibel turbulence in relativistic blast waves
Lemoine, Martin
2014-01-01
The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the first-order non-linear terms associated to the diffusive nature of the particle trajectories. These corrections are found to systematically increase the damping rate, assuming that the scattering length remains larger than the coherence length of the magnetic fluctuations. The relevance of such corrections is discussed in a broader astrophysical perspective, in particular regarding the physics of the external relativistic ...
The non-local content of quantum operations
Collins, D; Popescu, S; Collins, Daniel; Linden, Noah; Popescu, Sandu
2000-01-01
We show that quantum operations on multi-particle systems have a non-local content; this mirrors the non-local content of quantum states. We introduce a general framework for discussing the non-local content of quantum operations, and give a number of examples. Quantitative relations between quantum actions and the entanglement and classical communication resources needed to implement these actions are also described. We also show how entanglement can catalyse classical communication from a quantum action.
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective.
Bylicka, B; Chruściński, D; Maniscalco, S
2014-07-21
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication.
Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective
Bylicka, B.; Chruściński, D.; Maniscalco, S.
2014-01-01
Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication. PMID:25043763
Testing the Higgs sector directly in the non-relativistic domain
Zhang, Zhentao
2016-01-01
Directly measuring the Higgs self-coupling is of great importance for testing the Brout-Englert-Higgs mechanism in the Standard Model. As a scattering that contains the direct information from the Higgs self-coupling, we investigate the process $\\mu^-\\mu^+\\rightarrow HH$ in the threshold region. We calculate the one-loop corrections to the cross section and consider the non-perturbative contribution from the Higgs self-interactions in the final state. It is found that the scattering in the non-relativistic domain could be an especial process to testing the Higgs sector directly.
Tachyonic quantum densities of relativistic electron plasmas: Cherenkov spectra of γ-ray pulsars
Energy Technology Data Exchange (ETDEWEB)
Tomaschitz, Roman, E-mail: tom@geminga.org
2014-06-27
Tachyonic Cherenkov radiation in second quantization can explain the subexponential spectral tails of GeV γ-ray pulsars (Crab pulsar, PSR J1836+5925, PSR J0007+7303, PSR J2021+4026) recently observed with the Fermi-LAT, VERITAS and MAGIC telescopes. The radiation is emitted by a thermal ultra-relativistic electron plasma. The Cherenkov effect is derived from a Maxwell–Proca field with negative mass-square in a dispersive spacetime. The frequency variation of the tachyon mass results in exp(−β{sup ^}ω{sup 1−ρ}) attenuation of the asymptotic Cherenkov energy flux, where β{sup ^} is a decay constant related to the electron temperature and ρ is the frequency scaling exponent of the tachyon mass. An exponent in the range 0<ρ<1 can reproduce the observed subexponential decay of the energy flux. For the Crab pulsar, we find ρ=0.81±0.02, inferred from the substantially weaker-than-exponential decay of its spectral tail measured by MAGIC over an extended energy range. The scaling exponent ρ determines whether the group velocity of the tachyonic γ-rays is sub- or superluminal. - Highlights: • Quantized tachyonic Cherenkov densities lead to subexponential spectral decay. • γ-Ray spectral fits to Crab pulsar, PSR J1836+5925, PSR J0007+7303, PSR J2021+4026. • The polarization of γ-rays is analyzed in the quasiclassical regime and quantum limit. • Three degrees of polarization due to the negative mass-square of the Maxwell–Proca field. • Weibull decay of spectral tails caused by frequency scaling of the tachyon mass.
Scattering in Relativistic Particle Mechanics.
de Bievre, Stephan
Fokker's action principle. To study the Moller operators in the manifestly covariant approach, we extend techniques developed for dealing with non-relativistic two-body scattering and determine precise conditions on the dynamical vectorfields under which the Moller operators can be proven to exist. We then show how Moller operators can be used to construct the Hamiltonian structure in the manifestly covariant approach. Finally, we turn our attention to the quantization of the models discussed. We determine a notion of position in a model for the quantum mechanical treatment of the free relativistic particle that does not violate causality. This result must be compared to recent proofs of the fact that the notions of strict localization and of causality are not mutually compatible in relativistic quantum mechanics. (Abstract shortened with permission of author.).
Berkovitz, Joseph
In this paper and its sequel, I consider the significance of Jarrett's and Shimony's analyses of the so-called factorisability (Bell-locality) condition for clarifying the nature of quantum non-locality. In this paper, I focus on four types of non-locality: superluminal signalling, action-at-a-distance, non-separability and holism. In the second paper, I consider a fifth type of non-locality: superluminal causation according to 'logically weak' concepts of causation, where causal dependence requires neither action nor signalling. In this connection, I pay special attention to the difficulties that superluminal causation raises in relativistic space-time. I conclude by evaluating the relevance of Jarrett's and Shimony's analyses for clarifying the question of the compatibility of quantum non-locality with relativity theory. My main conclusions are, first: these analyses are significant for clarifying the questions of superluminal signalling in quantum phenomena and for the compatibility of these phenomena with relativity. But, second, by contrast: these analyses are not very significant for the study of action-at-a distance, superluminal causation, non-separability and holism in quantum phenomena.
Institute of Scientific and Technical Information of China (English)
ZHANG Peng-Fei; RUAN Tu-Nan
2001-01-01
A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.
Non-Markovian Quantum State Diffusion
Diósi, L; Strunz, W T
1998-01-01
We present a nonlinear stochastic Schroedinger equation for pure states describing non-Markovian diffusion of quantum trajectories. It provides an unravelling of the evolution of a quantum system coupled to a finite or infinite number of harmonic oscillators, without any approximation. Its power is illustrated by several examples, including measurement-like situations, dissipation, and quantum Brownian motion. In some examples, we treat the environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite number of oscillators. In these quasi-periodic cases we see the reversible decay of a `Schroedinger cat' state. Finally, our description of open systems is compatible with different positions of the `Heisenberg cut' between system and environment.
Energy Technology Data Exchange (ETDEWEB)
Sahai, A. A.; Katsouleas, T. C.; Gessner, S.; Hogan, M.; Joshi, C.; Mori, W. B. [Electrical and Computer Engineering, Duke University, Durham, NC 27708 (United States); SLAC National Accelerator Laboratory, Menlo Park, CA 90309 (United States); University of California Los Angeles, Los Angeles, CA 90095 (United States)
2012-12-21
We study the various physical processes and their timescales involved in the excitation of wakefields in relativistically hot plasma. This has relevance to the design of a high repetition-rate plasma wakefield collider in which the plasma has not had time to cool between bunches in addition to understanding the physics of cosmic jets in relativistically hot astrophysical plasmas. When the plasma is relativistically hot (plasma temperature near m{sub e}c{sup 2}), the thermal pressure competes with the restoring force of ion space charge and can reduce or even eliminate the accelerating field of a wake. We will investigate explicitly the case where the hot plasma is created by a preceding Wakefield drive bunch 10's of picoseconds to many nanoseconds ahead of the next drive bunch. The relativistically hot plasma is created when the excess energy (not coupled to the driven e{sup -} bunch) in the wake driven by the drive e{sup -} bunch is eventually converted into thermal energy on 10's of picosecond timescale. We will investigate the thermalization and diffusion processes of this non-equilibrium plasma on longer time scales, including the effects of ambi-polar diffusion of ions driven by hot electron expansion, possible Columbic explosion of ions producing higher ionization states and ionization of surrounding neutral atoms via collisions with hot electrons. Preliminary results of the transverse and longitudinal wakefields at different timescales of separation between a first and second bunch are presented and a possible experiment to study this topic at the FACET facility is described.
Quantum Computing in Non Euclidean Geometry
Resconi, Germano
2009-01-01
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the essentially physical notion of computation. In Quantum mechanics we cannot use the traditional Euclidean geometry but we introduce more sophisticate non Euclidean geometry which include a new kind of information diffuse in the entire universe and that we can represent as Fisher information or active information. We remark that from the Fisher information we can obtain the Bohm and Hiley quantum potential and the classical Schrodinger equation. We can see the quantum phenomena do not affect a limited region of the space but is reflected in a change of the geometry of all the universe. In conclusion any local physical change or physical process is reflected in all the universe by the change of its geometry, This is the deepest meaning of the entanglement in Quantum mechanics a...
Emritte, M S; Marchegiani, P
2016-01-01
[Abridged] Inverse Compton scattering of CMB fluctuations off cosmic electron plasma generates a polarization of the associated Sunyaev-Zel'dovich (SZ) effect. This signal has been studied so far mostly in the non-relativistic regime and for a thermal electron population and, as such, has limited astrophysical applications. Partial attempts to extend this calculation for a thermal electron plasma in the relativistic regime have been done but cannot be applied to a general relativistic electron distribution. Here we derive a general form of the SZ effect polarization valid in the full relativistic approach for both thermal and non-thermal electron plasmas, as well as for a generic combination of various electron population co-spatially distributed in the environments of galaxy clusters or radiogalaxy lobes. We derive the spectral shape of the Stokes parameters induced by the IC scattering of every CMB multipole, focusing on the CMB quadrupole and octupole that provide the largest detectable signals in galaxy c...
Energy Technology Data Exchange (ETDEWEB)
Morales Villasevil, A.
1965-07-01
A method is introduced ta deal with relativistic quantum field theory for particles with m=0. Two mappings I and J, giving rise respectively to particle and anti particle states, are defined between a test space and the physical Hilbert space. The intrinsic field operator is then defined as the minimal causal linear combinations of operators belonging to the annihilation-creation algebra associated to the germ and antigerm parts of the element. Local elements are introduced as improper test elements and local field operators are constructed in the same way as the intrinsic ones. Commutation rules are given. (Author) 17 refs.
Simulations and Theory of Ion Injection at Non-relativistic Collisionless Shocks
Caprioli, Damiano; Pop, Ana-Roxana; Spitkovsky, Anatoly
2015-01-01
We use kinetic hybrid simulations (kinetic ions-fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also, by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for ion injection at non-relativistic astrophysical shocks with arbitrary strengths and magnetic inclinations, and represents a crucial ingredient for understanding the diffusive shock acceleration of cosmic rays.
Horwitz, L. P.; Land, Martin C.; Gill, Tepper; Lusanna, Luca; Salucci, Paolo
2013-04-01
Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics. The results of Lindner et al [Physical Review Letters 95 0040401 (2005)] as well as the more recent proposal of Palacios et al [Phys. Rev. Lett. 103 253001 (2009)] and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg [Helv. Phys. Acta 14 322, 588 (1941); 15 23 (1942); see also R P Feynman Phys. Rev. 80 4401 and J S Schwinger Phys. Rev. 82 664 (1951)] could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular
Search for non-relativistic magnetic monopoles with IceCube
Energy Technology Data Exchange (ETDEWEB)
Aartsen, M.G.; Hill, G.C.; Robertson, S.; Whelan, B.J. [University of Adelaide, School of Chemistry and Physics, Adelaide, SA (Australia); Abbasi, R.; Ahlers, M.; Arguelles, C.; Baker, M.; BenZvi, S.; Chirkin, D.; Day, M.; Desiati, P.; Diaz-Velez, J.C.; Eisch, J.; Fadiran, O.; Feintzeig, J.; Gladstone, L.; Halzen, F.; Hoshina, K.; Jacobsen, J.; Jero, K.; Karle, A.; Kauer, M.; Kelley, J.L.; Kopper, C.; Krasberg, M.; Kurahashi, N.; Landsman, H.; Maruyama, R.; McNally, F.; Merck, M.; Morse, R.; Riedel, B.; Rodrigues, J.P.; Santander, M.; Tobin, M.N.; Toscano, S.; Van Santen, J.; Weaver, C.; Wellons, M.; Wendt, C.; Westerhoff, S.; Whitehorn, N. [University of Wisconsin, Department of Physics and Wisconsin IceCube Particle Astrophysics Center, Madison, WI (United States); Ackermann, M.; Benabderrahmane, M.L.; Berghaus, P.; Bernardini, E.; Bretz, H.P.; Cruz Silva, A.H.; Gluesenkamp, T.; Jacobi, E.; Kaminsky, B.; Karg, T.; Middell, E.; Mohrmann, L.; Nahnhauer, R.; Schoenwald, A.; Shanidze, R.; Spiering, C.; Stoessl, A.; Yanez, J.P. [DESY, Zeuthen (Germany); Adams, J.; Brown, A.M.; Hickford, S.; Macias, O. [University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch (New Zealand); Aguilar, J.A.; Christov, A.; Montaruli, T.; Rameez, M.; Vallecorsa, S. [Universite de Geneve, Departement de physique nucleaire et corpusculaire, Geneva (Switzerland); Altmann, D.; Classen, L.; Gora, D.; Kappes, A.; Tselengidou, M. [Friedrich-Alexander-Universitaet Erlangen-Nuernberg, Erlangen Centre for Astroparticle Physics, Erlangen (Germany); Arlen, T.C.; De Andre, J.P.A.M.; DeYoung, T.; Dunkman, M.; Eagan, R.; Groh, J.C.; Huang, F.; Quinnan, M.; Smith, M.W.E.; Stanisha, N.A.; Tesic, G. [Pennsylvania State University, Department of Physics, University Park, PA (United States); Auffenberg, J.; Bissok, M.; Blumenthal, J.; Gretskov, P.; Haack, C.; Hallen, P.; Heinen, D.; Jagielski, K.; Kriesten, A.; Krings, K.; Leuermann, M.; Paul, L.; Raedel, L.; Reimann, R.; Schoenen, S.; Schukraft, A.; Vehring, M.; Wallraff, M.; Wiebusch, C.H.; Zierke, S. [RWTH Aachen University, III. Physikalisches Institut, Aachen (Germany); Bai, X.; Evenson, P.A.; Gaisser, T.K.; Gonzalez, J.G.; Hussain, S.; Kuwabara, T.; Ruzybayev, B.; Seckel, D.; Stanev, T.; Tamburro, A.; Tilav, S. [University of Delaware, Bartol Research Institute and Department of Physics and Astronomy, Newark, DE (United States); Barwick, S.W.; Yodh, G. [University of California, Department of Physics and Astronomy, Irvine, CA (United States); Baum, V.; Eberhardt, B.; Koepke, L.; Kroll, G.; Luenemann, J.; Sander, H.G.; Schatto, K.; Wiebe, K. [University of Mainz, Institute of Physics, Mainz (Germany); Bay, R.; Filimonov, K.; Price, P.B.; Woschnagg, K. [University of California, Department of Physics, Berkeley, CA (United States); Beatty, J.J. [Ohio State University, Department of Physics and Center for Cosmology and Astro-Particle Physics, Columbus, OH (United States); Ohio State University, Department of Astronomy, Columbus, OH (United States); Becker Tjus, J.; Eichmann, B.; Fedynitch, A.; Saba, S.M.; Schoeneberg, S.; Unger, E. [Ruhr-Universitaet Bochum, Fakultaet fuer Physik and Astronomie, Bochum (Germany); Becker, K.H.; Bindig, D.; Fischer-Wasels, T.; Helbing, K.; Hoffmann, R.; Klaes, J.; Kopper, S.; Naumann, U.; Obertacke, A.; Omairat, A.; Posselt, J.; Soldin, D.; Tepe, A. [University of Wuppertal, Department of Physics, Wuppertal (Germany); Berley, D.; Blaufuss, E.; Christy, B.; Goodman, J.A.; Hellauer, R.; Hoffman, K.D.; Huelsnitz, W.; Meagher, K.; Olivas, A.; Redl, P.; Richman, M.; Schmidt, T.; Sullivan, G.W.; Wissing, H. [University of Maryland, Department of Physics, College Park, MD (United States); Bernhard, A.; Coenders, S.; Gross, A.; Leute, J.; Resconi, E.; Schulz, O.; Sestayo, Y. [T.U. Munich, Garching (Germany); Besson, D.Z. [University of Kansas, Department of Physics and Astronomy, Lawrence, KS (United States); Binder, G.; Gerhardt, L.; Ha, C.; Klein, S.R.; Miarecki, S. [University of California, Department of Physics, Berkeley, CA (United States); Lawrence Berkeley National Laboratory, Berkeley, CA (United States); Boersma, D.J.; Botner, O.; Euler, S.; Hallgren, A.; Perez de los Heros, C.; Stroem, R.; Taavola, H. [Uppsala University, Department of Physics and Astronomy, Box 516, Uppsala (Sweden); Bohm, C.; Danninger, M.; Finley, C.; Flis, S.; Hulth, P.O.; Hultqvist, K.; Walck, C.; Wolf, M.; Zoll, M. [Stockholm University, Oskar Klein Centre and Department of Physics, Stockholm (Sweden); Bose, D.; Rott, C. [Sungkyunkwan University, Department of Physics, Suwon (Korea, Republic of); Collaboration: IceCube Collaboration; and others
2014-07-15
The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting 1 km{sup 3} of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the Grand Unified Theory (GUT) era shortly after the Big Bang. Depending on the underlying gauge group these monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of 10{sup -27} to 10{sup -21} cm{sup 2}. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal was observed. For catalysis cross sections of 10{sup -22} (10{sup -24}) cm{sup 2} the flux of non-relativistic GUT monopoles is constrained up to a level of Φ{sub 90} ≤ 10{sup -18} (10{sup -17}) cm{sup -2} s{sup -1} sr{sup -1} at a 90 % confidence level, which is three orders of magnitude below the Parker bound. The limits assume a dominant decay of the proton into a positron and a neutral pion. These results improve the current best experimental limits by one to two orders of magnitude, for a wide range of assumed speeds and catalysis cross sections. (orig.)
Quantum Loops in Non-Local Gravity
Talaganis, Spyridon
2015-01-01
In this proceedings, I will consider quantum aspects of a non-local, infinite-derivative scalar field theory - a ${\\it toy \\, model}$ depiction of a covariant infinite-derivative, non-local extension of Einstein's general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it ${\\it asymptotically \\, free}$, thus providing strong prospects of resolving various classical and quantum divergences. In particular, I will find that at $1$-loop, the $2$-point function is still divergent, but once this amplitude is renormalized by adding appropriate counter terms, the ultraviolet (UV) behavior of all other $1$-loop diagrams as well as the $2$-loop, $2$-point function remains well under control. I will go on to discuss how one may be able to generalize our computations and arguments to arbitrary loops.
Geometric Representation of Interacting Non-Relativistic Open Strings using Extended Objects
Arias, P J; Fuenmayor, E; Leal, L
2013-01-01
Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model consists of open-strings interacting through a Kalb-Ramond field in four dimensions. The geometric representation proposed uses lines and surfaces that can be interpreted as an extension of the picture of Faraday's lines of classical electromagnetism. This representation results to be consistent, provided the coupling constant (the "charge" of the string) is quantized. The Schr\\"odinger equation in this representation is also presented.
Quantum Communication Scheme Using Non-symmetric Quantum Channel
Institute of Scientific and Technical Information of China (English)
CAO Hai-Jing; CHEN Zhong-Hua; SONG He-Shan
2008-01-01
A theoretical quantum communication scheme based on entanglement swapping and superdense coding is proposed with a 3-dimensional Bell state and 2-dimensional Bell state function as quantum channel quantum key distribution and quantum secure direct communication can be simultaneously accomplished in the scheme. The scheme is secure and has high source capacity. At last, we generalize the quantum communication scheme to d-dimensional quantum channel.
English, W.; Hardcastle, M. J.; Krause, M. G. H.
2016-09-01
We present results from two suites of simulations of powerful radio galaxies in poor cluster environments, with a focus on the formation and evolution of the radio lobes. One suite of models uses relativistic hydrodynamics and the other relativistic magnetohydrodynamics; both are set up to cover a range of jet powers and velocities. The dynamics of the lobes are shown to be in good agreement with analytical models and with previous numerical models, confirming in the relativistic regime that the observed widths of radio lobes may be explained if they are driven by very light jets. The ratio of energy stored in the radio lobes to that put into the intracluster gas is seen to be the same regardless of jet power, jet velocity or simulation type, suggesting that we have a robust understanding of the work done on the ambient gas by this type of radio source. For the most powerful jets, we at times find magnetic field amplification by up to a factor of 2 in energy, but mostly the magnetic energy in the lobes is consistent with the magnetic energy injected. We confirm our earlier result that for jets with a toroidally injected magnetic field, the field in the lobes is predominantly aligned with the jet axis once the lobes are well developed, and that this leads to radio flux anisotropies of up to a factor of about two for mature sources. We reproduce the relationship between 151 MHz luminosity and jet power determined analytically in the literature.
Quantum metrology in non-Markovian environments.
Chin, Alex W; Huelga, Susana F; Plenio, Martin B
2012-12-07
We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.
EDITORIAL: CAMOP: Quantum Non-Stationary Systems CAMOP: Quantum Non-Stationary Systems
Dodonov, Victor V.; Man'ko, Margarita A.
2010-09-01
Although time-dependent quantum systems have been studied since the very beginning of quantum mechanics, they continue to attract the attention of many researchers, and almost every decade new important discoveries or new fields of application are made. Among the impressive results or by-products of these studies, one should note the discovery of the path integral method in the 1940s, coherent and squeezed states in the 1960-70s, quantum tunneling in Josephson contacts and SQUIDs in the 1960s, the theory of time-dependent quantum invariants in the 1960-70s, different forms of quantum master equations in the 1960-70s, the Zeno effect in the 1970s, the concept of geometric phase in the 1980s, decoherence of macroscopic superpositions in the 1980s, quantum non-demolition measurements in the 1980s, dynamics of particles in quantum traps and cavity QED in the 1980-90s, and time-dependent processes in mesoscopic quantum devices in the 1990s. All these topics continue to be the subject of many publications. Now we are witnessing a new wave of interest in quantum non-stationary systems in different areas, from cosmology (the very first moments of the Universe) and quantum field theory (particle pair creation in ultra-strong fields) to elementary particle physics (neutrino oscillations). A rapid increase in the number of theoretical and experimental works on time-dependent phenomena is also observed in quantum optics, quantum information theory and condensed matter physics. Time-dependent tunneling and time-dependent transport in nano-structures are examples of such phenomena. Another emerging direction of study, stimulated by impressive progress in experimental techniques, is related to attempts to observe the quantum behavior of macroscopic objects, such as mirrors interacting with quantum fields in nano-resonators. Quantum effects manifest themselves in the dynamics of nano-electromechanical systems; they are dominant in the quite new and very promising field of circuit
Contrasting Classical and Quantum Vacuum States in Non-Inertial Frames
Boyer, Timothy H
2013-01-01
Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. It makes no difference whether a box of classical zero-point radiati...
Vitória, R. L. L.; Belich, H.; Bakke, K.
2017-01-01
We consider a background of the violation of the Lorentz symmetry determined by the tensor (KF)_{μναβ} which governs the Lorentz symmetry violation out of the Standard Model Extension, where this background gives rise to a Coulomb-type potential, and then, we analyse its effects on a relativistic quantum oscillator. Furthermore, we analyse the behaviour of the relativistic quantum oscillator under the influence of a linear scalar potential and this background of the Lorentz symmetry violation. We show in both cases that analytical solutions to the Klein-Gordon equation can be achieved.
Dielectric laser acceleration of non-relativistic electrons at a photonic structure
Energy Technology Data Exchange (ETDEWEB)
Breuer, John
2013-08-29
This thesis reports on the observation of dielectric laser acceleration of non-relativistic electrons via the inverse Smith-Purcell effect in the optical regime. Evanescent modes in the vicinity of a periodic grating structure can travel at the same velocity as the electrons along the grating surface. A longitudinal electric field component is used to continuously impart momentum onto the electrons. This is only possible in the near-field of a suitable photonic structure, which means that the electron beam has to pass the structure within about one wavelength. In our experiment we exploit the third spatial harmonic of a single fused silica grating excited by laser pulses derived from a Titanium:sapphire oscillator and accelerate non-relativistic 28 keV electrons. We measure a maximum energy gain of 280 eV, corresponding to an acceleration gradient of 25 MeV/m, already comparable with state-of-the-art radio-frequency linear accelerators. To experience this acceleration gradient the electrons approach the grating closer than 100 nm. We present the theory behind grating-based particle acceleration and discuss simulation results of dielectric laser acceleration in the near-field of photonic grating structures, which is excited by near-infrared laser light. Our measurements show excellent agreement with our simulation results and therefore confirm the direct acceleration with the light field. We further discuss the acceleration inside double grating structures, dephasing effects of non-relativistic electrons as well as the space charge effect, which can limit the attainable peak currents of these novel accelerator structures. The photonic structures described in this work can be readily concatenated and therefore represent a scalable realization of dielectric laser acceleration. Furthermore, our structures are directly compatible with the microstructures used for the acceleration of relativistic electrons demonstrated in parallel to this work by our collaborators in
Non-Markovian Dynamics of Quantum Systems
Chruściński, Dariusz; Kossakowski, Andrzej
2011-01-01
We analyze a local approach to the non-Markovian evolution of open quantum systems. It turns out that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. The price one pays for the local approach is that the corresponding generator might be highly singular and it keeps the memory about the starting point 't0'. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement.
Dark matter as a Bose-Einstein Condensate: the relativistic non-minimally coupled case
Energy Technology Data Exchange (ETDEWEB)
Bettoni, Dario; Colombo, Mattia; Liberati, Stefano, E-mail: bettoni@sissa.it, E-mail: mattia.colombo@studenti.unitn.it, E-mail: liberati@sissa.it [SISSA, Via Bonomea 265, Trieste, 34136 (Italy)
2014-02-01
Bose-Einstein Condensates have been recently proposed as dark matter candidates. In order to characterize the phenomenology associated to such models, we extend previous investigations by studying the general case of a relativistic BEC on a curved background including a non-minimal coupling to curvature. In particular, we discuss the possibility of a two phase cosmological evolution: a cold dark matter-like phase at the large scales/early times and a condensed phase inside dark matter halos. During the first phase dark matter is described by a minimally coupled weakly self-interacting scalar field, while in the second one dark matter condensates and, we shall argue, develops as a consequence the non-minimal coupling. Finally, we discuss how such non-minimal coupling could provide a new mechanism to address cold dark matter paradigm issues at galactic scales.
Entanglement Concentration with Quantum Non Demolition Hamiltonians
Tatham, Richard
2011-01-01
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
Search for non-relativistic Magnetic Monopoles with IceCube
Aartsen, M G; Ackermann, M; Adams, J; Aguilar, J A; Ahlers, M; Altmann, D; Arguelles, C; Arlen, T C; Auffenberg, J; Bai, X; Baker, M; Barwick, S W; Baum, V; Bay, R; Beatty, J J; Tjus, J Becker; Becker, K -H; Benabderrahmane, M L; BenZvi, S; Berghaus, P; Berley, D; Bernardini, E; Bernhard, A; Besson, D Z; Binder, G; Bindig, D; Bissok, M; Blaufuss, E; Blumenthal, J; Boersma, D J; Bohm, C; Bose, D; Böser, S; Botner, O; Brayeur, L; Bretz, H -P; Brown, A M; Bruijn, R; Casey, J; Casier, M; Chirkin, D; Christov, A; Christy, B; Clark, K; Classen, L; Clevermann, F; Coenders, S; Cohen, S; Cowen, D F; Silva, A H Cruz; Danninger, M; Daughhetee, J; Davis, J C; Day, M; de André, J P A M; De Clercq, C; De Ridder, S; Desiati, P; de Vries, K D; de With, M; DeYoung, T; Díaz-Vélez, J C; Dunkman, M; Eagan, R; Eberhardt, B; Eichmann, B; Eisch, J; Euler, S; Evenson, P A; Fadiran, O; Fazely, A R; Fedynitch, A; Feintzeig, J; Feusels, T; Filimonov, K; Finley, C; Fischer-Wasels, T; Flis, S; Franckowiak, A; Frantzen, K; Fuchs, T; Gaisser, T K; Gallagher, J; Gerhardt, L; Gladstone, L; Glüsenkamp, T; Goldschmidt, A; Golup, G; Gonzalez, J G; Goodman, J A; Góra, D; Grandmont, D T; Grant, D; Gretskov, P; Groh, J C; Groß, A; Ha, C; Haack, C; Ismail, A Haj; Hallen, P; Hallgren, A; Halzen, F; Hanson, K; Hebecker, D; Heereman, D; Heinen, D; Helbing, K; Hellauer, R; Hickford, S; Hill, G C; Hoffman, K D; Hoffmann, R; Homeier, A; Hoshina, K; Huang, F; Huelsnitz, W; Hulth, P O; Hultqvist, K; Hussain, S; Ishihara, A; Jacobi, E; Jacobsen, J; Jagielski, K; Japaridze, G S; Jero, K; Jlelati, O; Kaminsky, B; Kappes, A; Karg, T; Karle, A; Kauer, M; Kelley, J L; Kiryluk, J; Kläs, J; Klein, S R; Köhne, J -H; Kohnen, G; Kolanoski, H; Köpke, L; Kopper, C; Kopper, S; Koskinen, D J; Kowalski, M; Krasberg, M; Kriesten, A; Krings, K; Kroll, G; Kunnen, J; Kurahashi, N; Kuwabara, T; Labare, M; Landsman, H; Larson, M J; Lesiak-Bzdak, M; Leuermann, M; Leute, J; Lünemann, J; Macías, O; Madsen, J; Maggi, G; Maruyama, R; Mase, K; Matis, H S; McNally, F; Meagher, K; Meli, A; Merck, M; Meures, T; Miarecki, S; Middell, E; Milke, N; Miller, J; Mohrmann, L; Montaruli, T; Morse, R; Nahnhauer, R; Naumann, U; Niederhausen, H; Nowicki, S C; Nygren, D R; Obertacke, A; Odrowski, S; Olivas, A; Omairat, A; O'Murchadha, A; Palczewski, T; Paul, L; Pepper, J A; Heros, C Pérez de los; Pfendner, C; Pieloth, D; Pinat, E; Posselt, J; Price, P B; Przybylski, G T; Quinnan, M; Rädel, L; Rameez, M; Rawlins, K; Redl, P; Reimann, R; Resconi, E; Rhode, W; Ribordy, M; Richman, M; Riedel, B; Robertson, S; Rodrigues, J P; Rott, C; Ruhe, T; Ruzybayev, B; Ryckbosch, D; Saba, S M; Sander, H -G; Santander, M; Sarkar, S; Schatto, K; Scheriau, F; Schmidt, T; Schmitz, M; Schoenen, S; Schöneberg, S; Schönwald, A; Schukraft, A; Schulte, L; Schulz, O; Seckel, D; Sestayo, Y; Seunarine, S; Shanidze, R; Sheremata, C; Smith, M W E; Soldin, D; Spiczak, G M; Spiering, C; Stamatikos, M; Stanev, T; Stanisha, N A; Stasik, A; Stezelberger, T; Stokstad, R G; Stößl, A; Strahler, E A; Ström, R; Strotjohann, N L; Sullivan, G W; Taavola, H; Taboada, I; Tamburro, A; Tepe, A; Ter-Antonyan, S; Tešić, G; Tilav, S; Toale, P A; Tobin, M N; Toscano, S; Tselengidou, M; Unger, E; Usner, M; Vallecorsa, S; van Eijndhoven, N; van Santen, J; Vehring, M; Voge, M; Vraeghe, M; Walck, C; Wallraff, M; Weaver, Ch; Wellons, M; Wendt, C; Westerhoff, S; Whelan, B J; Whitehorn, N; Wiebe, K; Wiebusch, C H; Williams, D R; Wissing, H; Wolf, M; Wood, T R; Woschnagg, K; Xu, D L; Xu, X W; Yanez, J P; Yodh, G; Yoshida, S; Zarzhitsky, P; Ziemann, J; Zierke, S; Zoll, M
2014-01-01
The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting $1\\,\\mathrm{km}^3$ of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand Unified Theory) era shortly after the Big Bang. These monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of $10^{-27}\\,\\mathrm{cm^2}$ to $10^{-21}\\,\\mathrm{cm^2}$. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow-particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal ...
Non-Markovian dynamics of open quantum systems
Fleming, Chris H.
An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature
Magnetic structures propagating in non-equilibrium relativistic plasma of pulsar wind nebulae
Petrov, A. E.; Bykov, A. M.
2016-11-01
The kinetic model of highly non-equilibrium relativistic electron-positron plasma is used to study dynamical magnetic structures in pulsar wind nebulae (PWNe). The evolution equation which describes a propagation of a long-wavelength magnetosonic type perturbation of small but finite amplitude is derived. The wavelength is assumed to be longer than the scattering length of the background positrons and electrons. The rates of scattering of electrons and positrons by the stochastic magnetic field fluctuations are distinguished but the difference is supposed to be small compared with the gyrofrequencies of particles. The phase velocity, the dissipation rate and the dispersion length of the magnetic pulse are studied as the functions of plasma parameters and the scattering rates of electrons and positrons. The model being confronted to observations can help to determine the pulsar wind composition, particle distribution and non-thermal pressure in PWNe.
Relativistic heavy ion collisions with realistic non-equilibrium mean fields
Fuchs, C; Wolter, H H
1996-01-01
We study the influence of non-equilibrium phase space effects on the dynamics of heavy ion reactions within the relativistic BUU approach. We use realistic Dirac-Brueckner-Hartree-Fock (DBHF) mean fields determined for two-Fermi-ellipsoid configurations, i.e. for colliding nuclear matter, in a local phase space configuration approximation (LCA). We compare to DBHF mean fields in the local density approximation (LDA) and to the non-linear Walecka model. The results are further compared to flow data of the reaction Au on Au at 400 MeV per nucleon measured by the FOPI collaboration. We find that the DBHF fields reproduce the experiment if the configuration dependence is taken into account. This has also implications on the determination of the equation of state from heavy ion collisions.
Non-linear Ion-wake Excitation by Ultra-relativistic Electron Wakefields
Sahai, Aakash A
2015-01-01
The excitation of a non-linear ion-wake by a train of ultra-relativistic plasmons is modeled and its use for a novel regime of positron acceleration is explored. Its channel-like structure is independent of the energy-source driving the bubble-shaped slowly-propagating high phase-velocity electron density waves. The back of the bubble electron compression sucks-in the ions and the space-charge within the bubble expels them, forming a near-void channel with on-axis and bubble-edge density-spikes. The channel-edge density-spike is driven radially outwards as a non-linear ion acoustic-wave by the wake electron thermal pressure. OSIRIS PIC simulations are used to study the ion-wake structure, its evolution and its use for positron acceleration.
Quantum Metrology in Non-Markovian Environments
Chin, Alex W; Plenio, Martin B
2011-01-01
We analyze optimal bounds for precision spectroscopy in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite band-width dephasing environment, we show that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states but otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and, as a result, possesses general validity that goes beyond specific models.
The Sagnac Phase Shift Suggested by the Aharonov-Bohm Effect for Relativistic Matter Beams
Rizzi, Guido; Ruggiero, Matteo Luca
2003-10-01
The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a formal analogy with the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and Newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.
The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams
Rizzi, G; Rizzi, Guido; Ruggiero, Matteo Luca
2003-01-01
The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.
High-energy emission from non-relativistic radiative shocks: application to gamma-ray novae
Vurm, Indrek
2016-01-01
Multiwavelength radiation from relativistic particles accelerated at shocks in novae and other astrophysical sources carries a wealth of information about the outflow properties and the microphysical processes at work near the shocks. The observation of GeV gamma-rays from novae by Fermi/LAT demonstrates that the shocks in these systems can accelerate particles to energies of at least $\\sim 10$ GeV. The low-energy extension of the same non-thermal particle distribution inevitably gives rise to emission extending into the X-ray band. Above $\\gtrsim 10$ keV this radiation can escape the system without significant absorption/attenuation, and can potentially be detected by NuSTAR. We present theoretical models for hard X-ray and gamma-ray emission from radiative shocks in both leptonic and hadronic scenarios, accounting for the rapid evolution of the downstream properties due to the fast cooling of thermal plasma. Due to strong Coulomb cooling of the mildly relativistic electrons nominally responsible for produci...
``Pheudo-cyclotron'' radiation of non-relativistic particles in small-scale magnetic turbulence
Keenan, Brett; Ford, Alex; Medvedev, Mikhail V.
2014-03-01
Plasma turbulence in some astrophysical objects (e.g., weakly magnetized collisionless shocks in GRBs and SN) has small-scale magnetic field fluctuations. We study spectral characteristics of radiation produced by particles moving in such turbulence. It was shown earlier that relativistic particles produce jitter radiation, which spectral characteristics are markedly different from synchrotron radiation. Here we study radiation produced by non-relativistic particles. In the case of a homogeneous fields, such radiation is cyclotron and its spectrum consists of just a single harmonic at the cyclotron frequency. However, in the sub-Larmor-scale turbulence, the radiation spectrum is much reacher and reflects statistical properties of the underlying magnetic field. We present both analytical estimates and results of ab initio numerical simulations. We also show that particle propagation in such turbulence is diffusive and evaluate the diffusion coefficient. We demonstrate that the diffusion coefficient correlates with some spectral parameters. These results can be very valuable for remote diagnostics of laboratory and astrophysical plasmas. Supported by grant DOE grant DE-FG02-07ER54940 and NSF grant AST-1209665.
Non-trivial topologies in quantum gravity
Hawking, S. W.
1984-09-01
This paper examines recent objections to the proposal that topologically non-trivial metrics could cause pure quantum states to decay into mixed states. It is shown that the Kaluza-Klein examples proposed by Gross in which this did not happen are special cases and that there are other Kaluza-Klein metrics in which it does. The objections of Banks, Peskin and Susskind about energy and momentum conservation arise because they assume that the evolution of density operator can be localized to a few Planck lengths. However, it is shown that energy and momentum are conserved only because of the asymptotic field equations and that this requires a large asymptotic region.
Relativistic Harmonic Oscillators and Hadronic Structures in the Quantum-Mechanics Curriculum
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A relativistic harmonic-oscillator formalism which is mathematically simple as the nonrelativistic harmonic oscillator is given. In view of its effectiveness in describing Lorentz-deformed hadrons, the inclusion of this formalism in a first-year graduate course will make the results of high-energy experiments more understandable. (BB)
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
Energy Technology Data Exchange (ETDEWEB)
Ko, Sung Moon [Department of Physics, Sogang University,Seoul 121-742 (Korea, Republic of); Melby-Thompson, Charles M. [Kavli Institute for the Physics and Mathematics of the Universe (WPI),The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo,Kashiwanoha, Kashiwa, 277-8583 (Japan); Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI),The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo,Kashiwanoha, Kashiwa, 277-8583 (Japan); Park, Jeong-Hyuck [Department of Physics, Sogang University,Seoul 121-742 (Korea, Republic of)
2015-12-22
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry — not only globally (‘non-geometry’), but even locally (‘non-Riemannian’). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri http://dx.doi.org/10.1063/1.1372697 arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of http://dx.doi.org/10.1016/j.nuclphysb.2014.01.003 on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrödinger conformal symmetry.
Non-exponential decay in Quantum Mechanics and Quantum Field Theory
Giacosa, Francesco
2014-10-01
We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.
Non-exponential decay in Quantum Mechanics and Quantum Field Theory
Giacosa, Francesco
2013-01-01
We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.
Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics
Directory of Open Access Journals (Sweden)
Lorenzo Fatibene
2010-04-01
Full Text Available We review the Lagrangian formulation of (generalised Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called “Natural Theories” and “Gauge-Natural Theories” that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.. It is discussed how the use of Poincar´e–Cartan forms and decompositions of natural (or gauge-natural variational operators give rise to notions such as “generators of Noether symmetries”, energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-calledADMlaws in General Relativity with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.. A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer; one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation “à la Palatini” and in its extensions to Non-Linear Gravity Theories; one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero–Immirzi connections.
Quantum simulation of the Dirac equation.
Gerritsma, R; Kirchmair, G; Zähringer, F; Solano, E; Blatt, R; Roos, C F
2010-01-07
The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation-relativistic quantum mechanics-is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein's paradox and 'Zitterbewegung', an unexpected quivering motion of a free relativistic quantum particle. These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups, in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate textbook examples of relativistic quantum physics.
Towards Relativistic Atomic Physics and Post-Minkowskian Gravitational Waves
Lusanna, Luca
2009-01-01
A review is given of the formulation of relativistic atomic theory, in which there is an explicit realization of the Poincare' generators, both in the inertial and in the non-inertial rest-frame instant form of dynamics in Minkowski space-time. This implies the need to solve the problem of the relativistic center of mass of an isolated system and to describe the transitions from different conventions for clock synchronization, namely for the identifications of instantaneous 3-spaces, as gauge transformations. These problems, stemming from the Lorentz signature of space-time, are a source of non-locality, which induces a spatial non-separability in relativistic quantum mechanics, with implications for relativistic entanglement. Then the classical system of charged particles plus the electro-magnetic field is studied in the framework of ADM canonical tetrad gravity in asymptotically Minkowskian space-times admitting the ADM Poincare' group at spatial infinity, which allows to get the general relativistic extens...
Quantum Physics Without Quantum Philosophy
Dürr, Detlef; Zanghì, Nino
2013-01-01
It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Wundt, B J; 10.1103/PhysRevA.80.022505
2009-01-01
We calculate the relativistic corrections of relative order (Z alpha)^2$ to the two-photon decay rate of higher excited S and D states in ionic atomic systems, and we also evaluate the leading radiative corrections of relative order alpha (Z alpha)^2 ln[(Z alpha)^(-2)]. We thus complete the theory of the two-photon decay rates up to relative order alpha^3 ln(alpha). An approach inspired by nonrelativistic quantum electrodynamics is used. We find that the corrections of relative order (Z alpha)^2 to the two-photon decay are given by the zitterbewegung, the spin-orbit coupling and by relativistic corrections to the electron mass, and by quadrupole interactions. We show that all corrections are separately gauge-invariant with respect to a "hybrid" transformation from velocity to length gauge, where the gauge transformation of the wave function is neglected. The corrections are evaluated for the two-photon decay from 2S, 3S, 3D, and 4S states in one-electron (hydrogenlike) systems, with 1S and 2S final states.
Caprioli, Damiano
2014-01-01
We use large hybrid (kinetic ions-fluid electrons) simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of energetic particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient (at quasi-parallel shocks), we find that the magnetic field develops transverse components and is significantly amplified in the pre-shock medium. The total amplification factor is larger than 10 for shocks with Mach number $M=100$, and scales with the square root of $M$. We find that in the shock precursor the energy spectral density of excited magnetic turbulence is proportional to spectral energy distribution of accelerated particles at corresponding resonant momenta, in good agreement with the predictions of quasilinear theory of diffusive shock acceleration. We discuss the role of Bell's instability, which is predicted and found to grow faster than resonant instability in shocks with $M\\gtrsim 30$. Ahead of these strong shocks we distinguis...
Bancelin, D; Thuillot, W
2016-01-01
The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical integration. Among the different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie series has shown some advantages. In its original form (Hanslmeier 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the method by deriving an expression of the Lie-terms when other major forces are considered. As a matter of fact, previous studies had been made but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations: relativistic acceleration in the framework ...
Kinetic turbulence in relativistic plasma: from thermal bath to non-thermal continuum
Zhdankin, Vladimir; Uzdensky, Dmitri A; Begelman, Mitchell C
2016-01-01
We present results from particle-in-cell simulations of driven turbulence in collisionless, relativistic pair plasma. We find that turbulent fluctuations are consistent with the classical $k_\\perp^{-5/3}$ magnetic energy spectrum at fluid scales and a steeper $k_\\perp^{-4}$ spectrum at sub-Larmor scales, where $k_\\perp$ is the wavevector perpendicular to the mean field. We demonstrate the development of a non-thermal, power-law particle energy distribution, $f(E) \\sim E^{-\\alpha}$, with index well fit by $\\alpha \\sim 1 + C_0 (\\sigma \\rho_e/L)^{-1/2}$, where $C_0$ is a constant, $\\sigma$ is magnetization, and $\\rho_e/L$ is the ratio of characteristic Larmor radius to system size. In the absence of asymptotic system-size independent scalings, our results challenge the viability of turbulent particle acceleration in high-energy astrophysical systems such as pulsar wind nebulae.
Ultra high energy cosmic rays from non-relativistic quasar outflows
Wang, Xiawei
2016-01-01
It has been suggested that non-relativistic outflows from quasars can naturally account for the missing component of the extragalactic $\\gamma$-ray background and explain the cumulative neutrino background through pion decay in collisions between protons accelerated by the outflow shock and interstellar protons. Here we show that the same quasar outflows are capable of accelerating protons to energies of $\\sim 10^{20}$ eV during the early phase of their propagation. The overall quasar population is expected to produce a cumulative ultra high energy cosmic ray flux of $\\sim10^{-7}\\,\\rm GeV\\,cm^{-2}s^{-1}sr^{-1}$ at $E_{\\rm CR}\\gtrsim10^{18}$ eV. The spectral shape and amplitude is consistent with recent observations for outflow parameters constrained to fit secondary $\\gamma$-rays and neutrinos without any additional parameter tuning. This indicates that quasar outflows simultaneously account for all three messengers at their observed levels.
Non relativistic limit of the Landau-Lifshitz equation: A new equation
Ares de Parga, G.; Domínguez-Hernández, S.; Salinas-Hernández, E.
2016-06-01
It is shown that Ford equation is not adequate in general to describe the motion of a charged particle including the reaction force in the non relativistic limit. As in General Relativity where a post-Newtonian method is developed in order to describe the gravitational effects at low velocities and small energies, an extra term inherited from Special Relativity must be added to the Ford equation. This is due to that the new term is greater than the reaction force in many physical situations. The Coulombic case is analyzed showing the necessity of including the new term. Comparison with General Relativity results is analyzed. The Vlasov equation to first order in 1 /c2 is proposed for the constant electric and magnetic fields.
On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field
Amour, Laurent; Grebert, Benoit; Guillot, Jean-Claude
2008-01-01
We consider a non-relativistic electron interacting with a classical magnetic field pointing along the $x_3$-axis and with a quantized electromagnetic field. The system is translation invariant in the $x_3$-direction and we consider the reduced Hamiltonian $H(P_3)$ associated with the total momentum $P_3$ along the $x_3$-axis. For a fixed momentum $P_3$ sufficiently small, we prove that $H(P_3)$ has a ground state in the Fock representation if and only if $E'(P_3)=0$, where $P_3 \\mapsto E'(P_3)$ is the derivative of the map $P_3 \\mapsto E(P_3) = \\inf \\sigma (H(P_3))$. If $E'(P_3) \
Relativistic particles with rigidity generating non-standard examples of Willmore-Chen hypersurfaces
Energy Technology Data Exchange (ETDEWEB)
Arroyo, Josu; Garay, Oscar J. [Departamento de Matematicas, Universidad del Pais Vasco, Bilbao (Spain)]. E-mails: mtparolj@lg.ehu.es; mtpgabeo@lg.ehu.es; Barros, Manuel [Departamento de Geometria y Topologia, Universidad de Granada, Granada (Spain)]. E-mail: mbarros@ugr.es
2002-08-16
We study a natural extension to higher dimensions of the Nambu-Goto-Polyakov action. In particular, those dynamical objects evolving with SO(3) symmetry in four dimensions. We show that this problem is strongly related to that of relativistic particles with rigidity of order three in a hyperbolic plane. The moduli space of solitonic solutions is completely determined in terms of the so-called rotation number. A quantization principle for closed solutions is also obtained and this gives a rational one-parameter family of Willmore-Chen hypersurfaces in the standard conformal structure of dimension four. Moreover, these are the first non-standard examples of this kind of hypersurfaces. (author)
Non-Markovian quantum dynamics: local versus non-local
Chruscinski, Dariusz
2009-01-01
We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. Theses two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point `t_0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular, nevertheless, the corresponding dynamics is perfectly regular. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement.
Ionization and bound-state relativistic quantum dynamics in laser-driven multiply charged ions
Energy Technology Data Exchange (ETDEWEB)
Hetzheim, Henrik
2009-01-14
The interaction of ultra-strong laser fields with multiply charged hydrogen-like ions can be distinguished in an ionization and a bound dynamics regime. Both are investigated by means of numerically solving the Dirac equation in two dimensions and by a classical relativistic Monte-Carlo simulation. For a better understanding of highly nonlinear physical processes the development of a well characterized ultra-intense relativistic laser field strength has been driven forward, capable of studying e.g. the magnetic field effects of the laser resulting in an additional electron motion in the laser propagation direction. A novel method to sensitively measure these ultra-strong laser intensities is developed and employed from the optical via the UV towards the XUV frequency regime. In the bound dynamics field, the determination of multiphoton transition matrixelements has been investigated between different bound states via Rabi oscillations. (orig.)
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Jaksic, V; Pillet, C -A; Seiringer, R
2011-01-01
We extend the mathematical theory of quantum hypothesis testing to the general $W^*$-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.
Applying the relativistic quantization condition to a three-particle bound state in a periodic box
Hansen, Maxwell T
2016-01-01
Using our recently developed relativistic three-particle quantization condition, we study the finite-volume energy shift of a three-particle bound state. We reproduce the result obtained using non-relativistic quantum mechanics by Mei{\\ss}ner, R{\\'i}os and Rusetsky, and generalize the result to a moving frame.
Contribution of relativistic quantum chemistry to electron’s electric dipole moment for CP violation
Energy Technology Data Exchange (ETDEWEB)
Abe, M., E-mail: minoria@tmu.ac.jp; Gopakumar, G., E-mail: gopakumargeetha@gmail.com; Hada, M., E-mail: hada@tmu.ac.jp [Tokyo Metropolitan University, 1-1, Minami-Osawa, Hachioji-city, Tokyo 192-0397 (Japan); JST, CREST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Das, B. P., E-mail: das@iiap.ernet.in [Indian Institute of Astrophysics, Bangalore 560 034 (India); Tatewaki, H., E-mail: htatewak@nsc.nagoya-cu.ac.jp [Graduate School of Natural Sciences, Nagoya City University, Nagoya, Aichi 467-8501 (Japan); Mukherjee, D., E-mail: pcdm@iacs.res.in [Raman Center of Atomic, Molecular and Optical Sciences, IACS, Kolkata 700 032 (India)
2015-12-31
The search for the electric dipole moment of the electron (eEDM) is important because it is a probe of Charge Conjugation-Parity (CP) violation. It can also shed light on new physics beyond the standard model. It is not possible to measure the eEDM directly. However, the interaction energy involving the effective electric field (E{sub eff}) acting on an electron in a molecule and the eEDM can be measured. This quantity can be combined with E{sub eff}, which is calculated by relativistic molecular orbital theory to determine eEDM. Previous calculations of E{sub eff} were not sufficiently accurate in the treatment of relativistic or electron correlation effects. We therefore developed a new method to calculate E{sub eff} based on a four-component relativistic coupled-cluster theory. We demonstrated our method for YbF molecule, one of the promising candidates for the eEDM search. Using very large basis set and without freezing any core orbitals, we obtain a value of 23.1 GV/cm for E{sub eff} in YbF with an estimated error of less than 10%. The error is assessed by comparison of our calculations and experiments for two properties relevant for E{sub eff}, permanent dipole moment and hyperfine coupling constant. Our method paves the way to calculate properties of various kinds of molecules which can be described by a single-reference wave function.
De Soto, F
2006-01-01
The numerical solutions of the non-relativistic Yukawa model on a 3-dimensional size lattice with periodic boundary conditions are obtained. The possibility to extract the corresponding -- infinite space -- low energy parameters and bound state binding energies from eigensates computed at finite lattice size is discussed.
Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations
Energy Technology Data Exchange (ETDEWEB)
Lindesay, James V
2002-03-19
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
An Introduction to Relativistic Quantum Mechanics. I. From Relativity to Dirac Equation
De Sanctis, M
2007-01-01
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear algebra are employed for the development of the present work.
Quantum leap from Dirac and Feynman, across the universe, to human body and mind
Ivancevic, Vladimir G
2008-01-01
This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body - all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosm
Buchert, Thomas
2012-01-01
In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology, and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate consequences by functionally evaluating relevant variables. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to address non-perturbatively, e.g. problems of structu...
Quantum entropy of non-Hermitian entangled systems
Zhang, Shi-Yang; Fang, Mao-Fa; Xu, Lan
2017-10-01
Non-Hermitian Hamiltonians are an effective tool for describing the dynamics of open quantum systems. Previous research shows that the restrictions of conventional quantum mechanics may be violated in the non-Hermitian cases. We studied the entropy of a system of entangled qubits governed by a local non-Hermitian Hamiltonian operator. We find that local non-Hermitian operation influences the entropies of the two subsystems equally and simultaneously. This indicates that non-Hermitian operators possess the property of non-locality, which makes information exchange possible between subsystems. These information exchanges reduce the uncertainty of outcomes associated with two incompatible quantum measurements.
Quantum and classical theories of scattering of relativistic electrons in ultrathin crystals
Shulga, N F
2016-01-01
Quantum and classical theories are proposed of scattering of high energy electrons in ultrathin crystals. The quantum theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and on the spectral method of determination of the wave function. The classical theory is based upon the solution of the equation of motion by numerical methods. The comparison is performed of quantum and classical differential cross-sections of scattering in the transitional range of crystal thicknesses, from those at which the channeling phenomenon is not developed up to those at which it is realized. It is shown that in this range of crystal thicknesses substantial difference of quantum and classical scattering cross-sections takes place for the electrons with the energy up to tens of MeV. With the energy increase such difference decreases but some quantum effects in scattering still remain.
Lin, M. C.; Chang, P. C.; Lu, P. S.; Verboncoeur, J. P.
2011-10-01
Influence of ion effects on a space charge limited field emission flow has been studied systematically, by employing both analytical and numerical approaches. In our model, the field emission of electrons is described by the Fowler-Nordheim equation. The cathode plasma and surface properties are considered within the framework of an effective work function approximation. Ionization effects at the anode as well as electron space-charge effects are described by Poisson's equation coupled with the energy conservation equation including the relativistic effects. The calculations are carried out self-consistently to yield the steady states of the bipolar flow. The electric field on the cathode surface is found to be saturated due to space charge effects and is determined by the effective work function approximately. In addition, the upstream ion current bas been treated as a tuning parameter. It is found that the field emission currents in the presence of saturated ion currents can be enhanced to be nearly 1.8, 1.5, and 1.4 times of the cases with no upstream ion current in non-relativistic, intermediate, and ultra-relativistic regimes, respectively. The solutions have also been verified using 1D PIC simulations, as implemented in the OOPD1 code developed by PTSG of UC Berkeley. Work supported by the National Science Council, Taiwan, R.O.C. under Grant No. NSC 96-2112-M-030-004-MY3, National Center for Theoretical Sciences, and National Center for High-Performance Computing, Taiwan, ROC which provides the computing resources.
Peschanski, R
1993-01-01
Phenomenological and theoretical aspects of fragmentation for elementary particles (resp. nuclei) are discussed. It is shown that some concepts of classical fragmentation remain relevant in a microscopic framework, exhibiting non-trivial properties of quantum relativistic field theory (resp. lattice percolation). Email contact: pesch@amoco.saclay.cea.fr
Constructing quantum games from symmetric non-factorizable joint probabilities
Chappell, James M; Abbott, Derek
2010-01-01
We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations for a game based on non-factorizable joint probabilities, which embeds the classical game. We study a quantum version of Prisoners' Dilemma, Stag Hunt, and the Chicken game constructed from a given table of non-factorizable joint probabilities to find new outcomes in these games. We show that this approach provides a general framework for both classical and quantum games without recourse to the formalism of quantum mechanics.
Relativistic spectrum of hydrogen atom in the space-time non-commutativity
Energy Technology Data Exchange (ETDEWEB)
Moumni, Mustafa; BenSlama, Achour; Zaim, Slimane [Matter Sciences Department, Faculty of SE and SNV, University of Biskra (Algeria); Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria); Matter Sciences Department, Faculty of Sciences, University of Batna (Algeria)
2012-06-27
We study space-time non-commutativity applied to the hydrogen atom and its phenomenological effects. We find that it modifies the Coulomb potential in the Hamiltonian and add an r{sup -3} part. By calculating the energies from Dirac equation using perturbation theory, we study the modifications to the hydrogen spectrum. We find that it removes the degeneracy with respect to the total angular momentum quantum number and acts like a Lamb shift. Comparing the results with experimental values from spectroscopy, we get a new bound for the space-time non-commutative parameter.
Lewin, Mathieu
2011-01-01
In a recent paper published in Nonlinear Analysis: Theory, Methods & Applications, C. Argaez and M. Melgaard studied excited states for pseudo-relativistic multi-configuration methods. Their paper follows a previous work of mine in the non-relativistic case (Arch. Rat. Mech. Anal., 171, 2004). The main results of the paper of C. Argaez and M. Melgaard are correct, but the proofs are both wrong and incomplete.
The one-way quantum computer - a non-network model of quantum computation
Raussendorf, R; Briegel, H J; Raussendorf, Robert; Browne, Daniel E.; Briegel, Hans J.
2001-01-01
A one-way quantum computer works by only performing a sequence of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. No non-local operations are required in the process of computation. Any quantum logic network can be simulated on the one-way quantum computer. On the other hand, the network model of quantum computation cannot explain all ways of processing quantum information possible with the one-way quantum computer. In this paper, two examples of the non-network character of the one-way quantum computer are given. First, circuits in the Clifford group can be performed in a single time step. Second, the realisation of a particular circuit --the bit-reversal gate-- on the one-way quantum computer has no network interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)
The relativistic invariant Lie algebra for the kinematical observables in quantum space-time
Khrushchov, V V
2003-01-01
The deformation of the canonical algebra for the kinematical observables in Minkowski space has been considered under the condition of Lorentz invariance. A new relativistic invariant algebra depends on the fundamental constants $M$, $L$ and $H$ with the dimensionality of mass, length and action, respectively. In some limit cases the algebra obtained goes over into the well-known Snyder or Yang algebras. In general case the algebra represents a class of Lie algebras, which are either simple algebras, or semidirect sums of simple algebras integrable ones. T and C noninvariance for certain algebras of this class have been elucidated.
Non-binary Entanglement-assisted Stabilizer Quantum Codes
Riguang, Leng
2011-01-01
In this paper, we show how to construct non-binary entanglement-assisted stabilizer quantum codes by using pre-shared entanglement between the sender and receiver. We also give an algorithm to determine the circuit for non-binary entanglement-assisted stabilizer quantum codes and some illustrated examples. The codes we constructed do not require the dual-containing constraint, and many non-binary classical codes, like non-binary LDPC codes, which do not satisfy the condition, can be used to construct non-binary entanglement-assisted stabilizer quantum codes.
Quantum mechanics in non-inertial reference frames: Time-dependent rotations and loop prolongations
Energy Technology Data Exchange (ETDEWEB)
Klink, W.H., E-mail: william-klink@uiowa.edu [Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242 (United States); Wickramasekara, S., E-mail: wickrama@grinnell.edu [Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242 (United States); Department of Physics, Grinnell College, Grinnell, IA 50112 (United States)
2013-09-15
This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle as well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelerations. We show that the incorporation of rotational accelerations requires a class of loop prolongations of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-established framework for implementing symmetry transformations in quantum mechanics. -- Highlights: •A formulation of Galilean quantum mechanics in non-inertial reference frames is presented. •The Galilei group is generalized to infinite dimensional Galilean line group. •Loop prolongations of Galilean line group contain central extensions of Galilei group. •Unitary representations of the loops are constructed. •These representations lead to terms in the Hamiltonian corresponding to fictitious forces, including centrifugal and Coriolis
Ahamad, Shakeb; Patra, S K
2012-01-01
The ground state and first intrinsic excited state of superheavy nuclei with Z=120 and N=160-204 are investigated using both non-relativistic Skyrme-Hartree-Fock and the axially deformed Relativistic Mean Field formalisms. We employ a simple BCS pairing approach for calculating the energy contribution from pairing interaction. The results for isotopic chain of binding energy, quadrupole deformation parameter, two neutron separation energies and some other observables are compared with the FRDM and some recent macroscopic-microscopic calculations. We predict superdeformed ground state solutions for almost all the isotopes. Considering the possibility of magic neutron number, two different mode of \\alpha-decay chains (292)120 and (304)120 are also studied within these frameworks. The Q_{\\alpha}-values and the half-life T^{\\alpha}_{1/2} for these two different mode of decay chains are compared with FRDM and recent macroscopic-microscopic calculations. The calculation is extended for the \\alpha-decay chains of 29...
"It Ain't Necessarily So" - Interpretations and Misinterpretations of Quantum Theory
Stachel, John
After describing some recent misinterpretations of Bohr's views on quantum theory, largely based on their conflation with those of Heisenberg, a correct account of Bohr's approach is given in his own words. Then some guidelines toward a valid interpretation of quantization are discussed, including: the role of the quantum of action, the primacy of processes over states, the difference between classical and quantum ensembles, and between non-relativistic quantum mechanics and relativistic quantum field theory.
Institute of Scientific and Technical Information of China (English)
刘铁路; 王云良; 路彦珍
2015-01-01
The nonlinear propagation of quantum ion acoustic wave (QIAW) is investigated in a four-component plasma com-posed of warm classical positive ions and negative ions, as well as inertialess relativistically degenerate electrons and positrons. A nonlinear Schr ¨odinger equation is derived by using the reductive perturbation method, which governs the dynamics of QIAW packets. The modulation instability analysis of QIAWs is considered based on the typical parameters of the white dwarf. The results exhibit that both in weakly relativistic limit and in ultrarelativistic limit, the modulational instability regions are sensitively dependent on the ratios of temperature and number density of negative ions to those of positive ions respectively, and on relativistically degenerate effect as well.
Colloquium: Non-Markovian dynamics in open quantum systems
Breuer, Heinz-Peter; Laine, Elsi-Mari; Piilo, Jyrki; Vacchini, Bassano
2016-04-01
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry, and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations, and entanglement. Here recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely, to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This Colloquium further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom, and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification, and control of
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Ali [National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan); Masood, W. [National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan); COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad (Pakistan)
2016-05-15
Linear and nonlinear electrostatic ion acoustic waves in a weakly relativistic magnetorotating plasma in the presence of non-Maxwellian electrons and warm ions have been examined. The system under consideration has yielded two solutions, namely, the fast and slow acoustic modes which have been observed to depend on the streaming velocity, ion to electron temperature ratio, and the nonthermality parameter of the non-Maxwellian electrons. Using the multiple time scale analysis, we have derived the three dimensional nonlinear Zakharov–Kuznetsov equation and also presented its solution. Both compressive and rarefactive solitary structures have been found in consonance with the satellite observations. It has been observed that although the linear dispersion relation gives both fast and slow ion acoustic waves, the solitary structures form only for the fast acoustic mode. The dependence of the characteristics of the solitary structures on several plasma parameters has also been explored. The present investigation may be beneficial to understanding the rotating plasma environments such as those found in the planetary magnetospheres of Saturn and Jupiter.
Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
Hartong, Jelle; Obers, Niels A
2016-01-01
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a...
Energy Technology Data Exchange (ETDEWEB)
Goncalves, Bruno; Dias Junior, Mario Marcio [Instituto Federal de Educacacao, Ciencia e Tecnologia Sudeste de Minas Gerais, Juiz de Fora, MG (Brazil)
2013-07-01
Full text: The discussion of experimental manifestations of torsion at low energies is mainly related to the torsion-spin interaction. In this respect the behavior of Dirac field and the spinning particle in an external torsion field deserves and received very special attention. In this work, we consider the combined action of torsion and magnetic field on the massive spinor field. In this case, the Dirac equation is not straightforward solved. We suppose that the spinor has two components. The equations have mixed terms between the two components. The electromagnetic field is introduced in the action by the usual gauge transformation. The torsion field is described by the field S{sub μ}. The main purpose of the work is to get an explicit form to the equation of motion that shows the possible interactions between the external fields and the spinor in a Hamiltonian that is independent to each component. We consider that S{sub 0} is constant and is the unique non-vanishing term of S{sub μ}. This simplification is taken just to simplify the algebra, as our main point is not to describe the torsion field itself. In order to get physical analysis of the problem, we consider the non-relativistic approximation. The final result is a Hamiltonian that describes a half spin field in the presence of electromagnetic and torsion external fields. (author)
Accurate determination of the free-free Gaunt factor; I - non-relativistic Gaunt factors
van Hoof, P A M; Volk, K; Chatzikos, M; Ferland, G J; Lykins, M; Porter, R L; Wang, Y
2014-01-01
Modern spectral synthesis codes need the thermally averaged free-free Gaunt factor defined over a very wide range of parameter space in order to produce an accurate prediction for the spectrum emitted by an ionized plasma. Until now no set of data exists that would meet this need in a fully satisfactory way. We have therefore undertaken to produce a table of very accurate non-relativistic Gaunt factors over a much wider range of parameters than has ever been produced before. We first produced a table of non-averaged Gaunt factors, covering the parameter space log10(epsilon_i) = -20 to +10 and log10(w) = -30 to +25. We then continued to produce a table of thermally averaged Gaunt factors covering the parameter space log10(gamma^2) = -6 to +10 and log10(u) = -16 to +13. Finally we produced a table of the frequency integrated Gaunt factor covering the parameter space log10(gamma^2) = -6 to +10. All the data presented in this paper are available online.
Golubovic, Leonardo; Knudsen, Steven
2017-01-01
We consider general problem of modeling the dynamics of objects sliding on moving strings. We introduce a powerful computational algorithm that can be used to investigate the dynamics of objects sliding along non-relativistic strings. We use the algorithm to numerically explore fundamental physics of sliding climbers on a unique class of dynamical systems, Rotating Space Elevators (RSE). Objects sliding along RSE strings do not require internal engines or propulsion to be transported from the Earth's surface into outer space. By extensive numerical simulations, we find that sliding climbers may display interesting non-linear dynamics exhibiting both quasi-periodic and chaotic states of motion. While our main interest in this study is in the climber dynamics on RSEs, our results for the dynamics of sliding object are of more general interest. In particular, we designed tools capable of dealing with strongly nonlinear phenomena involving moving strings of any kind, such as the chaotic dynamics of sliding climbers observed in our simulations.
How quantum are non-negative wavefunctions?
Energy Technology Data Exchange (ETDEWEB)
Hastings, M. B. [Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA and Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052 (United States)
2016-01-15
We consider wavefunctions which are non-negative in some tensor product basis. We study what possible teleportation can occur in such wavefunctions, giving a complete answer in some cases (when one system is a qubit) and partial answers elsewhere. We use this to show that a one-dimensional wavefunction which is non-negative and has zero correlation length can be written in a “coherent Gibbs state” form, as explained later. We conjecture that such holds in higher dimensions. Additionally, some results are provided on possible teleportation in general wavefunctions, explaining how Schmidt coefficients before measurement limit the possible Schmidt coefficients after measurement, and on the absence of a “generalized area law” [D. Aharonov et al., in Proceedings of Foundations of Computer Science (FOCS) (IEEE, 2014), p. 246; e-print arXiv.org:1410.0951] even for Hamiltonians with no sign problem. One of the motivations for this work is an attempt to prove a conjecture about ground state wavefunctions which have an “intrinsic” sign problem that cannot be removed by any quantum circuit. We show a weaker version of this, showing that the sign problem is intrinsic for commuting Hamiltonians in the same phase as the double semion model under the technical assumption that TQO-2 holds [S. Bravyi et al., J. Math. Phys. 51, 093512 (2010)].
Non-unitary probabilistic quantum computing circuit and method
Williams, Colin P. (Inventor); Gingrich, Robert M. (Inventor)
2009-01-01
A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained.
Quantum mechanics, strong emergence and ontological non-reducibility
Gambini, Rodolfo; Pullin, Jorge
2015-01-01
We show that a new interpretation of quantum mechanics, in which the notion of event is defined without reference to measurement or observers, allows to construct a quantum general ontology based on systems, states and events. Unlike the Copenhagen interpretation, it does not resort to elements of a classical ontology. The quantum ontology in turn allows us to recognize that a typical behavior of quantum systems exhibits strong emergence and ontological non-reducibility. Such phenomena are not exceptional but natural, and are rooted in the basic mathematical structure of quantum mechanics.
Non Hermitian quantum mechanics in non commutative space
Giri, Pulak Ranjan
2008-01-01
We study non Hermitian quantum systems in noncommutative space as well as a \\cal{PT} symmetric deformation of this space. Specifically, a \\mathcal{PT}-symmetric harmonic oscillator together with iC(x_1+x_2) interaction is discussed in this space and solutions are obtained. It is shown that in the \\cal{PT} deformed noncommutative space the Hamiltonian may or may not possess real eigenvalues depending on the choice of the noncommutative parameters. However, it is shown that in standard noncommutative space, the iC(x_1+x_2) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not \\mathcal{PT}-symmetric. A complex interacting anisotropic oscillator system has also been discussed.
Directory of Open Access Journals (Sweden)
Suparmi
2014-12-01
Full Text Available The bound state solution of the Dirac equation for generalized PöschlTeller and trigonometric Pöschl-Teller non-central potentials was obtained using SUSY quantum mechanics and the idea of shape invariance potential. The approximate relativistic energy spectrum was expressed in the closed form. The radial and polar wave functions were obtained using raising and lowering of radial and polar operators. The orbital quantum numbers were found from the polar Dirac equation, which was solved using SUSY quantum mechanics and the idea of shape invariance.
Bliokh, Konstantin Y
2011-01-01
We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, mechanical flywheel, and discuss various fundamental aspects of the phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes.
Non Mechanical (Mezic Type Forces in the Foundations of Quantum Mechanics
Directory of Open Access Journals (Sweden)
Č. Šimáně
2010-01-01
Full Text Available Many authors have attempted to derive the fundamental equations of quantum mechanics from classical hydrodynamics. In the present contribution we presume that the continuous, electrically charged material substance moves simultaneously under the influence of the electric field and at the same time undergoes a diffusion process. This assumption leads to the appearance of non-mechanical (mezic type forces responsible for inner sources of matter (positive or negative, similar to those whose existence is supposed to exist in relativistic hydrodynamics. We obtained a non-linear differential equation, convertible by linearization to a form coinciding with the Schrödinger equation, as a condition for the establishment of the same steady states with discrete energies.
Effects of high-order operators in non-relativistic Lifshitz holography
Wang, Xinwen; Tian, Miao; Wang, Anzhong; Deng, Yanbin; Cleaver, Gerald
2014-01-01
In this paper, we study the effects of high-order operators on the non-relativistic Lifshitz holography in the framework of the Ho\\v{r}ava-Lifshitz (HL) theory of gravity, which naturally contains high-order operators in order for the theory to be power-counting renormalizble, and provides an ideal place to study these effects. In particular, we show that the Lifshitz space-time is still a solution of the full theory of the HL gravity. The effects of the high-oder operators on the space-time itself is simply to shift the Lifshitz dynamical exponent. However, while in the infrared the asymptotic behavior of a (probe) scalar field near the boundary is similar to that studied in the literature, it gets dramatically modified in the UV limit, because of the presence of the high-order operators in this regime. Then, according to the gauge/gravity duality, this in turn affects the two-point correlation functions.
Simulations of ion acceleration at non-relativistic shocks: i) Acceleration efficiency
Caprioli, Damiano
2013-01-01
We use 2D and 3D hybrid (kinetic ions - fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasi-parallel configurations (i.e., when the background magnetic field is almost aligned with the shock normal) and, for large sonic and Alfv\\'enic Mach numbers, produces universal power-law spectra proportional to p^(-4), where p is the particle momentum. The maximum energy of accelerated ions increases with time, and it is only limited by finite box size and run time. Acceleration is mainly efficient for parallel and quasi-parallel strong shocks, where 10-20% of the bulk kinetic energy can be converted to energetic particles, and becomes ineffective for quasi-perpendicular shocks. Also, the generation of magnetic turbulence correlates with efficient ion acceleration, and vanishes for quasi-perpendicular configurations. At very oblique shocks, ions can be accelerated via shoc...
Fu, X.; Waters, T.; Gary, S. P.
2014-12-01
Collisionless space plasmas often deviate from Maxwellian-like velocity distributions. To study kinetic waves and instabilities in such plasmas, the dispersion relation, which depends on the velocity distribution, needs to be solved numerically. Most current dispersion solvers (e.g. WHAMP) take advantage of mathematical properties of the Gaussian (or generalized Lorentzian) function, and assume that the velocity distributions can be modeled by a combination of several drift-Maxwellian (or drift-Lorentzian) components. In this study we are developing a kinetic dispersion solver that admits nearly arbitrary non-relativistic parallel velocity distributions. A key part of any dispersion solver is the evaluation of a Hilbert transform of the velocity distribution function and its derivative along Landau contours. Our new solver builds upon a recent method to compute the Hilbert transform accurately and efficiently using the fast Fourier transform, while simultaneously treating the singularities arising from resonances analytically. We have benchmarked our new solver against other codes dealing with Maxwellian distributions. As an example usage of our code, we will show results for several instabilities that occur for electron velocity distributions observed in the solar wind.
Non-relativistic radiation mediated shock breakouts: II. Bolometric properties of SN shock breakout
Katz, Boaz; Waxman, Eli
2011-01-01
Exact bolometric light curves of supernova shock breakouts are derived based on the universal, non relativistic, planar breakout solutions (Sapir et al. 2011), assuming spherical symmetry, constant Thomson scattering opacity, \\kappa, and angular intensity corresponding to the steady state planar limit. These approximations are accurate for progenitors with a scale height much smaller than the radius. The light curves are insensitive to the density profile and are determined by the progenitor radius R, and the breakout velocity and density, v_0 and \\rho_0 respectively, and \\kappa. The total breakout energy, E_BO, and the maximal ejecta velocity, v_max, are shown to be E_BO=8.0\\pi R^2\\kappa^-1cv_0 and v_max=2.0v_0 respectively, to an accuracy of about 10%. The calculated light curves are valid up to the time of transition to spherical expansion, t_sph\\approx R/4v_0. Approximate analytic expressions for the light curves are provided for breakouts in which the shock crossing time at breakout, t_0=c/\\kappa\\rho_0v_...
Pair Production of Open Strings Relativistic versus Dissipative Dynamics
Acatrinei, C S
1999-01-01
We study the pair production of open strings in constant electric fields, using a general framework which encodes both relativistic string theory and generic linearly extended systems as well. In the relativistically invariant case we recover previous results, both for pair production and for the effective Born-Infeld action. We then derive a non-relativistic limit - where the propagation velocity along the string is much smaller than the velocity of light - obtaining quantum dissipation. We calculate the pair nucleation rate for this case, which could be relevant for applications.
Non-selfadjoint operators in quantum physics mathematical aspects
Gazeau, Jean Pierre; Szafraniec, Franciszek Hugon; Znojil, Miloslav
2015-01-01
A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses recent emergence of the unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis, with potentially significant physical consequences. In addition to prompting a discussion of the role of mathematical methods in the contemporary development of quantum physics, the book features: * Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area *...
Non-monotonicity in the quantum-classical transition: Chaos induced by quantum effects
Kapulkin, A; Kapulkin, Arie; Pattanayak, Arjendu K.
2007-01-01
The transition from classical to quantum behavior for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative size of $\\hbar$ is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the double-well Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective $\\hbar$ is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantum-classical transition in this case is non-monotonic in $\\hbar$.
Quantum objects non-local correlation, causality and objective indefiniteness in the quantum world
Jaeger, Gregg
2013-01-01
This monograph identifies the essential characteristics of the objects described by current quantum theory and considers their relationship to space-time. In the process, it explicates the senses in which quantum objects may be consistently considered to have parts of which they may be composed or into which they may be decomposed. The book also demonstrates the degree to which reduction is possible in quantum mechanics, showing it to be related to the objective indefiniteness of quantum properties and the strong non-local correlations that can occur between the physical quantities of quantum
Kotikov, A V
2013-01-01
We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics for an arbitrary gauge using the method of integration by parts. Focusing on the limit where the photon field is four-dimensional, our formula involves only recursively one-loop integrals and can therefore be evaluated exactly. From this formula, we deduce the anomalous scaling dimension of the fermion field as well as the renormalized fermion propagator up to two loops. The results are then applied to the ultra-relativistic limit of graphene and compared with similar results obtained for four-dimensional and three-dimensional quantum electrodynamics.
A Bilocal Model for the Relativistic Spinning Particle
Rempel, Trevor
2016-01-01
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for spinning particles allows for a natural description of particle interactions as a local interaction at each of the constituents. This form of the interaction vertex provides a resolution to a long standing issue on the nature of relativistic interactions for spinning objects in the context of the worldline formalism. It also potentially brings a dynamical explanation for why massive fundamental objects are naturally of lowest spin. We analyze first a non-relativistic system where spin is modeled as an entangled state of two particles with the entanglement encoded into a set of constraints. It is shown that these constraints can be made relativistic and that the resulting description is isomorphic to the usual description of the phase space of massive relativistic particles ...
Stahl, A.; Landreman, M.; Embréus, O.; Fülöp, T.
2017-03-01
Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modeling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.
Stahl, A; Embréus, O; Fülöp, T
2016-01-01
Energetic electrons are of interest in many types of plasmas, however previous modelling of their properties have been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a fully non-linear kinetic-equation solver, capable of handling large electric-field strengths (compared to the Dreicer field) and relativistic temperatures. This tool allows modelling of the momentum-space dynamics of the electrons in cases where strong departures from Maxwellian distributions may arise. As an example, we consider electron runaway in magnetic-confinement fusion plasmas and describe a transition to electron slide-away at field strengths significantly lower than previously predicted.
A histories perspective on characterising quantum non-locality
Dowker, Fay; Wallden, Petros
2013-01-01
We introduce a framework for studying non-locality and contextuality inspired by the path integral formulation of quantum theory. We prove that the existence of a strongly positive joint quantum measure -- the quantum analogue of a joint probability measure -- on a set of experimental probabilities implies the Navascues-Pironio-Acin (NPA) condition $Q^1$ and is implied by the stronger NPA condition $Q^{1+AB}$. A related condition is shown to be equivalent to $Q^{1+AB}$.
Kobayashi, Michikazu
2014-01-01
We show that a momentum operator of a translational symmetry may not commute with an internal symmetry operator in the presence of a topological soliton in non-relativistic theories. As a striking consequence, there appears a coupled Nambu-Goldstone mode with a quadratic dispersion consisting of translational and internal zero modes in the vicinity of a domain wall in an O(3) sigma model, a magnetic domain wall in ferromagnets with an easy axis.
Le Yaouanc, A; Morénas, V; Oliver, L; Pène, O; Raynal, J C
2000-01-01
The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $\\delta m/m_b^2$.
Is a non-relativist post-modernism possible? The attempts of William Dean and Wentzel van Huyssteen
Directory of Open Access Journals (Sweden)
J. A. Stone
1993-01-01
Full Text Available This paper aims at creating a third option to foundationalism and relativism. It criticizes William Dean’s historicist radical empiricism for going too far toward a relativ ist deconstructionism, and Wentzel van Huyss teen’s critical realism for not leaving modernism. Both, however, succeed in creating a third option. This paper examines their respective contributions to a non relativist, reconstructionist post-modernism.
Beneke, M.; Hellmann, C.; Ruiz-Femenia, P.
2012-01-01
We compute analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM, including the previously unknown off-diagonal rates. The results are prerequisites to the calculation of the Sommerfeld enhancement in the MSSM, which will be presented in subsequent work. They can also be used to obtain concise analytic expressions for MSSM dark matter pair annihilation in the present Universe for a large number of exc...
Non-classical state engineering for quantum networks
Energy Technology Data Exchange (ETDEWEB)
Vollmer, Christina E.
2014-01-24
The wide field of quantum information processing and quantum networks has developed very fast in the last two decades. Besides the regime of discrete variables, which was developed first, the regime of continuous variables represents an alternative approach to realize many quantum applications. Non-classical states of light, like squeezed or entangled states, are a fundamental resource for quantum applications like quantum repeaters, quantum memories, quantum key distribution, quantum spectroscopy, and quantum metrology. These states can be generated successfully in the infrared wavelength regime. However, for some tasks other wavelengths, especially in the visible wavelength regime, are desirable. To generate non-classical states of light in this wavelength regime frequency up-conversion can be used, since all quantum properties are maintained in this process. The first part of this thesis deals with the experimental frequency up-conversion of quantum states. Squeezed vacuum states of light at 1550 nm were up-converted to 532 nm and a noise reduction of -1.5 dB at 532 nm was achieved. These states can be used for increasing the sensitivity of gravitational wave detectors or spectroscopic measurements. Furthermore, one part of an entangled state at 1550 nm was up-converted to 532 nm and, thus, entanglement between these two wavelengths was generated and characterized to -1.4 dB following Duan et al. With such a quantum link it is possible to establish a quantum network, which takes advantage of the low optical loss at 1550 nm for information transmission and of atomic transitions around 532 nm for a quantum memory in a quantum repeater. For quantum networks the distribution of entanglement and especially of a quantum key is essential. In the second part of this thesis the experimental distribution of entanglement by separable states is demonstrated. The underlying protocol requires a special three-mode state, which is separable in two of the three splittings. With
Reinisch, Gilbert C.; Gazeau, Maxime
2016-07-01
In this paper we consider a basic two-level nonlinear quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrödinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant α is provided within 99.95% accuracy by the present first-order non-relativistic and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).
Quantum heat engine in the relativistic limit: The case of a Dirac particle
Muñoz, Enrique; Peña, Francisco J.
2012-12-01
We studied the efficiency of two different schemes for a quantum heat engine, by considering a single Dirac particle trapped in an infinite one-dimensional potential well as the “working substance.” The first scheme is a cycle, composed of two adiabatic and two isoenergetic reversible trajectories in configuration space. The trajectories are driven by a quasistatic deformation of the potential well due to an external applied force. The second scheme is a variant of the former, where isoenergetic trajectories are replaced by isothermal ones, along which the system is in contact with macroscopic thermostats. This second scheme constitutes a quantum analog of the classical Carnot cycle. Our expressions, as obtained from the Dirac single-particle spectrum, converge in the nonrelativistic limit to some of the existing results in the literature for the Schrödinger spectrum.
An origin of the Universe determined by quantum physics and relativistic gravity
Unnikrishnan, C. S.; Gillies, G. T.; Ritter, R. C.
2001-01-01
We discuss the evolution of the Universe from what might be called its quantum origin. We apply the uncertainty principle to the origin of the Universe with characteristic time scale equal to the Planck time to obtain its initial temperature and density. We establish that the subsequent evolution obeying the Einstein equation gives the present temperature of the microwave background close to the observed value. The same origin allows the possibility that the Universe started with exactly the ...
Horwitz, L. P.
2015-05-01
The most recent meeting took place at the University of Connecticut, Storrs, on June 9-13, 2014. This meeting forms the basis for the Proceedings that are recorded in this issue of the Journal of Physics: Conference Series. Along with the work of some of the founding members of the Association, we were fortunate to have lecturers from application areas that provided strong challenges for further developments in quantum field theory, cosmological problems, and in the dynamics of systems subject to accelerations and the effects of general relativity. Topics treated in this issue include studies of the dark matter problem, rotation curves, and, in particular, for the (relatively accessible) Milky Way galaxy, compact stellar objects, a composite particle model, and the properties of a conformally invariant theory with spontaneous symmetry breaking. The Stueckelberg theory is further investigated for its properties in producing bremsstrahlung and pair production and apparent superluminal effects, and, as mentioned above, the implications of low energy nuclear reactions for such off-shell theories. Other "proper time" theories are investigated as well, and a study of the clock synchronization problem is presented. A mathematical study of to quantum groupo associated with the Toda lattice and its implications for quantum field theory, as well as a phenomenological discussion of supernova mechanics as well as a semiclassical discussion of electron spin and the question of the compatibility of special relativity and the quantum theory. A careful analysis of the covariant Aharonov-Bohm effect is given as well. The quantization of massless fields and the relation to the Maxwell theory is also discussed. We wish to thank the participants who contributed very much through their lectures, personal discussions, and these papers, to the advancement of the subject and our understanding.
Non-perturbative quantum gravity: a conformal perspective
Budd, T.G.
2012-01-01
The construction of meaningful observables in models of quantum gravity is a highly non-trivial task, but necessary in order to study their continuum physics. In this thesis several such observables are identified in lattice models of quantum gravity. In dynamical triangulations in two dimensions wi
The Anomalous Nambu-Goldstone Theorem in Relativistic/Nonrelativistic Quantum Field Theory
Ohsaku, Tadafumi
2013-01-01
The anomalous Nambu-Goldstone (NG) theorem which is found as a violation of counting law of the number of NG bosons of the normal NG theorem in nonrelativistic and Lorentz-symmetry-violated relativistic theories is studied in detail, with emphasis on its mathematical aspect from Lie algebras, geometry to number theory. The basis of counting law of NG bosons in the anomalous NG theorem is examined by Lie algebras (local) and Lie groups (global). A quasi-Heisenberg algebra is found generically in various symmetry breaking schema of the anomalous NG theorem, and it indicates that it causes a violation/modification of the Heisenberg uncertainty relation in an NG sector which can be experimentally confirmed. The formalism of effective potential is presented for understanding the mechanism of anomalous NG theorem with the aid of our result of Lie algebras. After an investigation on a bosonic kaon condensation model with a finite chemical potential as an explicit Lorentz-symmetry-breaking parameter, a model Lagrangi...
Scott, Tony C.
It has been shown that the Fokker-Wheeler-Feynman (FWF) model could be rewritten to yield a physically acceptable relativistic many-particle Lagrangian. Contrary to Wheeler and Feynman's postulates, the model satisfies causality and can be generalised to include arbitrary forces. The 1/c power series of the FWF Lagrangian to order (1/c) ^4 contains accelerations. A procedure of quantizing the theory for such a Lagrangian is presented and it is then found that the accelerations approximately introduce an independent harmonic mode which is in agreement with resonances recently observed in Positronium collisions processes. This result may be of fundamental physical importance and requires further investigation. However, the refinement of this calculation requires the creation of new computational tools. To this end, a new method is presented in which both the eigenfunctions and eigenenergies are determined algebraically as power series in the order parameter, where each coefficient of the series is obtained in closed form. This method avoids the complications of a basis set and makes extensive use of symbolic computation. It is then applied to two model problems, namely the one-body Dirac equation for testing purposes and a special case of the two-body Dirac equation for which one obtains previously unknown closed form solutions.
Electromagnetic rho-meson form factors in point-form relativistic quantum mechanics
Biernat, Elmar P
2014-01-01
The relativistic point-form formalism which we proposed for the study of the electroweak structure of few-body bound states is applied to calculate the elastic form factors of spin-1 mesons, such as the rho, within constituent-quark models. We treat electron-meson scattering as a Poincare-invariant coupled-channel problem for a Bakamjian-Thomas mass operator and extract the meson current from the resulting invariant 1-photon-exchange amplitude. Wrong cluster properties inherent in the Bakamjian-Thomas framework are seen to cause spurious contributions in the current. These contributions, however, can be separated unambiguously from the physical ones and we end up with a meson current with all required properties. Numerical results for the rho-meson form factors are presented assuming a simple harmonic-oscillator bound-state wave function. The comparison with other approaches reveals a remarkable agreement of our results with those obtained within the covariant light-front scheme proposed by Carbonell et al.
Wuthrich, Christian
2014-01-01
There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istv\\'an N\\'emeti and Gyula D\\'avid (2006) have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour Istv\\'an's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in N\\'emeti and D\\'avid (2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing ...
Non-standard loop quantum cosmology
Piechocki, Wlodzimierz
2010-01-01
We present results concerning the nature of the cosmological big bounce(BB) transition within the loop geometry underlying loop quantum cosmology (LQC). Our canonical quantization method is an alternative to the standard LQC. An evolution parameter we use has clear interpretation both at classical and quantum levels. The physical volume operator has discrete spectrum which is bounded from below. The minimum gap in the spectrum defines a quantum of the volume. The spectra of operators are parametrized by a free parameter to be determined.
Quantum Discord of Non-X State
Institute of Scientific and Technical Information of China (English)
YAO Jing-Ying; DONG Yu-Li; ZHU Shi-Qun
2013-01-01
The level surfaces of quantum discord for a class of two-qubit states are investigated when the Bloch vectors (r) and (s) are perpendicularly oriented.The geometric objects of tetrahedron T and octahedron O are deformed.The level surfaces of constant discord are formed by three interaction “tubes” along three orthogonal directions.They shrink to the center when the Bloch vectors are increased and are expanded and cut off by the state tetrahedron T when the quantum discord is increased.In the phase damping channel,the quantum discord keeps approximately a constant when the time increases.
Quantum physics without quantum philosophy
Energy Technology Data Exchange (ETDEWEB)
Duerr, Detlef [Muenchen Univ. (Germany). Mathematisches Inst.; Goldstein, Sheldon [Rutgers State Univ., Piscataway, NJ (United States). Dept. of Mathematics; Zanghi, Nino [Genova Univ. (Italy); Istituto Nazionale Fisica Nucleare, Genova (Italy)
2013-02-01
Integrates and comments on the authors' seminal papers in the field. Emphasizes the natural way in which quantum phenomena emerge from the Bohmian picture. Helps to answer many of the objections raised to Bohmian quantum mechanics. Useful overview and summary for newcomers and students. It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schroedinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Quantum non-Markovianity: characterization, quantification and detection.
Rivas, Ángel; Huelga, Susana F; Plenio, Martin B
2014-09-01
We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.
Non-Markovian spontaneous emission from a single quantum dot
DEFF Research Database (Denmark)
Madsen, Kristian Høeg; Ates, Serkan; Lund-Hansen, Toke;
2011-01-01
We observe non-Markovian dynamics of a single quantum dot when tuned into resonance with a cavity mode. Excellent agreement between experiment and theory is observed providing the first quantitative description of such a system....
Energy Technology Data Exchange (ETDEWEB)
NONE
2012-07-01
The following topics were dealt with: Superfluidity and quantum turbulence, quantum vortices and their reconnections, quantum hydrodynamics and turbulence in Bose-Einstein condensates, phase transitions in turbulence, perfect fluidity in relativistic heavy ion collisions, off-shell dynamical approach for relativistic heavy ion collisions, turbulence in the early universe, a superfluid universe, superfluidity and hydrodynamic excitations in out-of-equilibrium polariton condensates, two-dimensional quantum turbulence in Bose-Einstein condensates, nonequilibrium Bose gases with classical fields, turbulence in superfluid {sup 4}He in the T=0 limit, condensation, superfluidity and lasing of coupled light-matter systems, tachyon condensation in Bose-Einstein condensates, Bose-Einstein condensation of magnons in superfluid {sup 3}He-B and its application to vortex studies, wave turbulence in Bose-Einstein condensates, instability in an expanding non-Abelian system, nonabelian plasma instabilities, quantum turbulence in an atomic trapped superfluid, nonthermal fixed points and superfluid turbulence, macroscopic quantum tunneling in Bose-Einstein condensates, pair coherence in many-body quenches, sound waves in non-stationary media, thermalization induced by chaotic behavior in classical Yang-Mills dynamics, chiral superfluidity of the quark-gluon plasma, functional renormalization-group flow for Burger's equation, anomalous scaling in the random-force-driven Burger's equation, Kadanoff-Baym approach to thermalization, many-body resonant tunneling in the Wannier system, generalized Boltzmann equation in ultrasoft region, dynamical view of the Schwinger mechanism, parity violation in hydrogen and squeezing. (HSI)
Quantum gases finite temperature and non-equilibrium dynamics
Szymanska, Marzena; Davis, Matthew; Gardiner, Simon
2013-01-01
The 1995 observation of Bose-Einstein condensation in dilute atomic vapours spawned the field of ultracold, degenerate quantum gases. Unprecedented developments in experimental design and precision control have led to quantum gases becoming the preferred playground for designer quantum many-body systems. This self-contained volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose-Einstein condensates, degenerate Fermi gases, and the more recently realised exciton-polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics. Thematically organised chapters on different methodologies, contributed by key researchers using a unified notation, provide the first integrated view of the relative merits of individual approaches, aided by pertinent introductory chapters and the guidance of ed...
Quantum correlations in non-inertial cavity systems
Harsij, Zeynab; Mirza, Behrouz
2016-10-01
Non-inertial cavities are utilized to store and send Quantum Information between mode pairs. A two-cavity system is considered where one is inertial and the other accelerated in a finite time. Maclaurian series are applied to expand the related Bogoliubov coefficients and the problem is treated perturbatively. It is shown that Quantum Discord, which is a measure of quantumness of correlations, is degraded periodically. This is almost in agreement with previous results reached in accelerated systems where increment of acceleration decreases the degree of quantum correlations. As another finding of the study, it is explicitly shown that degradation of Quantum Discord disappears when the state is in a single cavity which is accelerated for a finite time. This feature makes accelerating cavities useful instruments in Quantum Information Theory.
On the Origins of the Planck Zero Point Energy in Relativistic Quantum Field Theory
Widom, A; Srivastava, Y N
2015-01-01
It is argued that the zero point energy in quantum field theory is a reflection of the particle anti-particle content of the theory. This essential physical content is somewhat disguised in electromagnetic theory wherein the photon is its own anti-particle. To illustrate this point, we consider the case of a charged Boson theory $(\\pi^+,\\pi^-)$ wherein the particle and anti-particle can be distinguished by the charge $\\pm e$. Starting from the zero point energy, we derive the Boson pair production rate per unit time per unit volume from the vacuum in a uniform external electric field. The result is further generalized for arbitrary spin $s$.
Nonlinear relativistic and quantum equations with a common type of solution.
Nobre, F D; Rego-Monteiro, M A; Tsallis, C
2011-04-08
Generalizations of the three main equations of quantum physics, namely, the Schrödinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index q, are considered in such a way that the standard linear equations are recovered in the limit q→1. Interestingly, these equations present a common, solitonlike, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In all cases, the well-known Einstein energy-momentum relation is preserved for arbitrary values of q.
Directory of Open Access Journals (Sweden)
Maruyama Tomoyuki
2016-01-01
Full Text Available We study pion production from proton synchrotron radiation in the presence of strong magnetic fields by using the exact proton propagator in a strong magnetic field and explicitly including the anomalous magnetic moment. Results in this exact quantum approach do not agree with those obtained in the semi-classical approach. Then, we find that the anomalous magnetic moment of the proton greatly enhances the production rate by about two orders magnitude, and that the decay width satisfies a robust scaling law.
Entanglement and non-Markovianity of quantum evolutions
Rivas, Ángel; Plenio, Martin B
2009-01-01
We address the problem of quantifying the non-Markovian character of quantum time-evolutions of general systems in contact with an environment. We introduce two different measures of non-Markovianity that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts, one requiring complete tomographic knowledge about the evolution and the other one requiring no knowledge at all. Remarkably, no optimization procedure underlies our derivation, which greatly enhances the practical relevance of the proposed criteria.
Non-Schroedinger forces and pilot waves in quantum cosmology
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1987-09-01
The author argues that the version of the pilot wave interpretation of quantum mechanics which uses a non-local non-Schroedinger force is inconsistent when applied to distributions with small numbers of particles. Thus, no version of the pilot wave interpretation (some-times called the de Broglie-Bohm, or causal, interpretation) can be applied to the wavefunction of quantum cosmology because in any version of this interpretation, there is only one particle, the universe.
Quantum Mechanics: Harbinger of a Non-Commutative Probability Theory?
Hiley, Basil J.
2014-01-01
In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to see the structure of quantum processes in terms of non-commutative probability theory, a non-Boolean structure of the implicate order which contains Boolean sub-structures which accommodates the explicate classical world. We move away from mechanical `wave...
Understanding quantum non-locality through pseudo-telepathy game
Kunkri, Samir
2006-11-01
Usually by quantum non-locality we mean that quantum mechanics can not be replaced by local realistic theory. On the other hand this nonlocal feature of quantum mechanics can not be used for instantaneous communication and hence it respect Einstein's special theory of relativity. But still it is not trivial as proved by various quantum information processing using entangled states. Recently there have been studies of hypothetical non-local system again respecting no-signalling which is beyond quantum mechanics. Here we study the power of such a hypothetical nonlocal box first suggested by Popescu et.al. in the context of recently suggested pseudo-telepathy game constructed from a Kochen-Specker set.
Bashir, M F
2012-01-01
Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those electromagnetic modes whose magnetic field perturbations are perpendicular to the ambient magneticeld, i.e.,B1 \\perp B0, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them and the O-mode are affected by thermal anisotropies, since they satisfy the required condition B1\\perpB0. By contrast, the perpendicular...
Cencek, Wojciech; Przybytek, Michał; Komasa, Jacek; Mehl, James B; Jeziorski, Bogumił; Szalewicz, Krzysztof
2012-06-14
The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound
Contrasting Classical and Quantum Vacuum States in Non-inertial Frames
Boyer, Timothy H.
2013-08-01
Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the "Minkowski vacuum" for a box at rest in an inertial frame and a "Rindler vacuum" for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The
Matrix Algebras in Non-Hermitian Quantum Mechanics
Institute of Scientific and Technical Information of China (English)
Alessandro Sergi
2011-01-01
In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schr(o)dinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of commutators, defining the time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The logic behind such a derivation is reversible, so that any Hermitian Hamiltonian can be used in the formulation of non-Hermitian dynamics through a suitable algebra of generalized (non-Hamiltonian)commutators. These results provide a general structure (a template) for non-Hermitian equations of motion to be used in the computer simulation of open quantum systems dynamics.