Lincoln, Don
2016-07-12
The strongest force in the universe is the strong nuclear force and it governs the behavior of quarks and gluons inside protons and neutrons. The name of the theory that governs this force is quantum chromodynamics, or QCD. In this video, Fermilabâs Dr. Don Lincoln explains the intricacies of this dominant component of the Standard Model.
Lincoln, Don
2016-06-17
The strongest force in the universe is the strong nuclear force and it governs the behavior of quarks and gluons inside protons and neutrons. The name of the theory that governs this force is quantum chromodynamics, or QCD. In this video, Fermilab’s Dr. Don Lincoln explains the intricacies of this dominant component of the Standard Model.
Three dimensional quantum chromodynamics
NASA Astrophysics Data System (ADS)
Ferretti, G.; Rajeev, S. G.; Yang, Z.
1992-02-01
The subject of this talk is the study of the low energy behavior of three (2+1) dimensional Quantum Chromodynamics. We show the existence of a phase where parity is unbroken and the flavor group U(2n) is broken into a subgroup U(n)×U(n). We derive the low energy effective action for the theory and show that it has solitonic excitations with Fermi statistic, to be identified with the three dimensional ``baryon''. Finally, we study the current algebra for this effective action and we find a co-homologically nontrivial generalization of Kac-Moody algebras to three dimension.
Quantum chromodynamics with advanced computing
Kronfeld, Andreas S.; /Fermilab
2008-07-01
We survey results in lattice quantum chromodynamics from groups in the USQCD Collaboration. The main focus is on physics, but many aspects of the discussion are aimed at an audience of computational physicists.
Advances in Lattice Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
McGlynn, Greg
In this thesis we make four contributions to the state of the art in numerical lattice simulations of quantum chromodynamics (QCD). First, we present the most detailed investigation yet of the autocorrelations of topological observations in hybrid Monte Carlo simulations of QCD and of the effects of the boundary conditions on these autocorrelations. This results in a numerical criterion for deciding when open boundary conditions are useful for reducing these autocorrelations, which are a major barrier to reliable calculations at fine lattice spacings. Second, we develop a dislocation-enhancing determinant, and demonstrate that it reduces the autocorrelation time of the topological charge. This alleviates problems with slow topological tunneling at fine lattice spacings, enabling simulations on fine lattices to be completed with much less computational effort. Third, we show how to apply the recently developed zMobius technique to hybrid Monte Carlo evolutions with domain wall fermions, achieving nearly a factor of two speedup in the light quark determinant, the single most expensive part of the calculation. The dislocation-enhancing determinant and the zMobius technique have enabled us to begin simulations of fine ensembles with four flavors of dynamical domain wall quarks. Finally, we show how to include the previously-neglected G1 operator in nonperturbative renormalization of the DeltaS = 1 effective weak Hamiltonian on the lattice. This removes an important systematic error in lattice calculations of weak matrix elements, in particular the important K → pipi decay.
Dynamics of nonrelativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Efthimiades, Spyros
2017-01-01
We show that the wavefunction of an electron interacting with an electric potential is accurately represented by the superposition of plane waves that fulfills the total energy relation. As a result, we explicitly derive the Schrödinger, Pauli, Klein-Gordon, and Dirac equations. While the traditional nonrelativistic quantum dynamics is based on postulates, the dynamics we introduce is theoretically justified, in agreement with experimental measurements, and consistent with the fundamental theory of quantum electrodynamics.
Exclusive Processes in Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; Peter Lepage, G.
The following sections are included: * INTRODUCTION * NONRELATIVISTIC FORM FACTORS FOR HEAVY-QUARK MESONS * HADRONIC WAVEFUNCTIONS * DEFINITIONS * LIGHT-CONE BOUND-STATE EQUATIONS * GENERAL PROPERTIES OF LIGHT-CONE WAVEFUNCTIONS * RENORMALIZATION * CALCULATING * A PERTURBATIVE ANALYSIS * FACTORIZATION—LEADING ORDER ANALYSIS * THE QUARK DISTRIBUTION AMPLITUDE * DETERMINATION OF DISTRIBUTION AMPLITUDES * HIGHER ORDER ANALYSIS * COMPLICATIONS * How LARGE IS ASYMPTOTIC Q? * APPLICATIONS OF QCD TO THE PHENOMENOLOGY OF EXCLUSIVE REACTIONS * GENERAL FEATURES OF EXCLUSIVE PROCESSES IN QCD * ELECTROMAGNETIC FORM FACTORS * COMPARISON OF QCD SCALING WITH EXPERIMENT * EXCLUSIVE ANTI-PROTON PROTON ANNIHILATION PROCESSES * ADDITIONAL TESTS OF GLUON SPIN IN EXCLUSIVE PROCESSES * HADRONIC WAVEFUNCTION PHENOMENOLOGY * CALCULATING TH * THE PRE-QCD DEVELOPMENT OF EXCLUSIVE REACTIONS * EXCLUSIVE e+ e- ANNIHILATION PROCESSES * J/ψ DECAY TO HADRON PAIRS * THE π-ρ PUZZLE * FORM FACTOR ZEROS IN QCD * EXCLUSIVE γγ REACTIONS * QCD PROCESSES IN NUCLEI * EXCLUSIVE NUCLEAR REACTIONS - REDUCED AMPLITUDES * COLOR TRANSPARENCY * SPIN CORRELATIONS IN PROTON-PROTON SCATTERING * CONCLUSIONS * APPENDIX I BARYON FORM FACTORS AND EVOLUTION EQUATIONS * APPENDIX II LIGHT CONE QUANTIZATION AND PERTURBATION THEORY * APPENDIX III A NONPERTURBATIVE ANALYSIS OF EXCLUSIVE REACTIONS-DISCRETIZED LIGHT-CONE QUANTIZATION * ACKNOWLEDGEMENTS * REFERENCES
Synthesis of quantum chromodynamics and nuclear physics
Brodsky, S.J.; Lepage, G.P.
1980-08-01
The asymptotic freedom behavior of quantum chromodynamics allows the rigorous calculation of hadronic and nuclear amplitudes at short distances by perturbative methods. The implications of QCD for large-momentum-transfer nuclear form factors and scattering processes, as well as for the structure of nuclear wave functions and nuclear interactions at short distances, are discussed. The necessity for color-polarized internal nuclear states is also discussed. 6 figures.
Lamb Shift in Nonrelativistic Quantum Electrodynamics.
ERIC Educational Resources Information Center
Grotch, Howard
1981-01-01
The bound electron self-energy or Lamb shift is calculated in nonrelativistic quantum electrodynamics. Retardation is retained and also an interaction previously dropped in other nonrelativistic approaches is kept. Results are finite without introducing a cutoff and lead to a Lamb shift in hydrogen of 1030.9 MHz. (Author/JN)
Lamb Shift in Nonrelativistic Quantum Electrodynamics.
ERIC Educational Resources Information Center
Grotch, Howard
1981-01-01
The bound electron self-energy or Lamb shift is calculated in nonrelativistic quantum electrodynamics. Retardation is retained and also an interaction previously dropped in other nonrelativistic approaches is kept. Results are finite without introducing a cutoff and lead to a Lamb shift in hydrogen of 1030.9 MHz. (Author/JN)
Pions in large N quantum chromodynamics.
Weinberg, Steven
2010-12-31
An effective field theory of quarks, gluons, and pions, with the number N of colors treated as large, is proposed as a basis for calculations of hadronic phenomena at moderate energies. The qualitative consequences of the large N limit are similar though not identical to those in pure quantum chromodynamics, but because constituent quark masses appear in the effective Lagrangian, the 't Hooft coupling in the effective theory need not be strong at moderate energies. To leading order in 1/N the effective theory is renormalizable, with only a finite number of terms in the Lagrangian.
Clothed Particles in Quantum Electrodynamics and Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Shebeko, Alexander
2016-03-01
The notion of clothing in quantum field theory (QFT), put forward by Greenberg and Schweber and developed by M. Shirokov, is applied in quantum electrodynamics (QED) and quantum chromodynamics (QCD). Along the guideline we have derived a novel analytic expression for the QED Hamiltonian in the clothed particle representation (CPR). In addition, we are trying to realize this notion in QCD (to be definite for the gauge group SU(3)) when drawing parallels between QCD and QED.
Hadron Structure in Holographic Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Lyubovitskij, V. E.; Gutsche, T.; Schmidt, I.
2017-08-01
Hadrons and multiquark states are discussed within the context of holographic quantum chromodynamics. This approach is based on an action that describes the hadron structure with breaking of conformal and chiral symmetry and includes confinement through the presence of a background dilaton field. According to gauge/gravity duality, five-dimensional boson and fermion fields, moving in AdS space, are dual to the four-dimensional fields on the surface of the AdS sphere, which correspond to hadrons. In this framework, the hadron wave functions - the building blocks of the hadron properties - are dual to the profiles of the AdS fields in the fifth (holographic) dimension, which is identified with a scale. As applications, we consider the properties of hadrons and multiquark states.
Hadronic and nuclear phenomena in quantum chromodynamics
Brodsky, S.J.
1987-06-01
Many of the key issues in understanding quantum chromodynamics involves processes at intermediate energies. We discuss a range of hadronic and nuclear phenomena - exclusive processes, color transparency, hidden color degrees of freedom in nuclei, reduced nuclear amplitudes, jet coalescence, formation zone effects, hadron helicity selection rules, spin correlations, higher twist effects, and nuclear diffraction - as tools for probing hadron structure and the propagation of quark and gluon jets in nuclei. Many of these processes can be studied in electroproduction, utilizing internal targets in storage rings. We also review several areas where there has been significant theoretical progress in determining the form of hadron and nuclear wavefunctions, including QCD sum rules, lattice gauge theory, and discretized light-cone quantization. 98 refs., 40 figs., 2 tabs.
Novel nuclear phenomena in quantum chromodynamics
Brodsky, S.J.
1987-08-01
Many of the key issues in understanding quantum chromodynamics involve processes in nuclear targets at intermediate energies. A range of hadronic and nuclear phenomena-exclusive processes, color transparency, hidden color degrees of freedom in nuclei, reduced nuclear amplitudes, jet coalescence, formation zone effects, hadron helicity selection rules, spin correlations, higher twist effects, and nuclear diffraction were discussed as tools for probing hadron structure and the propagation of quark and gluon jets in nuclei. Several areas were also reviewed where there has been significant theoretical progress determining the form of hadron and nuclear wave functions, including QCD sum rules, lattice gauge theory, and discretized light-cone quantization. A possible interpretation was also discussed of the large spin correlation A/sub NN/ in proton-proton scattering, and how relate this effect to an energy and angular dependence of color transparency in nuclei. 76 refs., 24 figs.
QCD: results from lattice quantum chromodynamics
Kronfeld, Andreas S.; /Fermilab
2006-10-01
Quantum chromodynamics (QCD) is the modern theory of the strong force. In this theory, the main objects are quarks and gluons, which are bound by the strong force into protons, neutrons, and other particles called hadrons. In the framework of QCD, the strong nuclear force binding protons and neutrons together into nuclei is actually only a residue of the much stronger forces acting between quarks and gluons. In fact, inside the proton, even the concept of force is not very useful. Within all hadrons they have a swirl of gluons being exchanged back and forth as a manifestation of the strong force. To make matters worse, gluons can split into two, and then rejoin, or they can split into a quark-antiquark pair. Even the simplest hadron is a complex system hosting constantly interacting components. Despite this complexity, QCD is well established experimentally. This is because at short distances (or high energies), the coupling between the particles is effectively small and particles move around with relative freedom. This is called asymptotic freedom and QCD is amenable to the traditional methods of quantum field theory in this regime. High-energy experiments have tested and confirmed QCD in this realm, which led to the 2004 Nobel Prize in Physics for Drs. David Gross, David Politzer, and Frank Wilczek, the theorists who provided the theory for short-range QCD and asymptotic freedom.
Does perturbative quantum chromodynamics imply a Regge singularity above unity
Bishari, M.
1982-07-15
It is investigated whether perturbative quantum chromodynamics can have some implications on Regge behavior of deep-inelastic structure functions. The possible indirect but important role of unitarity, in constraining the theory, is pointed out.
Considerations concerning diffraction scattering in quantum chromodynamics
NASA Astrophysics Data System (ADS)
Nachtmann, O.
1991-08-01
A model for diffractive, especially elastic hadron-hadron scattering at high c.m. energies squared s and small momentum transfer squared | t| is developed, based on quantum chromodynamics (QCD). First the scattering of hadron constituents, partons, is considered. In this paper we study mainly the scattering of quarks and antiquarks. The s-dependence of the amplitudes is treated by analytical means using a functional integral approach and an eikonal approximation. The t-dependence of the amplitudes is then shown to be governed by a certain correlation function of gluon string operators. A calculation of this function by non-perturbative methods in the framework of lattice OCD or in the stochastic vacuum field model should be feasible. The transition from the parton to the hadron level is accomplished by constructing an effective S-operator in terms of local tensor operators. In this way we avoid dealing explicitly with hadronic wave functions. In our approach the bound state nature of the hadrons enters through matrix elements of the local operators, where information from deep inelastic lepton-hadron scattering exists. The resulting expression for the elastic hadron-hadron scattering amplitude is discussed and is shown to lead to an understanding of various phenomenological findings. The physical picture emerging is one where single partons of the hadrons interact at a time, i.e., the "Pomeron" couples to single partons. This was suggested previously by phenomenological analyses of experiments and by theoretical investigations of an abelian gluon model.
Nonrelativistic Quantum Mechanics with Fundamental Environment
NASA Astrophysics Data System (ADS)
Gevorkyan, Ashot S.
2011-03-01
Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.
NASA Astrophysics Data System (ADS)
Porter, William J.; Drut, Joaquín E.
2017-05-01
Path-integral analyses originally pioneered in the study of the complex-phase problem afflicting lattice calculations of finite-density quantum chromodynamics are generalized to nonrelativistic Fermi gases with repulsive interactions. Using arguments similar to those previously applied to relativistic theories, we show that the analogous problem in nonrelativistic systems manifests itself naturally in Tan's contact as a nontrivial cancellation between terms with varied dependence on extensive thermodynamic quantities. We analyze that case under the assumption of a Gaussian phase distribution, which is supported by our Monte Carlo calculations and perturbative considerations. We further generalize these results to observables other than the contact, as well as to polarized systems and systems with fixed particle number. Our results are quite general in that they apply to repulsive multicomponent fermions, they are independent of dimensionality or trapping potential, and they hold in the ground state as well as at finite temperature.
Thermal quantum electrodynamics of nonrelativistic charged fluids.
Buenzli, Pascal R; Martin, Philippe A; Ryser, Marc D
2007-04-01
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for nonrelativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems, which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It still has the r(-6) decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.
Thermal quantum electrodynamics of nonrelativistic charged fluids
NASA Astrophysics Data System (ADS)
Buenzli, Pascal R.; Martin, Philippe A.; Ryser, Marc D.
2007-04-01
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for nonrelativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems, which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It still has the r-6 decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.
Tetraquark mesons in large-N quantum chromodynamics.
Weinberg, Steven
2013-06-28
It is argued that exotic mesons consisting of two quarks and two antiquarks are not ruled out in quantum chromodynamics with a large number N of colors, as generally thought. Tetraquarks of one class are typically long-lived, with decay rates proportional to 1/N.
Quantum Chromodynamics and Nuclear Physics at Extreme Energy Density
Mueller, B.; Bass, S.A.; Chandrasekharan, S.; Mehen, T.; Springer, R.P.
2005-11-07
The report describes research in theoretical quantum chromodynamics, including effective field theories of hadronic interactions, properties of strongly interacting matter at extreme energy density, phenomenology of relativistic heavy ion collisions, and algorithms and numerical simulations of lattice gauge theory and other many-body systems.
Aspects of Pure Quantum Chromodynamics on Large Lattices.
NASA Astrophysics Data System (ADS)
Ford, Ian John
1987-09-01
Available from UMI in association with The British Library. Requires signed TDF. We use Monte Carlo methods to study pure quantum chromodynamics on a four-dimensional Euclidean spacetime lattice consisting of 32^4 points. The features we investigate are relevant to hadron spectroscopy. We take values of the bare coupling beta equal to 6.29, 6.585 and 6.88 in order to monitor the approach towards the continuum limit of the lattice system. To exploit the available Monte Carlo configurations as far as possible, we study correlation functions of extended operators whose overlap with the required lattice state is enhanced. Through the correlations of improved quarkonium operators and also through those of extended Polyakov lines we study the potential between static triplet and antitriplet colour charges (which represent a heavy quark and antiquark). The resulting string tensions do not vary with beta according to the expectations of asymptotic scaling, and consequently it is not possible to confirm that our lattices exhibit continuum behaviour. With similar methods we investigate the potential between two static octet colour charges, the potential between sextet and antisextet colour charges and also the energies of static quark and antiquark systems which have E_{u} and A_{1u} excitations of the gluon field. We also calculate the masses of glueballs with J^{PC} of 0 ^{++} and 2^{++ } using these extended operator techniques. The 32^4 lattice configurations are supplemented by additional configurations of a 10 ^4 lattice at beta = 6.0 and a 20^4 lattice at beta = 6.2 for a study of the spin-dependent corrections to the non-relativistic potential between a heavy quark and antiquark. One of the two spin-orbit potentials, V_1, is found to have long range behaviour, whilst the other, V_2, and the tensor and scalar spin-spin potentials (V _3 and V_4 respectively) are short range. The pattern of this behaviour is consistent with scalar confinement and a vector Coulomb
The mass-gap in Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Larin, S. A.
2016-10-01
It is shown that the fundamental Lagrangian of Quantum Chromodynamis should be modified by the adding gluon masses to produce the mass-gap in accordance with the Källen-Lehmann spectral representation. On mass-shell renormalizability and unitarity of the resulting theory is demonstrated.
Light-cone quantization of quantum chromodynamics
Brodsky, S.J. ); Pauli, H.C. )
1991-06-01
We discuss the light-cone quantization of gauge theories from two perspectives: as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The light-cone Fock state expansion of wavefunctions at fixed light cone time provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of light-cone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavy-quark contributions to structure functions. A general nonperturbative method for numerically solving quantum field theories, discretized light-cone quantization,'' is outlined and applied to several gauge theories, including QCD in one space and one time dimension, and quantum electrodynamics in physical space-time at large coupling strength. The DLCQ method is invariant under the large class of light-cone Lorentz transformations, and it can be formulated such at ultraviolet regularization is independent of the momentum space discretization. Both the bound-state spectrum and the corresponding relativistic light-cone wavefunctions can be obtained by matrix diagonalization and related techniques. We also discuss the construction of the light-cone Fock basis, the structure of the light-cone vacuum, and outline the renormalization techniques required for solving gauge theories within the light-cone Hamiltonian formalism.
On flavor symmetry in lattice quantum chromodynamics
NASA Astrophysics Data System (ADS)
Saidi, El Hassan
2012-02-01
Using a well established method to engineer non-abelian symmetries in superstring compactifications, we study the link between the point splitting method of Creutz et al. [PoS: Lattice 2010, 078 (2010) and Creutz et al. JHEP 041, 1012 (2010)] for implementing flavor symmetry in lattice QCD; and singularity theory in complex algebraic geometry. We show amongst others that Creutz flavors for naive fermions are intimately related with toric singularities of a class of complex Kahler manifolds that are explicitly built here. In the case of naive fermions of QCD2N, Creutz flavors are shown to live at the poles of real 2-spheres and carry quantum charges of the fundamental of [SU(2)]2N. We show moreover that the two Creutz flavors in Karsten-Wilczek model, with Dirac operator in reciprocal space of the form i{γ }1F1+i{γ }2F2+ i{γ }3F3+ i/sin α {γ }_{4}F4, are related with the small resolution of conifold singularity that live at sin α = 0. Other related features are also studied.
Unification of Einstein's Gravity with Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Sarfatti, Jack
2010-02-01
The four tetrad and six spin-connection Cartan 1-forms of Einstein's GeoMetroDynamic (GMD) field emerge from the eight virtual gluon macro-quantum coherent QCD post-inflation vacuum condensates that form in the inflationary phase transition. This joint emergence of gravity and the strong force is similar to the emergence of irrotational superflow with vortex defects in liquid helium below the Lambda Point. Repulsive dark energy is from the residual random virtual bosons that did not cohere in the moment of inflation. Similarly, attractive dark matter is from the residual random virtual fermion-antifermion pairs. Therefore, I predict that the LHC will not detect any on-mass-shell real particles that can explain φDM˜0.23. As first suggested by Abdus Salam (f-gravity) the low energy tail of the nuclear force can be explained as strong short-range Yukawa gravity. QCD's IR confinement and UV asymptotic freedom are elementary consequences in this simple model. )
Quantum chromodynamics near the confinement limit
Quigg, C.
1985-09-01
These nine lectures deal at an elementary level with the strong interaction between quarks and its implications for the structure of hadrons. Quarkonium systems are studied as a means for measuring the interquark interaction. This is presumably (part of) the answer a solution to QCD must yield, if it is indeed the correct theory of the strong interactions. Some elements of QCD are reviewed, and metaphors for QCD as a confining theory are introduced. The 1/N expansion is summarized as a way of guessing the consequences of QCD for hadron physics. Lattice gauge theory is developed as a means for going beyond perturbation theory in the solution of QCD. The correspondence between statistical mechanics, quantum mechanics, and field theory is made, and simple spin systems are formulated on the lattice. The lattice analog of local gauge invariance is developed, and analytic methods for solving lattice gauge theory are considered. The strong-coupling expansion indicates the existence of a confining phase, and the renormalization group provides a means for recovering the consequences of continuum field theory. Finally, Monte Carlo simulations of lattice theories give evidence for the phase structure of gauge theories, yield an estimate for the string tension characterizing the interquark force, and provide an approximate description of the quarkonium potential in encouraging good agreement with what is known from experiment.
Disorder and Quantum Chromodynamics -- Non-Linear σ Models
NASA Astrophysics Data System (ADS)
Guhr, Thomas; Wilke, Thomas
2001-10-01
The statistical properties of Quantum Chromodynamics (QCD) show universal features which can be modeled by random matrices. This has been established in detailed analyses of data from lattice gauge calculations. Moreover, systematic deviations were found which link QCD to disordered systems in condensed matter physics. To furnish these empirical findings with analytical arguments, we apply and extend the methods developed in disordered systems to construct a non-linear σ model for the spectral correlations in QCD. Our goal is to derive connections to other low-energy effective theories, such as the Nambu-Jona-Lasinio model, and to chiral perturbation theory.
Disorder and Quantum Chromodynamics - Non-Linear σ Models
NASA Astrophysics Data System (ADS)
Guhr, Thomas; Wilke, Thomas
The statistical properties of Quantum Chromodynamics (QCD) show universal features which can be modeled by random matrices. This has been established in detailed analyses of data from lattice gauge calculations. Moreover, systematic deviations were found which link QCD to disordered systems in condensed matter physics. To furnish these empirical findings with analytical arguments, we apply and extend the methods developed in disordered systems to construct a non-linear σ model for the spectral correlations in QCD. Our goal is to derive connections to other low-energy effective theories, such as the Nambu-Jona-Lasinio model, and to chiral perturbation theory.
Noninertial effects on nonrelativistic topological quantum scattering
NASA Astrophysics Data System (ADS)
Mota, H. F.; Bakke, K.
2017-08-01
We investigate noninertial effects on the scattering problem of a nonrelativistic particle in the cosmic string spacetime. By considering the nonrelativistic limit of the Dirac equation we are able to show, in the regime of small rotational frequencies, that the phase shift has two contribution: one related to the noninertial reference frame, and the other, due to the cosmic string conical topology. We also show that both the incident wave and the scattering amplitude are altered as a consequence of the noninertial reference frame and depend on the rotational frequency.
Least-squares finite element methods for quantum chromodynamics
Ketelsen, Christian; Brannick, J; Manteuffel, T; Mccormick, S
2008-01-01
A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and ill-conditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on least-squares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed least-squares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.
Chiral relaxation time at the crossover of quantum chromodynamics
NASA Astrophysics Data System (ADS)
Ruggieri, M.; Peng, G. X.; Chernodub, M.
2016-09-01
We study microscopic processes responsible for chirality flips in the thermal bath of quantum chromodynamics at finite temperature and zero baryon chemical potential. We focus on the temperature range where the crossover from chirally broken phase to quark-gluon plasma takes place, namely, T ≃(150 ,200 ) MeV . The processes we consider are quark-quark scatterings mediated by collective excitations with the quantum number of pions and σ meson; hence we refer to these processes simply as one-pion (one-σ ) exchanges. We use a Nambu-Jona-Lasinio model to compute equilibrium properties of the thermal bath, as well as the relevant scattering kernel to be used in the collision integral to estimate the chiral relaxation time τ . We find τ ≃0.1 ÷1 fm /c around the chiral crossover.
Unstable particles in non-relativistic quantum mechanics?
Hernandez-Coronado, H.
2011-10-14
The Schroedinger equation is up-to-a-phase invariant under the Galilei group. This phase leads to the Bargmann's superselection rule, which forbids the existence of the superposition of states with different mass and implies that unstable particles cannot be described consistently in non-relativistic quantum mechanics (NRQM). In this paper we claim that Bargmann's rule neglects physical effects and that a proper description of non-relativistic quantum mechanics requires to take into account this phase through the Extended Galilei group and the definition of its action on spacetime coordinates.
Which Chiral Symmetry is Restored in High Temperature Quantum Chromodynamics?
Bernard, C.; Hetrick, J.E.; Blum, T.; DeTar, C.; Gottlieb, S.; Heller, U.M.; Rummukainen, K.; Sugar, R.; Toussaint, D.; Wingate, M.
1997-01-01
Sigma models for the high temperature phase transition in quantum chromodynamics suggest that at high temperature the SU(N{sub f}){times}SU( N{sub f}) chiral symmetry becomes exact, but the anomalous axial U(1) symmetry need not be restored. In numerical lattice simulations, traditional methods for detecting symmetry restoration have sought multiplets in the screening mass spectrum. However, these methods were imprecise and the results, so far, incomplete. With improved statistics and methodology, we are now able to offer evidence for a restoration of the SU(2){times}SU(2) chiral symmetry just above the crossover, but not of the axial U(1) chiral symmetry. {copyright} {ital 1997} {ital The American Physical Society}
Duality, Confinement and Supersymmetry in Restricted Quantum Chromodynamics (rcd)
NASA Astrophysics Data System (ADS)
Rana, J. M. S.
Electromagnetic duality has been utilized to study the isocolor charge-dyon interactions in Restricted Quantum Chromodynamics (RCD),in terms of current-current correlation (in magnetic gauge)using dielectric and permeability parameters of the associated vacuum. In the state of dyonic superconductivity, it has been shown that the dual propagators behave as 1/k4 (for small k2), which in analogy with superconductivity (dual superconductivity) leads to the confinement of colored fluxes associated with dyonic quarks vide generalized Meissner effect. Based on semi-quantitative analysis of vortex solutions of RCD and by calculating the masses for the massive collective modes of the condensed vacuum, the expressions for the London penetration depth, coherence length and the associated flux energy functions for the type I and type II superconducting media have been obtained. It has further been demonstrated that in the type I medium, vortices tend to coalesce and hence are attractive, while the energy function supports repulsive forces between vortices in the type II superconducting medium. The RCD has been supersymmetrized in N=1 limit and the supersymmetric dyonic solutions have been obtained. In the dyonic background gauge one-loop quantum corrections to the dyonic mass have been calculated and it has been shown that the one-loop quantum corrections lead no change in classical mass of the dyon.
Teaching Quantum ChromoDynamics using Rubik's Cube
NASA Astrophysics Data System (ADS)
Lundberg, Wayne R.
2008-04-01
A potential relationship between the combinatorial aspects of Quantum Chromodynamics and Rubik's cube algebra was first noted in 1982. The Scientific American cover story's mathematics failed to complete the analogy, but clearly demonstrated the value of a graphical, tangible tool for communicating the algebraic relationships of quarks in QCD. Symmetry breaking and restrictions imposed on Rubik's cube algebra were (http://arxiv.org/abs/physics/9712042) defined in a way which provides unified algebra. Construction of standard model particles as well as strong and weak interactions between quarks can be demonstrated with or without student participation. Quantum ElectroDynamics requires extension to a multi-cube superposition approach in which each particle naturally inhabits a separate cube. The three families of particles have been shown to be both necessary and sufficient. The restricted cube, symbolized by a Cyrillic Ya, is the only known non-commutative matrix algebra which passes Seiberg's causality criterion. Many topics of current research can be quickly and clearly introduced to the audience, e.g. a tripartite string (1-brane) has six intrinsic extra dimensions and is one-to-one and onto the standard model of particle physics. The restricted cube algebra has proven to be an active engagement technique well-suited to introducing QC/ED to physics students and the public. Several cubes will be available for reference and demonstrations.
J. J. Sakurai Prize: Precision Quantum Chromodynamics at the LHC
NASA Astrophysics Data System (ADS)
Kosower, David
2014-03-01
The Large Hadron Collider (LHC) at CERN in Geneva, Switzerland, is the highest-energy particle collider operating today. In 2012, the two general-purpose detector collaborations, ATLAS and CMS, announced the discovery of the long-sought Higgs boson, the last missing particle of the Standard Model. The two collaborations have also set limits on new physics beyond the Standard Model, such as supersymmetry. Future direct and indirect searches for new physics require a precise, quantitative understanding of the known physics of the Standard Model, and in particular of the scattering of quark and gluon constituents of the proton under the strong force, known today as quantum chromodynamics (QCD). Achieving this level of understanding requires at least the incorporation of the first quantum corrections in perturbation theory - next-to-leading order (NLO) corrections - in scattering processes with several constituents leading to several jets in the final state. The new ``on-shell'' techniques, described earlier by Lance Dixon, have allowed these computations to be made beyond the reach of traditional diagrammatic methods. I will describe a direct numerical application of the new techniques in the BlackHat software library, and several phenomenological studies of physics at the LHC. These include studies relevant to CMS's supersymmetry searches, and to ATLAS measurements of electroweak vector-boson production with up to five associated jets. Partly supported by the European Research Council under Advanced Investigator Grant ERC-AdG-228301.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
Condensates in quantum chromodynamics and the cosmological constant
Brodsky, Stanley J.; Shrock, Robert
2011-01-01
Casher and Susskind [Casher A, Susskind L (1974) Phys Rev 9:436–460] have noted that in the light-front description, spontaneous chiral symmetry breaking is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that, because of color confinement, quark and gluon condensates in quantum chromodynamics (QCD) are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the Anti de Sitter/conformal field theory correspondence, and the Bethe–Salpeter–Dyson–Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explicit demonstration of “in-hadron” condensates by Roberts and coworkers [Maris P, Roberts CD, Tandy PC (1998) Phys Lett B 420:267–273], using the Bethe–Salpeter–Dyson–Schwinger formalism for QCD-bound states. These results imply that QCD condensates give zero contribution to the cosmological constant, because all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.
Current-Current Interactions, Dynamical Symmetry - and Quantum Chromodynamics.
NASA Astrophysics Data System (ADS)
Neuenschwander, Dwight Edward, Jr.
Quantum Chromodynamics with massive gluons (gluon mass (TBOND) xm(,p)) in a contact-interaction limit called CQCD (strong coupling g (--->) (INFIN); x (--->) (INFIN)), despite its non-renormalizability and lack of hope of confinement, is nevertheless interesting for at least two reasons. (1) Some authors have suggested a relation between 4-Fermi and Yang-Mills theories. If g/x('2) << 1, then CQCD is not merely a 4-Fermi interaction, but includes 4, 6, 8, ...-Fermi non-Abelian contact interactions. (2) With the possibility of infrared slavery, perturbative evaluation of QCD in the infrared is a dubious practice. However, if g('2)/x('2) << 1 in CQCD, then the simplest 4-Fermi interaction is dominant, and CQCD admits perturbative treatment, but only in the infrared. With the dominant interaction, a dynamical Nambu-Goldstone realization of chiral symmetry -breaking (XSB) is found. Although in QCD the relation between confinement and XSB is controversial, XSB occurs in CQCD provided confinement is sacrificed.
Double-β decay matrix elements from lattice quantum chromodynamics
NASA Astrophysics Data System (ADS)
Tiburzi, Brian C.; Wagman, Michael L.; Winter, Frank; Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Orginos, Kostas; Savage, Martin J.; Shanahan, Phiala E.; Nplqcd Collaboration
2017-09-01
A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the n n →p p e e ν¯eν¯e transition is described in detail, expanding on the results presented in Ref. [P. E. Shanahan et al., Phys. Rev. Lett. 119, 062003 (2017), 10.1103/PhysRevLett.119.062003]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-β decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-β decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-β decay rates in heavy nuclei.
Multi-Hadron Observables from Lattice Quantum Chromodynamics
Hansen, Maxwell
2014-01-01
We describe formal work that relates the nite-volume spectrum in a quantum eld theory to scattering and decay amplitudes. This is of particular relevance to numerical calculations performed using Lattice Quantum Chromodynamics (LQCD). Correlators calculated using LQCD can only be determined on the Euclidean time axis. For this reason the standard method of determining scattering amplitudes via the Lehmann-Symanzik-Zimmermann reduction formula cannot be employed. By contrast, the nite-volume spectrum is directly accessible in LQCD calculations. Formalism for relating the spectrum to physical scattering observables is thus highly desirable. In this thesis we develop tools for extracting physical information from LQCD for four types of observables. First we analyze systems with multiple, strongly-coupled two-scalar channels. Here we accommodate both identical and nonidentical scalars, and in the latter case allow for degenerate as well as nondegenerate particle masses. Using relativistic eld theory, and summing to all orders in perturbation theory, we derive a result relating the nite-volume spectrum to the two-to-two scattering amplitudes of the coupled-channel theory. This generalizes the formalism of Martin L uscher for the case of single-channel scattering. Second we consider the weak decay of a single particle into multiple, coupled two-scalar channels. We show how the nite-volume matrix element extracted in LQCD is related to matrix elements of asymptotic two-particle states, and thus to decay amplitudes. This generalizes work by Laurent Lellouch and Martin L uscher. Third we extend the method for extracting matrix elements by considering currents which insert energy, momentum and angular momentum. This allows one to extract transition matrix elements and form factors from LQCD. Finally we look beyond two-particle systems to those with three-particles in asymptotic states. Working again to all orders in relativistic eld theory, we derive a relation between the
Multi-Hadron Observables from Lattice Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Hansen, Maxwell T.
We describe formal work that relates the finite-volume spectrum in a quantum field theory to scattering and decay amplitudes. This is of particular relevance to numerical calculations performed using Lattice Quantum Chromodynamics (LQCD). Correlators calculated using LQCD can only be determined on the Euclidean time axis. For this reason the standard method of determining scattering amplitudes via the Lehmann-Symanzik-Zimmermann reduction formula cannot be employed. By contrast, the finite-volume spectrum is directly accessible in LQCD calculations. Formalism for relating the spectrum to physical scattering observables is thus highly desirable. In this thesis we develop tools for extracting physical information from LQCD for four types of observables. First we analyze systems with multiple, strongly-coupled two-scalar channels. Here we accommodate both identical and nonidentical scalars, and in the latter case allow for degenerate as well as nondegenerate particle masses. Using relativistic field theory, and summing to all orders in perturbation theory, we derive a result relating the finite-volume spectrum to the two-to-two scattering amplitudes of the coupled-channel theory. This generalizes the formalism of Martin Luscher for the case of single-channel scattering. Second we consider the weak decay of a single particle into multiple, coupled two-scalar channels. We show how the finite-volume matrix element extracted in LQCD is related to matrix elements of asymptotic two-particle states, and thus to decay amplitudes. This generalizes work by Laurent Lellouch and Martin Luscher. Third we extend the method for extracting matrix elements by considering currents which insert energy, momentum and angular momentum. This allows one to extract transition matrix elements and form factors from LQCD. Finally we look beyond two-particle systems to those with three-particles in asymptotic states. Working again to all orders in relativistic field theory, we derive a relation
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
Gevorkyan, A. S.
2013-08-15
Spontaneous transitions between bound states of an atomic system, the 'Lamb Shift' of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations (fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schroedinger type and is defined on the extended space Double-Struck-Capital-R {sup 3} Circled-Times {Xi}{sup n}, where Double-Struck-Capital-R {sup 3} and {Xi}{sup n} are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Nonrelativistic quantum mechanics with consideration of influence of fundamental environment
NASA Astrophysics Data System (ADS)
Gevorkyan, A. S.
2013-08-01
Spontaneous transitions between bound states of an atomic system, the "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected with the influence of the quantum vacuum fluctuations ( fundamental environment (FE)), which are impossible to consider in the framework of standard quantum-mechanical approaches. The joint system quantum system (QS) and FE is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger type and is defined on the extended space ℝ3⊗Ξ n , where ℝ3 and Ξ n are the Euclidean and functional spaces, respectively. The method of stochastic density matrix is developed and the von Neumann equation for reduced density matrix of QS with FE is generalized. The entropy of QS entangled with FE is defined and investigated. It is proved that the interaction of QS with the environment leads to emerging structures of various topologies which present new quantum-field properties of QS. It is shown that when the physical system (irrelatively to its being micro ormacro) breaks up into two fragments by means of FE, there arises between these fragments a nonpotential interaction which does not disappear at large distances.
Deconfining phase transition and the continuum limit of lattice quantum chromodynamics
NASA Technical Reports Server (NTRS)
Gottlieb, S. A.; Kuti, J.; Toussaint, D.; Kennedy, A. D.; Meyer, S.
1985-01-01
A large-scale Monte Carlo calculation is presented of the deconfining phase-transition temperature in lattice quantum chromodynamics without fermions. By using the Wilson action, it is found that the transition temperature as a function of the lattice coupling g is consistent with scaling behavior dictated by the perturbative beta function for 6/g-squared greater than 6.15.
A signed particle formulation of non-relativistic quantum mechanics
Sellier, Jean Michel
2015-09-15
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 Schrödinger 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 validity of the suggested approach.
Variance of the Quantum Dwell Time for a Nonrelativistic Particle
NASA Technical Reports Server (NTRS)
Hahne, Gerhard
2012-01-01
Munoz, Seidel, and Muga [Phys. Rev. A 79, 012108 (2009)], following an earlier proposal by Pollak and Miller [Phys. Rev. Lett. 53, 115 (1984)] in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular those defined by constant values of the third (z) spatial coordinate. The mean Nth power, N = 1, 2, 3, . . ., of the quantum dwell time in the slab is given by an expression involving an N-flux-correlation function. All these means are shown to be nonnegative. The N = 1 formula reduces to an S-matrix result published previously [G. E. Hahne, J. Phys. A 36, 7149 (2003)]; an explicit formula for N = 2, and of the variance of the dwell time in terms of the S-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle s time flux and others) is derived.
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
NASA Astrophysics Data System (ADS)
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.
Variance of the quantum dwell time for a nonrelativistic particle
NASA Astrophysics Data System (ADS)
Hahne, G. E.
2013-01-01
Muñoz, Seidel, and Muga [Phys. Rev. A 79, 012108 (2009), 10.1103/PhysRevA.79.012108], following an earlier proposal by Pollak and Miller [Phys. Rev. Lett. 53, 115 (1984), 10.1103/PhysRevLett.53.115] in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular, those defined by constant values of the third (z) spatial coordinate. The mean Nth power, N = 1, 2, 3, …, of the quantum dwell time in the slab is given by an expression involving an N-flux-correlation function. All these means are shown to be nonnegative. The N = 1 formula reduces to an S-matrix result published previously [G. E. Hahne, J. Phys. A 36, 7149 (2003), 10.1088/0305-4470/36/25/316]; an explicit formula for N = 2, and of the variance of the dwell time in terms of the S-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle's time flux and others) is derived.
Variance of the quantum dwell time for a nonrelativistic particle
Hahne, G. E.
2013-01-15
Munoz, Seidel, and Muga [Phys. Rev. A 79, 012108 (2009)], following an earlier proposal by Pollak and Miller [Phys. Rev. Lett. 53, 115 (1984)] in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular, those defined by constant values of the third (z) spatial coordinate. The mean Nth power, N= 1, 2, 3, Horizontal-Ellipsis , of the quantum dwell time in the slab is given by an expression involving an N-flux-correlation function. All these means are shown to be nonnegative. The N= 1 formula reduces to an S-matrix result published previously [G. E. Hahne, J. Phys. A 36, 7149 (2003)]; an explicit formula for N= 2, and of the variance of the dwell time in terms of the S-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle's time flux and others) is derived.
Resonances in Coupled πK-ηK Scattering from Quantum Chromodynamics
Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.; ...
2014-10-01
Using first-principles calculation within Quantum Chromodynamics, we are able to reproduce the pattern of experimental strange resonances which appear as complex singularities within coupled πK, ηK scattering amplitudes. We make use of numerical computation within the lattice discretized approach to QCD, extracting the energy dependence of scattering amplitudes through their relation- ship to the discrete spectrum of the theory in a finite-volume, which we map out in unprecedented detail.
Time as an Observable in Nonrelativistic Quantum Mechanics
NASA Technical Reports Server (NTRS)
Hahne, G. E.
2003-01-01
The argument follows from the viewpoint that quantum mechanics is taken not in the usual form involving vectors and linear operators in Hilbert spaces, but as a boundary value problem for a special class of partial differential equations-in the present work, the nonrelativistic Schrodinger equation for motion of a structureless particle in four- dimensional space-time in the presence of a potential energy distribution that can be time-as well as space-dependent. The domain of interest is taken to be one of two semi-infinite boxes, one bounded by two t=constant planes and the other by two t=constant planes. Each gives rise to a characteristic boundary value problem: one in which the initial, input values on one t=constant wall are given, with zero asymptotic wavefunction values in all spatial directions, the output being the values on the second t=constant wall; the second with certain input values given on both z=constant walls, with zero asymptotic values in all directions involving time and the other spatial coordinates, the output being the complementary values on the z=constant walls. The first problem corresponds to ordinary quantum mechanics; the second, to a fully time-dependent version of a problem normally considered only for the steady state (time-independent Schrodinger equation). The second problem is formulated in detail. A conserved indefinite metric is associated with space-like propagation, where the sign of the norm of a unidirectional state corresponds to its spatial direction of travel.
Hoang, Andre H.; Ruiz-Femenia, Pedro
2006-12-01
We discuss the form and construction of general color singlet heavy particle-antiparticle pair production currents for arbitrary quantum numbers, and issues related to evanescent spin operators and scheme dependences in nonrelativistic QCD in n=3-2{epsilon} dimensions. The anomalous dimensions of the leading interpolating currents for heavy quark and colored scalar pairs in arbitrary {sup 2S+1}L{sub J} angular-spin states are determined at next-to-leading order in the nonrelativistic power counting.
Quarks, QCD (quantum chromodynamics) and the real world of experimental data
Lipkin, H.J.
1987-07-01
The experimental evidence that supports quantum chromodynamics as the theory that describes how the quarks interact is briefly discussed. The indications of the existence of quarks are reviewed, and calculation of hadron masses is discussed. Additional evidence of hadron substructure as seen in the antiproton is reviewed. Arguments for the existence of color as the ''charge'' carried by quarks by which they interact are given. Hadron masses and the hyperfine interaction are presented, followed by more exotic quark systems and a study of multiquark systems. Weak interactions in the quark model are discussed. (LEW)
NASA Astrophysics Data System (ADS)
Peshkin, Murray
2003-10-01
The preceding Comment states that I have assumed the conclusion in my proof from nonrelativistic quantum mechanics that spin-zero particles must be bosons, and that the theory presented is different from standard quantum mechanics. I show here that neither of those statements is true.
Fried, H.M.; Gabellini, Y.; Grandou, T.; Sheu, Y.-M.
2013-11-15
Removal of the quenched approximation in the mechanism which produced an analytic estimate of quark-binding potentials, along with a reasonable conjecture of the color structure of the nucleon formed by such a binding potential, is shown to generate an effective nucleon scattering and binding potential. The mass-scale factor on the order of the pion mass, previously introduced to define the transverse imprecision of quark coordinates, is again used, while the strength of the potential is proportional to the square of a renormalized quantum chromodynamics (QCD) coupling constant. The potential so derived does not include corrections due to spin, angular momentum, nucleon structure, and electroweak interactions; rather, it is qualitative in nature, showing how Nuclear Physics can arise from fundamental QCD. -- Highlights: •Nucleon–nucleon forces are derived qualitatively from basic realistic quantum chromodynamics. •An effective nucleon binding is obtained from the simplest unquenched approximation. •A model deuteron binding energy of −2.2 MeV follows with α{sub s,R}=12.5.
Quantum chromodynamics, antiferromagnets and XY models from a unified point of view
NASA Astrophysics Data System (ADS)
Hofmann, Christoph P.
2017-03-01
Antiferromagnets and quantum XY magnets in three space dimensions are described by an effective Lagrangian that exhibits the same structure as the effective Lagrangian of quantum chromodynamics with two light flavors. These systems all share a spontaneously broken internal symmetry O (N) → O (N - 1). Although the respective scales differ by many orders of magnitude, the general structure of the low-temperature expansion of the partition function is the same. In the nonabelian case (N ≥ 3), logarithmic terms of the form T8 ln T emerge at three-loop order, while for N = 2 the series only involves powers of T2. The manifestation of the Goldstone boson interaction in the pressure, order parameter, and susceptibility is explored in presence of an external field.
Minimal subtraction and momentum subtraction in quantum chromodynamics at two-loop order
Braaten, E.; Leveille, J.P.
1981-09-01
The momentum-subtraction coupling constant ..cap alpha../sub MOM/ yields consistently smaller one-loop corrections to many quantum-chromodynamics (QCD) processes than the minimal-subtraction couplings ..cap alpha../sub MS/ and ..cap alpha../sub M/S. By shifting the renormalization scale ..mu.. of ..cap alpha../sub MS/(..mu..), we obtain a minimal-subtraction coupling with the same small one-loop corrections. It is shown, by studying the effective charges of QCD, that at two-loop order this coupling constant will continue to yield corrections to physical quantities that are comparable to those obtained by momentum subtraction. We also introduce a momentum-subtraction scheme which treats the triple-gluon, quark, and ghost vertices equally at one-loop order and is more convenient for higher-order calculations than the MOM scheme.
Resonant π+γ→π+π0 amplitude from Quantum Chromodynamics
Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.; ...
2015-12-08
We present the first ab initio calculation of a radiative transition of a hadronic resonance within Quantum Chromodynamics (QCD). We compute the amplitude formore » $$\\pi\\pi \\to \\pi\\gamma^\\star$$, as a function of the energy of the $$\\pi\\pi$$ pair and the virtuality of the photon, in the kinematic regime where $$\\pi\\pi$$ couples strongly to the unstable $$\\rho$$ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to $$m_\\pi \\approx 400$$ MeV. As a result, we obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the $$\\rho$$ pole and identify from its residue the $$\\rho \\to \\pi\\gamma^\\star$$ form-factor.« less
Parallelizing the QUDA Library for Multi-GPU Calculations in Lattice Quantum Chromodynamics
Ronald Babich, Michael Clark, Balint Joo
2010-11-01
Graphics Processing Units (GPUs) are having a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations of importance in nuclear and particle physics. The QUDA library provides a package of mixed precision sparse matrix linear solvers for LQCD applications, supporting single GPUs based on NVIDIA's Compute Unified Device Architecture (CUDA). This library, interfaced to the QDP++/Chroma framework for LQCD calculations, is currently in production use on the "9g" cluster at the Jefferson Laboratory, enabling unprecedented price/performance for a range of problems in LQCD. Nevertheless, memory constraints on current GPU devices limit the problem sizes that can be tackled. In this contribution we describe the parallelization of the QUDA library onto multiple GPUs using MPI, including strategies for the overlapping of communication and computation. We report on both weak and strong scaling for up to 32 GPUs interconnected by InfiniBand, on which we sustain in excess of 4 Tflops.
Perturbative quantum chromodynamics predictions for very high-energy atmospheric neutrinos and muons
NASA Astrophysics Data System (ADS)
Varieschi, Gabriele Umberto
2000-12-01
We compare the leading and next-to-leading order Quantum Chromodynamics predictions for the flux of atmospheric muons and neutrinos from decays of charmed particles. We then compute this flux for different Partonic Distribution Functions (PDF's) and different extrapolations of these at small partonic momentum fraction x. We find that the predicted fluxes vary up to almost two orders of magnitude at the largest energies studied, depending on the chosen extrapolation of the PDF's. We show that the spectral index of the atmospheric leptonic fluxes depends linearly on the slope of the gluon distribution function at very small x. Finally, we analyze the uncertainties of our model and we consider the dependence of our simulation on the primary cosmic ray flux.
Resonant π^{+}γ→π^{+}π^{0} Amplitude from Quantum Chromodynamics.
Briceño, Raúl A; Dudek, Jozef J; Edwards, Robert G; Shultz, Christian J; Thomas, Christopher E; Wilson, David J
2015-12-11
We present the first ab initio calculation of a radiative transition of a hadronic resonance within quantum chromodynamics (QCD). We compute the amplitude for ππ→πγ^{⋆}, as a function of the energy of the ππ pair and the virtuality of the photon, in the kinematic regime where ππ couples strongly to the unstable ρ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to m_{π}≈400 MeV. We obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the ρ pole and identify from its residue the ρ→πγ^{⋆} form factor.
Padmanabhan, Hamsa; Padmanabhan, T.
2011-10-15
We discuss the nonrelativistic limit of quantum field theory in an inertial frame, in the Rindler frame and in the presence of a weak gravitational field, and attempt to highlight and clarify several subtleties. In particular, we study the following issues: (a) While the action for a relativistic free particle is invariant under the Lorentz transformation, the corresponding action for a nonrelativistic free particle is not invariant under the Galilean transformation, but picks up extra contributions at the end points. This leads to an extra phase in the nonrelativistic wave function under a Galilean transformation, which can be related to the rest energy of the particle even in the nonrelativistic limit. We show that this is closely related to the peculiar fact that the relativistic action for a free particle remains invariant even if we restrict ourselves to O(1/c{sup 2}) in implementing the Lorentz transformation. (b) We provide a brief critique of the principle of equivalence in the quantum mechanical context. In particular, we show how solutions to the generally covariant Klein-Gordon equation in a noninertial frame, which has a time-dependent acceleration, reduce to the nonrelativistic wave function in the presence of an appropriate (time-dependent) gravitational field in the c{yields}{infinity} limit, and relate this fact to the validity of the principle of equivalence in a quantum mechanical context. We also show that the extra phase acquired by the nonrelativistic wave function in an accelerated frame, actually arises from the gravitational time dilation and survives in the nonrelativistic limit. (c) While the solution of the Schroedinger equation can be given an interpretation as being the probability amplitude for a single particle, such an interpretation fails in quantum field theory. We show how, in spite of this, one can explicitly evaluate the path integral using the (nonquadratic) action for a relativistic particle (involving a square root) and
2012-11-19
temperature superconductors to the hydrodynamics of QGPs. These gases are mainly made of alkali metal New Journal of Physics 14 (2012) 115009 (http...condensed matter systems, this means that theories constructed from single-particle properties , such as the Hartree–Fock approximation, cannot describe a...correlated quantum fluids. Transport properties of the fluid can be 7 Fluids are materials that obey the equations of hydrodynamics. The word liquid
Quantum propagator for a nonrelativistic particle in the vicinity of a time machine
NASA Astrophysics Data System (ADS)
Goldwirth, Dalia S.; Perry, Malcolm J.; Piran, Tsvi; Thorne, Kip S.
1994-04-01
We study the propagator of a nonrelativistic, noninteracting particle in any nonrelativistic ``time-machine'' spacetime of the following type: an external, chronal spacetime in which two spatial regions V- at time t- and V+ at time t+ are connected by two temporal wormholes, one leading from the past side of V- to the future side of V+ and the other from the past side of V+ to the future side of V-. We express the propagator explicitly in terms of those for the chronal spacetime and for the two wormholes; and from that expression we show that the propagator satisfies completeness and unitarity in the initial and final ``chronal regions'' (regions without closed timelike curves) and its propagation from the initial region to the final region is unitary. However, within the time machine it satisfies neither completeness nor unitarity. We also give an alternative proof of initial-region-to-final-region unitarity based on a conserved current and Gauss's theorem. This proof can be carried over without change to most any nonrelativistic time-machine spacetime and it is valid as long as the particle is not interacting with itself or any other quantum particle; it can, however, interact with an external field (gravitational or otherwise). This result is the nonrelativistic version of a theorem by Friedman, Papastamatiou, and Simon, which says that for a free scalar field quantum-mechanical unitarity follows from the fact that the classical evolution preserves the Klein-Gordon inner product.
Nonrelativistic and Relativistic Quantum Theory Applied to Problems in Molecular Physics
NASA Astrophysics Data System (ADS)
Park, Changyok
1995-01-01
To describe molecules properly we need to use quantum theory. Nonrelativistic quantum mechanics can be used in such studies. For this, we need to solve the Schrodinger equation with a given proper Hamiltonian. As an application of nonrelativistic quantum mechanics, the ferrocene molecule has been studied. The metal-ligand distance in ferrocene has been calculated with several different electronic structure methods. The only treatment able to reproduce the experimental value is the MCPF (Modified Coupled Pair Functional) approach with all 66 valence electrons correlated. Large basis sets are necessary to account for the dispersion interaction between the rings. The speed of electron in the innermost shells of heavy atoms is close to the speed of light. Therefore, we need to include relativistic effect in the study of molecules composed of heavy atoms (e.g. Au or Pt). We can derive a proper electronic Hamiltonian for the study of relativistic effects from Bethe-Salpeter Hamiltonian. As an application of the relativistic quantum mechanics two-electron relativistic effects in molecules has been studied. A computationally efficient method to account for such effects in a spin free no-pair Hamiltonian has been investigated. The approach amounts to a modification of integrals familiar from non-relativistic theory, and is therefore compatible with a variety of different correlation treatments. We have applied the method in Hartree-Fock and MP2 calculations on dimers and hydrides of Ag, Au and Pt.
Renormalization-scheme dependence of the strong coupling constantin quantum chromodynamics
Blumenfeld, A.; Moshe, M.
1982-08-01
Quantum chromodynamics (QCD) lacks a limit analogous to the Thomson limit of quantum electrodynamics (QED) for defining its coupling constant. Nevertheless, the strong coupling constant in QCD can be determined from measurable quantities in an approximately scheme-independent manner as -q/sup 2/..-->..infinity. At finite q/sup 2/, however, high-order terms in the renormalization-group functions introduce scheme-dependent terms into ..cap alpha../sub s/(q/sup 2/). A recently suggested method for estimating high-order terms in solutions of Callan-Symanzik equation, which is similar in nature to techniques employed in QED, enables us to determine the size of these scheme-dependent terms. We also discuss a modified minimal-subtraction (MS) scheme which is very appealing. It has the same ..beta.. function as the MS scheme (to all orders) but it equals the momentum-subtraction (MOM) scheme up to two-loop calculations and differs from it at higher orders. We denote this scheme as MOM.
New parton distribution functions from a global analysis of quantum chromodynamics
NASA Astrophysics Data System (ADS)
Dulat, Sayipjamal; Hou, Tie-Jiun; Gao, Jun; Guzzi, Marco; Huston, Joey; Nadolsky, Pavel; Pumplin, Jon; Schmidt, Carl; Stump, Daniel; Yuan, C.-P.
2016-02-01
We present new parton distribution functions (PDFs) at next-to-next-to-leading order (NNLO) from the CTEQ-TEA global analysis of quantum chromodynamics. These differ from previous CT PDFs in several respects, including the use of data from LHC experiments and the new D0 charged-lepton rapidity asymmetry data, as well as the use of a more flexible parametrization of PDFs that, in particular, allows a better fit to different combinations of quark flavors. Predictions for important LHC processes, especially Higgs boson production at 13 TeV, are presented. These CT14 PDFs include a central set and error sets in the Hessian representation. For completeness, we also present the CT14 PDFs determined at the LO and the NLO in QCD. Besides these general-purpose PDF sets, we provide a series of (N)NLO sets with various αs values and additional sets in general-mass variable flavor number schemes, to deal with heavy partons, with up to three, four, and six active flavors.
Searching for new physics at the frontiers with lattice quantum chromodynamics.
Van de Water, Ruth S
2012-07-01
Numerical lattice-quantum chromodynamics (QCD) simulations, when combined with experimental measurements, allow the determination of fundamental parameters of the particle-physics Standard Model and enable searches for physics beyond-the-Standard Model. We present the current status of lattice-QCD weak matrix element calculations needed to obtain the elements and phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and to test the Standard Model in the quark-flavor sector. We then discuss evidence that may hint at the presence of new physics beyond the Standard Model CKM framework. Finally, we discuss two opportunities where we expect lattice QCD to play a pivotal role in searching for, and possibly discovery of, new physics at upcoming high-intensity experiments: rare decays and the muon anomalous magnetic moment. The next several years may witness the discovery of new elementary particles at the Large Hadron Collider (LHC). The interplay between lattice QCD, high-energy experiments at the LHC, and high-intensity experiments will be needed to determine the underlying structure of whatever physics beyond-the-Standard Model is realized in nature.
The application of light-cone quantization to quantum chromodynamics in one-plus-one dimensions
Hornbostel, K.J.
1988-12-01
Formal and computational aspects of light cone quantization are studied by application to quantum chromodynamics (QCD) in one spatial plus one temporal dimension. This quantization scheme, which has been extensively applied to perturbative calculations, is shown to provide an intuitively appealing and numerically tractable approach to non-perturbative computations as well. In the initial section, a light-cone quantization procedure is developed which incorporates fields on the boundaries. This allows for the consistent treatment of massless fermions and the construction of explicitly conserved momentum and charge operators. The next section, which comprises the majority of this work, focuses on the numerical solution of the light-cone Schrodinger equation for bound states. The state space is constructed and the Hamiltonian is evaluated and diagonalized by computer for arbitrary number of colors, baryon number and coupling constant strength. As a result, the full spectrum of mesons and baryons and their associated wavefunctions are determined. These results are compared with those which exist from other approaches to test the reliability of the method. The program also provides a preliminary test for the feasibility of, and an opportunity to develop approximation schemes for, an attack on three-plus-one dimensional QCD. Finally, analytic results are presented which include a discussion of integral equations for wavefunctions and their endpoint behavior. Solutions for hadronic masses and wavefunctions in the limits of both large and small quark mass are discussed. 49 refs., 32 figs., 10 tabs.
Calculation of the axion mass based on high-temperature lattice quantum chromodynamics
NASA Astrophysics Data System (ADS)
Borsanyi, S.; Fodor, Z.; Guenther, J.; Kampert, K.-H.; Katz, S. D.; Kawanai, T.; Kovacs, T. G.; Mages, S. W.; Pasztor, A.; Pittler, F.; Redondo, J.; Ringwald, A.; Szabo, K. K.
2016-11-01
Unlike the electroweak sector of the standard model of particle physics, quantum chromodynamics (QCD) is surprisingly symmetric under time reversal. As there is no obvious reason for QCD being so symmetric, this phenomenon poses a theoretical problem, often referred to as the strong CP problem. The most attractive solution for this requires the existence of a new particle, the axion—a promising dark-matter candidate. Here we determine the axion mass using lattice QCD, assuming that these particles are the dominant component of dark matter. The key quantities of the calculation are the equation of state of the Universe and the temperature dependence of the topological susceptibility of QCD, a quantity that is notoriously difficult to calculate, especially in the most relevant high-temperature region (up to several gigaelectronvolts). But by splitting the vacuum into different sectors and re-defining the fermionic determinants, its controlled calculation becomes feasible. Thus, our twofold prediction helps most cosmological calculations to describe the evolution of the early Universe by using the equation of state, and may be decisive for guiding experiments looking for dark-matter axions. In the next couple of years, it should be possible to confirm or rule out post-inflation axions experimentally, depending on whether the axion mass is found to be as predicted here. Alternatively, in a pre-inflation scenario, our calculation determines the universal axionic angle that corresponds to the initial condition of our Universe.
Azaria, P.; Konik, R. M.; Lecheminant, P.; Pálmai, T.; Takács, G.; Tsvelik, A. M.
2016-08-03
In our paper we study a (1+1)-dimensional version of the famous Nambu–Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, μ, is zero, we describe the formation of fermion three-quark (nucleons and Δ baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at μ=0 the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, the model has a rich phase diagram which includes phases with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). Finally, the QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).
Azaria, P.; Konik, R. M.; Lecheminant, P.; ...
2016-08-03
In our paper we study a (1+1)-dimensional version of the famous Nambu–Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, μ, is zero, we describe the formation of fermion three-quark (nucleons and Δ baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at μ=0 the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, the model has a rich phase diagram which includes phasesmore » with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). Finally, the QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).« less
Azaria, P.; Konik, R. M.; Lecheminant, P.; Pálmai, T.; Takács, G.; Tsvelik, A. M.
2016-08-03
In our paper we study a (1+1)-dimensional version of the famous Nambu–Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, μ, is zero, we describe the formation of fermion three-quark (nucleons and Δ baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at μ=0 the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, the model has a rich phase diagram which includes phases with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). Finally, the QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).
Maximal Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics
Brodsky, Stanley J.; Shrock, Robert; /YITP, Stony Brook
2008-08-01
Because quarks and gluons are confined within hadrons, they have a maximum wavelength of order the confinement scale. Propagators, normally calculated for free quarks and gluons using Dyson-Schwinger equations, are modified by bound-state effects in close analogy to the calculation of the Lamb shift in atomic physics. Because of confinement, the effective quantum chromodynamic coupling stays finite in the infrared. The quark condensate which arises from spontaneous chiral symmetry breaking in the bound state Dyson-Schwinger equation is the expectation value of the operator {bar q}q evaluated in the background of the fields of the other hadronic constituents, in contrast to a true vacuum expectation value. Thus quark and gluon condensates reside within hadrons. The effects of instantons are also modified. We discuss the implications of the maximum quark and gluon wavelength for phenomena such as deep inelastic scattering and annihilation, the decay of heavy quarkonia, jets, and dimensional counting rules for exclusive reactions. We also discuss implications for the zero-temperature phase structure of a vectorial SU(N) gauge theory with a variable number N{sub f} of massless fermions.
Current-current interactions, dynamical symmetry-breaking, and quantum chromodynamics
Neuenschwander, D.E. Jr.
1983-01-01
Quantum Chromodynamics with massive gluons (gluon mass triple bond xm/sub p/) in a contact-interaction limit called CQCD (strong coupling g..-->..infinity; x..-->..infinity), despite its non-renormalizability and lack of hope of confinement, is nevertheless interesting for at least two reasons. Some authors have suggested a relation between 4-Fermi and Yang-Mills theories. If g/x/sup 2/ much less than 1, then CQCD is not merely a 4-Fermi interaction, but includes 4,6,8 etc-Fermi non-Abelian contact interactions. With possibility of infrared slavery, perturbative evaluation of QCD in the infrared is a dubious practice. However, if g/sup 2//x/sup 2/ much less than 1 in CQCD, then the simplest 4-Fermi interaction is dominant, and CQCD admits perturbative treatment, but only in the infrared. With the dominant interaction, a dynamical Nambu-Goldstone realization of chiral symmetry-breaking (XSB) is found. Although in QCD the relation between confinement and XSB is controversial, XSB occurs in CQCD provided confinement is sacrificed.
New parton distribution functions from a global analysis of quantum chromodynamics
Dulat, Sayipjamal; Hou, Tie -Jiun; Gao, Jun; ...
2016-02-16
Here, we present new parton distribution functions (PDFs) up to next-to-next-to-leading order (NNLO) from the CTEQ-TEA global analysis of quantum chromodynamics. These differ from previous CT PDFs in several respects, including the use of data from LHC experiments and the new D0 charged lepton rapidity asymmetry data, as well as the use of more flexible parametrization of PDFs that, in particular, allows a better fit to different combinations of quark flavors. Predictions for important LHC processes, especially Higgs boson production at 13 TeV, are presented. These CT14 PDFs include a central set and error sets in the Hessian representation. Formore » completeness, we also present the CT14 PDFs determined at the leading order (LO) and the next-to-leading order (NLO) in QCD. Besides these general-purpose PDF sets, we provide a series of (N)NLO sets with various αs values and additional sets in general-mass variable flavor number (GM-VFN) schemes, to deal with heavy partons, with up to 3, 4, and 6 active flavors.« less
New parton distribution functions from a global analysis of quantum chromodynamics
Dulat, Sayipjamal; Hou, Tie -Jiun; Gao, Jun; Guzzi, Marco; Nadolsky, Pavel; Pumplin, Jon; Schmidt, Carl; Stump, Daniel; Yuan, C. -P.; Huston, Joey
2016-02-16
Here, we present new parton distribution functions (PDFs) up to next-to-next-to-leading order (NNLO) from the CTEQ-TEA global analysis of quantum chromodynamics. These differ from previous CT PDFs in several respects, including the use of data from LHC experiments and the new D0 charged lepton rapidity asymmetry data, as well as the use of more flexible parametrization of PDFs that, in particular, allows a better fit to different combinations of quark flavors. Predictions for important LHC processes, especially Higgs boson production at 13 TeV, are presented. These CT14 PDFs include a central set and error sets in the Hessian representation. For completeness, we also present the CT14 PDFs determined at the leading order (LO) and the next-to-leading order (NLO) in QCD. Besides these general-purpose PDF sets, we provide a series of (N)NLO sets with various α_{s} values and additional sets in general-mass variable flavor number (GM-VFN) schemes, to deal with heavy partons, with up to 3, 4, and 6 active flavors.
Woesler, Richard
2007-02-21
The computations of the present text with non-relativistic quantum teleportation equations and special relativity are totally speculative, physically correct computations can be done using quantum field theory, which remain to be done in future. Proposals for what might be called statistical time loop experiments with, e.g., photon polarization states are described when assuming the simplified non-relativistic quantum teleportation equations and special relativity. However, a closed time loop would usually not occur due to phase incompatibilities of the quantum states. Histories with such phase incompatibilities are called inconsistent ones in the present text, and it is assumed that only consistent histories would occur. This is called an exclusion principle for inconsistent histories, and it would yield that probabilities for certain measurement results change. Extended multiple parallel experiments are proposed to use this statistically for transmission of classical information over distances, and regarding time. Experiments might be testable in near future. However, first a deeper analysis, including quantum field theory, remains to be done in future.
Color transparency and the structure of the proton in quantum chromodynamics
Brodsky, S.J.
1989-06-01
Many anomalies suggest that the proton itself is a much more complex object than suggested by simple non-relativistic quark models. Recent analyses of the proton distribution amplitude using QCD sum rules points to highly-nontrivial proton structure. Solutions to QCD in one-space and one-time dimension suggest that the momentum distributions of non-valence quarks in the hadrons have a non-trivial oscillatory structure. The data seems also to be suggesting that the intrinsic'' bound state structure of the proton has a non-negligible strange and charm quark content, in addition to the extrinsic'' sources of heavy quarks created in the collision itself. As we shall see in this lecture, the apparent discrepancies with experiment are not so much a failure of QCD, but rather symptoms of the complexity and richness of the theory. An important tool for analyzing this complexity is the light-cone Fock state representation of hadron wavefunctions, which provides a consistent but convenient framework for encoding the features of relativistic many-body systems in quantum field theory. 121 refs., 44 figs., 1 tab.
Aoki, Y; Endrodi, G; Fodor, Z; Katz, S D; Szabó, K K
2006-10-12
Quantum chromodynamics (QCD) is the theory of the strong interaction, explaining (for example) the binding of three almost massless quarks into a much heavier proton or neutron--and thus most of the mass of the visible Universe. The standard model of particle physics predicts a QCD-related transition that is relevant for the evolution of the early Universe. At low temperatures, the dominant degrees of freedom are colourless bound states of hadrons (such as protons and pions). However, QCD is asymptotically free, meaning that at high energies or temperatures the interaction gets weaker and weaker, causing hadrons to break up. This behaviour underlies the predicted cosmological transition between the low-temperature hadronic phase and a high-temperature quark-gluon plasma phase (for simplicity, we use the word 'phase' to characterize regions with different dominant degrees of freedom). Despite enormous theoretical effort, the nature of this finite-temperature QCD transition (that is, first-order, second-order or analytic crossover) remains ambiguous. Here we determine the nature of the QCD transition using computationally demanding lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities. No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.
Proton-Proton Fusion and Tritium β Decay from Lattice Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Savage, Martin J.; Shanahan, Phiala E.; Tiburzi, Brian C.; Wagman, Michael L.; Winter, Frank; Beane, Silas R.; Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Orginos, Kostas; Nplqcd Collaboration
2017-08-01
The nuclear matrix element determining the p p →d e+ν fusion cross section and the Gamow-Teller matrix element contributing to tritium β decay are calculated with lattice quantum chromodynamics for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3) flavor-symmetric value of the quark masses, corresponding to a pion mass of mπ˜806 MeV . The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within 2 σ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated p p →d e+ν transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be L1 ,A=3.9 (0.2 )(1.0 )(0.4 )(0.9 ) fm3 at a renormalization scale set by the physical pion mass, also agreeing within the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics.
Simulation of quantum chromodynamics on the lattice with exactly chiral lattice fermions
NASA Astrophysics Data System (ADS)
Aoki, Sinya; Chiu, Ting-Wai; Cossu, Guido; Feng, Xu; Fukaya, Hidenori; Hashimoto, Shoji; Hsieh, Tung-Han; Kaneko, Takashi; Matsufuru, Hideo; Noaki, Jun-Ichi; Onogi, Tetsuya; Shintani, Eigo; Takeda, Kouhei
2012-09-01
Numerical simulation of the low-energy dynamics of quarks and gluons is now feasible based on the fundamental theory of strong interaction, i.e. quantum chromodynamics (QCD). With QCD formulated on a 4D hypercubic lattice (called lattice QCD or LQCD), one can simulate the QCD vacuum and hadronic excitations on the vacuum using teraflop-scale supercomputers, which have become available in the last decade. A great deal of work has been done on this subject by many groups around the world; in this article we summarize the work done by the JLQCD and TWQCD collaborations since 2006. These collaborations employ Neuberger's overlap fermion formulation, which preserves the exact chiral and flavor symmetries on the lattice, unlike other lattice fermion formulations. Because of this beautiful property, numerical simulation of the formulation can address fundamental questions on the QCD vacuum, such as the microscopic structure of the quark-antiquark condensate in the chirally broken phase of QCD and its relation to SU(3) gauge field topology. Tests of the chiral effective theory, which is based on the assumption that the chiral symmetry is spontaneously broken in the QCD vacuum, can be performed, including the pion-loop effect test. For many other phenomenological applications, we adopt the all-to-all quark propagator technique, which allows us to compute various correlation functions without substantial extra cost. The benefit of this is not only that the statistical signal is improved but that disconnected quark-loop diagrams can be calculated. Using this method combined with the overlap fermion formulation, we study a wide range of physical quantities that are of both theoretical and phenomenological interest.
Fukugita, M.; Ukawa, A.
1986-08-04
Finite-temperature behavior of quantum chromodynamics is investigated with the Langevin technique including the dynamical quark loops. The deconfining and chiral transitions occur at the same temperature. The strength of transition weakens initially as the quark mass decreases from infinity, but at small quark masses it strengthens again and shows the characteristic of a first-order transition. We estimate the inverse coupling constant at zero quark mass to be beta/sub c/ = 6/g/sub c//sup 2/approx. =4.9--5.0 for four flavors on an 8/sup 3/ x 4 lattice.
Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity
NASA Astrophysics Data System (ADS)
Wu, Ning
2006-03-01
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 Schrödinger 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 Schrödinger 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.
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2016-08-01
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.
Approximate light cone effects in a nonrelativistic quantum field theory after a local quench
NASA Astrophysics Data System (ADS)
Bertini, Bruno
2017-02-01
We study the spreading of correlations after a local quench in a nonrelativistic quantum field theory. We focus on noninteracting nonrelativistic fermions and study the time evolution after two identical systems in their ground states are suddenly joined together with a localized impurity at the junction. We find that, even if the quasiparticles of the system have unbounded dispersion, the correlations show light cone effects. We carry out a detailed study of these effects by developing an accurate asymptotic expansion of the two-point function and determining exactly the density of particles at any time after the quench. In particular, we find that the width of the light cone region is ∝t1 /2 . The structure of correlations, however, does not show a pure light cone form: "superluminal corrections" are much larger than in the bounded-dispersion case. These findings can be explained by inspecting the structure of excitations generated by the initial state. We show that a similar picture also emerges in the presence of a harmonic trapping potential and when more than two systems are suddenly joined at a single point.
NASA Astrophysics Data System (ADS)
Suganuma, H.; Fukushima, M.; Toki, H.
The Table of Contents for the book is as follows: * Preface * Opening Address * Monopole Condensation and Quark Confinement * Dual QCD, Effective String Theory, and Regge Trajectories * Abelian Dominance and Monopole Condensation * Non-Abelian Stokes Theorem and Quark Confinement in QCD * Infrared Region of QCD and Confining Configurations * BRS Quartet Mechanism for Color Confinement * Color Confinement and Quartet Mechanism * Numerical Tests of the Kugo-Ojima Color Confinement Criterion * Monopoles and Confinement in Lattice QCD * SU(2) Lattice Gauge Theory at T > 0 in a Finite Box with Fixed Holonomy * Confining and Dirac Strings in Gluodynamics * Cooling, Monopoles, and Vortices in SU(2) Lattice Gauge Theory * Quark Confinement Physics from Lattice QCD * An (Almost) Perfect Lattice Action for SU(2) and SU(3) Gluodynamics * Vortices and Confinement in Lattice QCD * P-Vortices, Nexuses and Effects of Gribov Copies in the Center Gauges * Laplacian Center Vortices * Center Vortices at Strong Couplings and All Couplings * Simulations in SO(3) × Z(2) Lattice Gauge Theory * Exciting a Vortex - the Cost of Confinement * Instantons in QCD * Deformation of Instanton in External Color Fields * Field Strength Correlators in the Instanton Liquid * Instanton and Meron Physics in Lattice QCD * The Dual Ginzburg-Landau Theory for Confinement and the Role of Instantons * Lattice QCD for Quarks, Gluons and Hadrons * Hadronic Spectral Functions in QCD * Universality and Chaos in Quantum Field Theories * Lattice QCD Study of Three Quark Potential * Probing the QCD Vacuum with Flavour Singlet Objects : η' on the Lattice * Lattice Studies of Quarks and Gluons * Quarks and Hadrons in QCD * Supersymmetric Nonlinear Sigma Models * Chiral Transition and Baryon-number Susceptibility * Light Quark Masses in QCD * Chiral Symmetry of Baryons and Baryon Resonances * Confinement and Bound States in QCD * Parallel Session * Off-diagonal Gluon Mass Generation and Strong Randomness of Off
Light Nuclei and HyperNuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
Beane, S R; Cohen, S D; Detmold, W; Lin, H W; Luu, T C; Orginos, K; Parreno, A; Savage, M J; Walker-Loud, A
2013-02-01
The binding energies of a range of nuclei and hypernuclei with atomic number A <= 4 and strangeness |s| <= 2, including the deuteron, di-neutron, H-dibaryon, {sup 3}He, {sub {Lambda}}{sup 3}He, {sub {Lambda}}{sup 4}He, and {sub {Lambda}{Lambda}}{sup 4}He, are calculated in the limit of flavor-SU(3) symmetry at the physical strange quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from Lattice QCD calculations performed with n{sub f}=3 dynamical light quarks using an isotropic clover discretization of the quark-action in three lattice volumes of spatial extent L ~ 3.4 fm, 4.5 fm and 6.7 fm, and with a single lattice spacing b ~ 0.145 fm.
Resonances in Coupled $\pi K\text{-}\eta K$ Scattering from Quantum Chromodynamics
Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.; Wilson, David J.
2014-10-01
Using first-principles calculation within Quantum Chromodynamics, we are able to reproduce the pattern of experimental strange resonances which appear as complex singularities within coupled πK, ηK scattering amplitudes. We make use of numerical computation within the lattice discretized approach to QCD, extracting the energy dependence of scattering amplitudes through their relation- ship to the discrete spectrum of the theory in a finite-volume, which we map out in unprecedented detail.
Challenges to quantum chromodynamics: Anomalous spin, heavy quark, and nuclear phenomena
Brodsky, S.J.
1989-11-01
The general structure of QCD meshes remarkably well with the facts of the hadronic world, especially quark-based spectroscopy, current algebra, the approximate point-like structure of large momentum transfer inclusive reactions, and the logarithmic violation of scale invariance in deep inelastic lepton-hadron reactions. QCD has been successful in predicting the features of electron-positron and photon-photon annihilation into hadrons, including the magnitude and scaling of the cross sections, the shape of the photon structure function, the production of hadronic jets with patterns conforming to elementary quark and gluon subprocesses. The experimental measurements appear to be consistent with basic postulates of QCD, that the charge and weak currents within hadrons are carried by fractionally-charged quarks, and that the strength of the interactions between the quarks, and gluons becomes weak at short distances, consistent with asymptotic freedom. Nevertheless in some cases, the predictions of QCD appear to be in dramatic conflict with experiment. The anomalies suggest that the proton itself as a much more complex object than suggested by simple non-relativistic quark models. Recent analyses of the proton distribution amplitude using QCD sum rules points to highly-nontrival proton structure. Solutions to QCD in one-space and one-time dimension suggest that the momentum distributions of non-valence quarks in the hadrons have a non-trival oscillatory structure. The data seems also to be suggesting that the intrinsic'' bound state structure of the proton has a non- negligible strange and charm quark content, in addition to the extrinsic'' sources of heavy quarks created in the collision itself. 144 refs., 46 figs., 2 tabs.
Testing quantum chromodynamics
Brodsky, S.J.
1982-09-01
The difficulties in isolating specific QCD mechanisms which control hadronic phenomena, and the complications in obtaining quantitative tests of QCD are discussed. A number of novel QCD effects are reviewed, including heavy quark and higher twist phenomena, initial and final state interactions, direct processes, multiparticle collisions, color filtering, and nuclear target effects. The importance of understanding hadron production at the amplitude level is stressed.
Quantum dwell-correlation times in the scattering of two nonrelativistic particles
Hahne, G. E.
2009-12-15
In a previous paper [G. E. Hahne, J. Phys. A 36, 7149 (2003)] the author studied a nontraditional boundary value problem associated with Schroedinger's partial differential equation for the wave function of a structureless particle moving in four-dimensional spacetime: in this boundary value problem, instead of the conventional specification of initial wave-function values on a time=constant surface, suitable time-dependent boundary and normal-derivative values are given on a three-dimensional space-time surface surrounding a slablike region of interaction in four-dimensional spacetime. The particle's time coordinate plays a natural role as an operator and observable in the modified formalism. In the present paper, the formalism is extended to describe a system of two nonrelativistic particles--each with its own time coordinate--scattering from background potentials and from one another in four-dimensional spacetime. The two-body interaction is taken as a generic noninstantaneous action-at-a-distance, which depends independently on the space-time positions of the two particles. The dynamics is expressed in terms of an integral equation for the wave function, that is, a nonrelativistic version of the Bethe-Salpeter equation. An optical theorem is derived for the transition operator associated with scattering processes; when the theorem holds, the pointwise probability current density derivable from the wave function is conserved globally, that is, in a region covering the space-time domain of significant interparticle interaction. A general formula for the expected dwell-correlation time for the two particles in the space-time region in terms of the scattering matrices is worked out.
Deta, U. A.; Suparmi,; Cari,; Husein, A. S.; Yuliani, H.; Khaled, I. K. A.; Luqman, H.; Supriyanto
2014-09-30
The Energy Spectra and Wave Function of Schrodinger equation in D-Dimensions for trigonometric Rosen-Morse potential were investigated analytically using Nikiforov-Uvarov method. This potential captures the essential traits of the quark-gluon dynamics of Quantum Chromodynamics. The approximate energy spectra are given in the close form and the corresponding approximate wave function for arbitrary l-state (l ≠ 0) in D-dimensions are formulated in the form of differential polynomials. The wave function of this potential unnormalizable for general case. The wave function of this potential unnormalizable for general case. The existence of extra dimensions (centrifugal factor) and this potential increase the energy spectra of system.
Mueller, B.; Springer, R.P.
1994-05-15
This report briefly discusses the following topics: quark-gluon plasma and high-energy collisions; hadron structure and chiral dynamics; nonperturbative studies and nonabelian gauge theories; and studies in quantum field theory.
Working Group Report: Quantum Chromodynamics
Campbell, J. M.
2013-10-18
This is the summary report of the energy frontier QCD working group prepared for Snowmass 2013. We review the status of tools, both theoretical and experimental, for understanding the strong interactions at colliders. We attempt to prioritize important directions that future developments should take. Most of the efforts of the QCD working group concentrate on proton-proton colliders, at 14 TeV as planned for the next run of the LHC, and for 33 and 100 TeV, possible energies of the colliders that will be necessary to carry on the physics program started at 14 TeV. We also examine QCD predictions and measurements at lepton-lepton and lepton-hadron colliders, and in particular their ability to improve our knowledge of strong coupling constant and parton distribution functions.
Testing Quantum Chromodynamics with Antiprotons
Brodsky, S.
2004-10-21
The antiproton storage ring HESR to be constructed at GSI will open up a new range of perturbative and nonperturbative tests of QCD in exclusive and inclusive reactions. I discuss 21 tests of QCD using antiproton beams which can illuminate novel features of QCD. The proposed experiments include the formation of exotic hadrons, measurements of timelike generalized parton distributions, the production of charm at threshold, transversity measurements in Drell-Yan reactions, and searches for single-spin asymmetries. The interactions of antiprotons in nuclear targets will allow tests of exotic nuclear phenomena such as color transparency, hidden color, reduced nuclear amplitudes, and the non-universality of nuclear antishadowing. The central tool used in these lectures are light-front Fock state wavefunctions which encode the bound-state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions. QCD becomes scale free and conformally symmetric in the analytic limit of zero quark mass and zero {beta} function. This ''conformal correspondence principle'' determines the form of the expansion polynomials for distribution amplitudes and the behavior of non-perturbative wavefunctions which control hard exclusive processes at leading twist. The conformal template also can be used to derive commensurate scale relations which connect observables in QCD without scale or scheme ambiguity. The AdS/CFT correspondence of large N{sub C} supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has important implications for hadron phenomenology in the conformal limit, including the nonperturbative derivation of counting rules for exclusive processes and the behavior of structure functions at large x{sub bj}. String/gauge duality also predicts the QCD power-law fall-off of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. I also review recent work which shows that the diffractive component of deep inelastic scattering, single spin asymmetries, as well as nuclear shadowing and antishadowing, cannot be computed from the LFWFs of hadrons in isolation.
Antiproton annihilation in quantum chromodynamics
Brodsky, S.J.
1988-10-01
Anti-proton annihilation has a number of important advantages as a probe of QCD in the low energy domain. Exclusive reaction in which complete annihilation of the valance quarks occur. There are a number of exclusive and inclusive /bar p/ reactions in the intermediate momentum transfer domain which provide useful constraints on hadron wavefunctions or test novel features of QCD involving both perturbative and nonperturbative dynamics. Inclusive reactions involving antiprotons have the advantage that the parton distributions are well understood. In these lectures, I will particularly focus on lepton pair production /bar p/A ..-->.. /ell//bar /ell//X as a means to understand specific nuclear features in QCD, including collision broadening, breakdown of the QCD ''target length condition''. Thus studies of low to moderate energy antiproton reactions with laboratory energies under 10 GeV could give further insights into the full structure of QCD. 112 refs., 40 figs.
Exclusive processes in quantum chromodynamics
Brodsky, S.J.; Lepage, G.P.
1981-06-01
Large momentum transfer exclusive processes and the short distance structure of hadronic wave functions can be systematically analyzed within the context of perturbative QCD. Predictions for meson form factors, two-photon processes ..gamma gamma.. ..-->.. M anti M, hadronic decays of heavy quark systems, and a number of other related QCD phenomena are reviewed.
Polarization phenomena in quantum chromodynamics
Brodsky, S.J.
1994-12-01
The author discusses a number of interrelated hadronic spin effects which test fundamental features of perturbative and nonperturbative QCD. For example, the anomalous magnetic moment of the proton and the axial coupling g{sub A} on the nucleon are shown to be related to each other for fixed proton radius, independent of the form of the underlying three-quark relativistic quark wavefunction. The renormalization scale and scheme ambiguities for the radiative corrections to the Bjorken sum rule for the polarized structure functions can be eliminated by using commensurate scale relations with other observables. Other examples include (a) new constraints on the shape and normalization of the polarized quark and gluon structure functions of the proton at large and small x{sub bj}; (b) consequences of the principle of hadron retention in high x{sub F} inclusive reactions; (c) applications of hadron helicity conservation to high momentum transfer exclusive reactions; and (d) the dependence of nuclear structure functions and shadowing on virtual photon polarization. The author also discusses the implications of a number of measurements which are in striking conflict with leading-twist perturbative QCD predictions, such as the extraordinarily large spin correlation A{sub NN} observed in large angle proton-proton scattering, the anomalously large {rho}{pi} branching ratio of the J/{psi}, and the rapidly changing polarization dependence of both J/{psi} and continuum lepton pair hadroproduction observed at large x{sub F}. The azimuthal angular dependence of the Drell-Yan process is shown to be highly sensitive to the projectile distribution amplitude, the fundamental valence light-cone wavefunction of the hadron.
Testing quantum chromodynamics in electroproduction
Brodsky, S.J.
1987-05-01
The exclusive channels in electroproduction are discussed. The study of color transparency, the formation zone, and other novel aspects of QCD by measuring exclusive reactions inside nuclear targets is covered. Diffractive electroproduction channels are discussed, and exclusive nuclear processes in QCD are examined. Non-additivity of nuclear structure functions (EMC effect) is also discussed, as well as jet coalescence in electroproduction. (LEW)
J/ψ polarization at the Tevatron and the LHC: nonrelativistic-QCD factorization at the crossroads.
Butenschoen, Mathias; Kniehl, Bernd A
2012-04-27
We study the polarization observables of J/ψ hadroproduction at next-to-leading order within the factorization formalism of nonrelativistic quantum chromodynamics. We complete the present knowledge of the relativistic corrections by also providing the contribution due to the intermediate (3)P(J)([8]) color-octet states at this order, which turns out to be quite significant. Exploiting the color-octet long-distance matrix elements previously extracted through a global fit to experimental data of unpolarized J/ψ production, we provide theoretical predictions in the helicity and Collins-Soper frames and compare them with data taken by CDF at Fermilab Tevatron I and II and by ALICE at CERN LHC. The notorious CDF J/ψ polarization anomaly familiar from leading-order analyses persists at the quantum level, while the situation looks promising for the LHC, which is bound to bring final clarification.
Is nonrelativistic gravity possible?
Kocharyan, A. A.
2009-07-15
We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti-)de Sitter black holes of Einstein gravity and IR limit of Horava gravity are locally identical.
Sharkey, Keeper L.; Bubin, Sergiy; Adamowicz, Ludwik
2011-10-15
Very accurate finite-nuclear-mass variational nonrelativistic calculations are performed for the lowest five {sup 1}D states (1s{sup 2} 2p{sup 2}, 1s{sup 2} 2s{sup 1} 3d{sup 1}, 1s{sup 2} 2s{sup 1} 4d{sup 1}, 1s{sup 2} 2s{sup 1} 5d{sup 1}, and 1s{sup 2} 2s{sup 1} 6d{sup 1}) of the beryllium atom ({sup 9}Be). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The calculations exemplify the level of accuracy that is now possible with Gaussians in describing bound states of a four-electron system where some of the electrons are excited into higher angular states.
Casalbuoni, Roberto; Gomis, Joaquim; Longhi, Giorgio
2007-12-15
We construct a classical nonrelativistic string model in 3+1 dimensions. The model contains a spurion tensor field that is responsible for the noncommutative structure of the model. Under double-dimensional reduction the model reduces to the exotic nonrelativistic particle in 2+1 dimensions.
NASA Astrophysics Data System (ADS)
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.
Bödeker, Dietrich; Wörmann, Mirco E-mail: mwoermann@physik.uni-bielefeld.de
2014-02-01
In many phenomenologically interesting models of thermal leptogenesis the heavy neutrinos are non-relativistic when they decay and produce the baryon asymmetry of the Universe. We propose a non-relativistic approximation for the corresponding rate equations in the non-resonant case, and a systematic way for computing relativistic corrections. We determine the leading order coefficients in these equations, and the first relativistic corrections. The non-relativistic approximation works remarkably well. It appears to be consistent with results obtained using a Boltzmann equation taking into account the momentum distribution of the heavy neutrinos, while being much simpler. We also compute radiative corrections to some of the coefficients in the rate equations. Their effect is of order 1% in the regime favored by neutrino oscillation data. We obtain the correct leading order lepton number washout rate in this regime, which leads to large ( ∼ 20%) effects compared to previous computations.
Holographic thermalization from nonrelativistic branes
NASA Astrophysics Data System (ADS)
Roychowdhury, Dibakar
2016-05-01
In this paper, based on the fundamental principles of gauge/gravity duality and considering a global quench, we probe the physics of thermalization for certain special classes of strongly coupled nonrelativistic quantum field theories that are dual to an asymptotically Schrödinger D p brane space time. In our analysis, we note that during the prelocal 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 postlocal 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 certain parameters of the theory in a specific way in order to have discontinuous transitions at the point of saturation.
Nonrelativistic superstring theories
Kim, Bom Soo
2007-12-15
We construct a supersymmetric version of the critical nonrelativistic bosonic string theory [B. S. Kim, Phys. Rev. D 76, 106007 (2007).] with its manifest global symmetry. We introduce the anticommuting bc conformal field theory (CFT) which is the super partner of the {beta}{gamma} CFT. The conformal weights of the b and c fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of type IIB superstring theory. There is one notable difference: the fermions are nonchiral. We further consider noncritical generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical nonrelativistic string theory and the lightlike linear dilaton theory.
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.
Moving nonrelativistic QCD for heavy-to-light form factors on the lattice
Horgan, R. R.; Khomskii, L.; Meinel, S.; Wingate, M.; Foley, K. M.; Lepage, G. P.; Hippel, G. M. von; Hart, A.; Mueller, E. H.; Davies, C. T. H.; Dougall, A.; Wong, K. Y.
2009-10-01
We formulate nonrelativistic quantum chromodynamics (NRQCD) on a lattice which is boosted relative to the usual discretization frame. Moving NRQCD allows us to treat the momentum for the heavy quark arising from the frame choice exactly. We derive moving NRQCD through O(1/m{sup 2},v{sub rel}{sup 4}), as accurate as the NRQCD action in present use, both in the continuum and on the lattice with O(a{sup 4}) improvements. We have carried out extensive tests of the formalism through calculations of two-point correlators for both heavy-heavy (bottomonium) and heavy-light (B{sub s}) mesons in 2+1 flavor lattice QCD and obtained nonperturbative determinations of energy shift and external momentum renormalization. Comparison to perturbation theory at O({alpha}{sub s}) is also made. The results demonstrate the effectiveness of moving NRQCD. In particular we show that the decay constants of heavy-light and heavy-heavy mesons can be calculated with small systematic errors up to much larger momenta than with standard NRQCD.
Classical behavior in high temperature chromodynamics
Sivers, D.
1984-01-01
In searching for tools to describe physical systems consisting of hadronic matter at high temperature, it is worthwhile to consider the application of classical chromodynamics. Classical non-Abelian gauge theories have been extensively studied and continue to attract theoretical interest. However, the thrust of most work has been to consider classical dynamics as merely a guide to the quantum mechanical path integral. Attention has therefore focussed on particle-like field configurations or on topological structures which may be important in the presence of color confinement. Confinement in low-temperature QCD provides a substantial barrier to the use of any classical approximations. With color fields confined to isolated spatial regions, it is vey implausible that any classical approximation can be made for bulk hadronic matter. However, at temperatures above the postulated deconfining phase transition there are reasons to believe that classical physics would be a valid approximation. Statistical fluctuations at high temperature can dominate quantum fluctuations and it is possible that the behavior of a large system can be described by averaged fields which obey classical equations. The use of the classical approximation for the non-Abelian dynamics is discussed. (WHK)
Trace anomaly for non-relativistic fermions
NASA Astrophysics Data System (ADS)
Auzzi, Roberto; Baiguera, Stefano; Nardelli, Giuseppe
2017-08-01
We study the coupling of a 2 + 1 dimensional non-relativistic spin 1/2 fermion to a curved Newton-Cartan geometry, using null reduction from an extra-dimensional relativistic Dirac action in curved spacetime. We analyze Weyl invariance in detail: we show that at the classical level it is preserved in an arbitrary curved background, whereas at the quantum level it is broken by anomalies. We compute the trace anomaly using the Heat Kernel method and we show that the anomaly coefficients a, c are proportional to the relativistic ones for a Dirac fermion in 3 + 1 dimensions. As for the previously studied scalar case, these coefficents are proportional to 1/ m, where m is the non-relativistic mass of the particle.
Windows on the axion. [quantum chromodynamics (QCD)
NASA Technical Reports Server (NTRS)
Turner, Michael S.
1989-01-01
Peccei-Quinn symmetry with attendant axion is a most compelling, and perhaps the most minimal, extension of the standard model, as it provides a very elegant solution to the nagging strong CP-problem associated with the theta vacuum structure of QCD. However, particle physics gives little guidance as to the axion mass; a priori, the plausible values span the range: 10(-12)eV is approx. less than m(a) which is approx. less than 10(6)eV, some 18 orders-of-magnitude. Laboratory experiments have excluded masses greater than 10(4)eV, leaving unprobed some 16 orders-of-magnitude. Axions have a host of interesting astrophysical and cosmological effects, including, modifying the evolution of stars of all types (our sun, red giants, white dwarfs, and neutron stars), contributing significantly to the mass density of the Universe today, and producting detectable line radiation through the decays of relic axions. Consideration of these effects has probed 14 orders-of-magnitude in axion mass, and has left open only two windows for further exploration: 10(-6)eV is approx. less than m(a) is approx. less than 10(-3)eV and 1eV is approx. less than m(a) is approx. less than 5eV (hadronic axions only). Both these windows are accessible to experiment, and a variety of very interesting experiments, all of which involve heavenly axions, are being planned or are underway.
Constraining Neutron Star Matter with Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Kurkela, Aleksi; Fraga, Eduardo S.; Schaffner-Bielich, Jürgen; Vuorinen, Aleksi
2014-07-01
In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount—or even presence—of quark matter inside the stars.
Single quark polarization in quantum chromodynamics subprocesses
Dharmaratna, W.G.; Goldstein, G.R.
1996-02-01
It is well known that the single-polarization asymmetries vanish in QCD with massless quarks. But, heavy quarks with a nonzero mass should be transversely polarized due to the breakdown of the helicity conservation. In this paper we give the exact fourth-order perturbative QCD predictions for the transverse polarization from all QCD subprocesses, {ital q}+{ital q}{prime}{r_arrow}{ital q}+{ital q}{prime}, {ital q}+{ital g}{r_arrow}{ital q}+{ital g}, {ital g}+{ital g}{r_arrow}{ital q}+{bar {ital q}}, and {ital q}+{bar {ital q}}{r_arrow}{ital q}{prime}+{bar {ital q}}{prime}, which are significant for heavy quark production, with a description of the method of calculation. The kinematical dependence of the polarization is discussed. Top quark polarization from gluon fusion and quark annihilation processes, which are the important subprocesses at high energies, is estimated and its significance is discussed. {copyright} {ital 1996 The American Physical Society.}
Quantum chromodynamics (QCD) and collider physics
Ellis, R.K. ); Stirling, W.J. )
1990-08-14
This report discusses: fundamentals of perturbative QCD; QCD in e{sup +}e{sup {minus}} {yields} hadrons; deep inelastic scattering and parton distributions; the QCD parton model in hadron-hadron collisions; large p{sub T} jet production in hadron-hadron collisions; the production of vector bosons in hadronic collisions; and the production of heavy quarks.
Quantum Chromodynamics and Deep Inelastic Scattering
NASA Astrophysics Data System (ADS)
Ellis, R. Keith
2016-10-01
This article first describes the parton model which was the precursor of the QCD description of hard scattering processes. After the discovery of QCD and asymptotic freedom, the first successful applications were to Deep Inelastic lepton-hadron scattering. The subsequent application of QCD to processes with two initial state hadrons required the understanding and proof of factorization. To take the fledgling theory and turn it into the robust calculational engine it has become today, required a number of technical and conceptual developments which will be described. Prospects for higher loop calculations are also reviewed.
Heavy-quark physics in quantum chromodynamics
Brodsky, S.J.
1991-04-01
Heavy quarks can expose new symmetries and novel phenomena in QCD not apparent in ordinary hadronic systems. In these lectures I discuss the use of effective-Lagrangian and light-cone Fock methods to analyze exclusive heavy hadron decays such as {Upsilon} {yields} p{bar p} and B {yields} {pi}{pi}, and also to derive effective Schroedinger and Dirac equations for heavy quark systems. Two contributions to the heavy quark structure functions of the proton and other light hadrons are identified: an extrinsic'' contribution associated with leading twist QCD evolution of the gluon distribution, and a higher twist intrinsic'' contribution due to the hardness of high-mass fluctuations of multi-gluon correlations in hadronic wavefunctions. A non-perturbative calculation of the heavy quark distribution of a meson in QCD in one space and one time is presented. The intrinsic higher twist contributions to the pion and proton structure functions can dominate the hadronic production of heavy quark systems at large longitudinal momentum fraction x{sub F} and give anomalous contributions to the quark structure functions of ordinary hadrons at large x{sub bj}. I also discuss a number of ways in which heavy quark production in nuclear targets can test fundamental QCD phenomena and provide constraints on hadronic wavefunctions. The topics include color transparency, finite formation time, and predictions for charm production at threshold, including nuclear-bound quarkonium. I also discuss a number of QCD mechanisms for the suppression of J/{psi} and {Upsilon} production in nuclear collisions, including gluon shadowing, the peripheral excitation of intrinsic heavy quark components at large x{sub F}, and the coalescence of heavy quarks with co-moving spectators at low x{sub F}.
Constraining neutron star matter with quantum chromodynamics
Kurkela, Aleksi; Fraga, Eduardo S.; Schaffner-Bielich, Jürgen; Vuorinen, Aleksi
2014-07-10
In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount—or even presence—of quark matter inside the stars.
Spin effects in perturbative quantum chromodynamics
Brodsky, S.J.; Lepage, G.P.
1980-12-01
The spin dependence of large momentum transfer exclusive and inclusive reactions can be used to test the gluon spin and other basic elements of QCD. In particular, exclusive processes including hadronic decays of heavy quark resonances have the potential of isolating QCD hard scattering subprocesses in situations where the helicities of all the interacting constituents are controlled. The predictions can be summarized in terms of QCD spin selection rules. The calculation of magnetic moment and other hadronic properties in QCD are mentioned.
Phenomenology of Heavy Quarkonia and Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Schmitz, Stefan Josef Anton
Heavy quarkonia, the cc, b(')b, and soon to be discovered t(')t families of states, are studied in the framework of potential theory. The earlier proposed, flavor independent "Riverside"-potential is fit to masses of cc and b(')b states and their electronic widths are calculated. An unusual feature of the potential is the use of a parameter b which controls the small r or "asymptotic freedom" behavior and which can be related to the QCD scale parameter (LAMDA)(,MS). This param- eter b is virtually undetermined by the cc and b(')b spectra, merely excluding the range b < 4 or (LAMDA)(,MS) < 120MeV and slightly favoring (LAMDA)(,MS) (DBLTURN) 250MeV. It is shown how even minimal information on the t(')t states will restrict the (LAMDA)(,MS) value to a range of the order of 50MeV. A recent Lattice Gauge potential shows a remarkable closeness to the phenomenological approach. In view of the approximations involved, the difference between the two potentials is small. This difference is investigated in terms of the strong coupling constant (alpha) which can be extracted from both potentials. In the main r regime the Lattice Gauge (alpha) is markedly smaller than the phenomenological one. It is shown that the absence of intermediate, virtual quark loops in the Lattice Gauge calculation, i.e. the so-called quenched approximation, accounts for at least some and possibly most of that difference. Overall, the phenomenology of heavy quarkonia as studied in this work is in no conflict with QCD.
Janiszewski, Stefan; Karch, Andreas
2013-02-22
We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.
Angular Distributions of Synchrotron Radiation in the Nonrelativistic Approximation
NASA Astrophysics Data System (ADS)
Bagrov, V. G.; Loginov, A. S.
2017-03-01
The angular distribution functions of the polarized components of synchrotron radiation in the nonrelativistic approximation are investigated using methods of classical and quantum theory. Particles of zero spin (bosons) and spin 1/2 (electrons) are considered in the quantum theory. It is shown that in the first nonzero approximation the angular distribution functions, calculated by methods of classical and quantum theory, coincide identically. Quantum corrections to the angular distribution functions appear only in the subsequent approximation whereas the total radiated power contains quantum and spin corrections already in the first approximation.
Microscopic picture of non-relativistic classicalons
Berkhahn, Felix; Müller, Sophia; Niedermann, Florian; Schneider, Robert E-mail: sophia.x.mueller@physik.uni-muenchen.de E-mail: robert.bob.schneider@physik.uni-muenchen.de
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.
Analytic form for the nonrelativistic Coulomb propagator
NASA Astrophysics Data System (ADS)
Blinder, S. M.
1991-01-01
An analytic form for the nonrelativistic Coulomb propagator is derived, thus resolving a long-standing problem in Feynman's path-integral formulation of quantum mechanics. Hostler's formula for the Coulomb Green's function is expanded according to the theorem of Mittag-Leffler, then Fourier transformed term by term to give the Coulomb propagator. The result is a discrete summation over the principal quantum number n, involving Whittaker, Laguerre, Hermite, and error functions. As is the case for other nonquadratic potentials, the Coulomb propagator does not have the canonical structure K=F exp(iS/ħ). Part of the expansion resembles a form derived by Crandall [J. Phys. A 16, 3005 (1983)] for the case of reflectionless potentials.
Sharkey, Keeper L.; Adamowicz, Ludwik
2014-05-07
An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground {sup 4}S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.
Sharkey, Keeper L; Adamowicz, Ludwik
2014-05-07
An algorithm for quantum-mechanical nonrelativistic variational calculations of L = 0 and M = 0 states of atoms with an arbitrary number of s electrons and with three p electrons have been implemented and tested in the calculations of the ground (4)S state of the nitrogen atom. The spatial part of the wave function is expanded in terms of all-electrons explicitly correlated Gaussian functions with the appropriate pre-exponential Cartesian angular factors for states with the L = 0 and M = 0 symmetry. The algorithm includes formulas for calculating the Hamiltonian and overlap matrix elements, as well as formulas for calculating the analytic energy gradient determined with respect to the Gaussian exponential parameters. The gradient is used in the variational optimization of these parameters. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all-particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. With that, the mass effect on the total ground-state energy is determined.
Resonant ${\pi}^{+}\gamma \to {\pi}^{+}{\pi}^{0}$ amplitude from Quantum Chromodynamics
Briceño, Raúl A.; Dudek, Jozef J.; Edwards, Robert G.; Shultz, Christian J.; Thomas, Christopher E.; Wilson, David J.
2015-12-08
We present the first ab initio calculation of a radiative transition of a hadronic resonance within Quantum Chromodynamics (QCD). We compute the amplitude for $\\pi\\pi \\to \\pi\\gamma^\\star$, as a function of the energy of the $\\pi\\pi$ pair and the virtuality of the photon, in the kinematic regime where $\\pi\\pi$ couples strongly to the unstable $\\rho$ resonance. This exploratory calculation is performed using a lattice discretization of QCD with quark masses corresponding to $m_\\pi \\approx 400$ MeV. As a result, we obtain a description of the energy dependence of the transition amplitude, constrained at 48 kinematic points, that we can analytically continue to the $\\rho$ pole and identify from its residue the $\\rho \\to \\pi\\gamma^\\star$ form-factor.
Nonrelativistic QED approach to the Lamb shift
Jentschura, Ulrich D.; Czarnecki, Andrzej; Pachucki, Krzysztof
2005-12-15
We calculate the one- and two-loop corrections of order {alpha}(Z{alpha}){sup 6} and {alpha}{sup 2}(Z{alpha}){sup 6}, respectively, to the Lamb shift in hydrogenlike systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results valid for all hydrogenic states with nonvanishing orbital angular momentum and for the normalized difference of S states. These results involve the expectation value of local effective operators and relativistic corrections to Bethe logarithms. The one-loop correction is in agreement with previous calculations for the particular cases of S, P, and D states. The two-loop correction in the order {alpha}{sup 2}(Z{alpha}){sup 6} includes the pure two-loop self-energy and all diagrams with closed fermion loops. The obtained results allow one to obtain improved theoretical predictions for all excited hydrogenic states.
Gravity duals for nonrelativistic conformal field theories.
Balasubramanian, Koushik; McGreevy, John
2008-08-08
We attempt to generalize the anti-de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.
Non-Relativistic Superstring Theories
Kim, Bom Soo
2007-12-14
We construct a supersymmetric version of the 'critical' non-relativistic bosonic string theory [1] with its manifest global symmetry. We introduce the anticommuting bc CFT which is the super partner of the {beta}{gamma} CFT. The conformal weights of the b and c fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of Type IIB superstring theory. There is one notable difference: the fermions are non-chiral. We further consider 'noncritical' generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical non-relativistic string theory and the lightlike Linear Dilaton theory.
Next-to-leading-order nonrelativistic QCD disfavors the interpretation of X(3872) as χc1(2P)
NASA Astrophysics Data System (ADS)
Butenschoen, Mathias; He, Zhi-Guo; Kniehl, Bernd A.
2013-07-01
We study χc1(2P)-inclusive hadroproduction at next-to-leading-order (NLO), both in αs and v2, within the factorization formalism of nonrelativistic quantum chromodynamics (NRQCD), including the color-singlet P1[1]3 and color-octet S1[8]3 cc¯ Fock states as well as the mixing of the latter with the D1[8]3 state. Assuming the recently discovered X(3872) hadron to be the JPC=1++ charmonium state χc1(2P), we perform a fit to the cross sections measured by the CDF, CMS, and LHCb Collaborations. We obtain either an unacceptably high value of χ2, a value of |R2P'(0)| incompatible with well-established potential models, or an intolerable violation of the NRQCD velocity rules. We thus conclude that NLO NRQCD is inconsistent with the hypothesis X(3872)≡χc1(2P).
Torsion and noninertial effects on a nonrelativistic Dirac particle
Bakke, K.
2014-07-15
We investigate torsion and noninertial effects on a spin-1/2 quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi–Walker reference frame. -- Highlights: •Torsion effects on a spin- 1/2 particle in a noninertial reference frame. •Fermi–Walker reference frame in the cosmic dislocation spacetime background. •Torsion and noninertial effects on the confinement to a hard-wall confining potential.
Do non-relativistic neutrinos oscillate?
NASA Astrophysics Data System (ADS)
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.
Semiclassical approach for nonrelativistic fermions in low dimensions
Karabali, D.; Sakita, B. )
1991-11-30
This paper presents a collective field formalism for nonrelativistic fermions in one spatial dimension. A bosonization technique is used to convert the quantum mechanical fermionic problem to a bosonic one, which is further described as a second quantized Schrodinger field theory. A formulation in terms of current and density variables gives rise to the collective field representation. Applications of our formalism to the D = 1 Hermitian matrix model and the system of one-dimensional fermions in the presence of a weak electromagnetic field are discussed.
Muonium Spectrum Beyond the Nonrelativistic Limit
Weber, Axel
2008-07-02
A generalization of the Gell-Mann-Low theorem is applied to the antimuon-electron system. The bound state spectrum is extracted numerically. As a result, fine and hyperfine structure are reproduced correctly near the nonrelativistic limit (and for arbitrary masses). We compare the spectrum for the relativistic value {alpha} = 0.3 with corresponding calculations in light-front quantization.
Inclusive and Exclusive Compton Processes in Quantum Chromodynamics
Psaker, Ales
2005-12-01
In our work, we describe two types of Compton processes. As an example of an inclusive process, we consider the high-energy photoproduction of massive muon pairs off the nucleon. We analyze the process in the framework of the QCD parton model, in which the usual parton distributions emerge as a tool to describe the nucleon in terms of quark and gluonic degrees of freedom. To study its exclusive version, a new class of phenomenological functions is required, namely, generalized parton distributions. They can be considered as a generalization of the usual parton distributions measured in deeply inelastic lepton-nucleon scattering. Generalized parton distributions (GPDs) may be observed in hard exclusive reactions such as deeply virtual Compton scattering. We develop an extension of this particular process into the weak interaction sector. We also investigate a possible application of the GPD formalism to wide-angle real Compton scattering.
Quantum chromodynamics and the statistical hydrodynamical model of hadron production
NASA Astrophysics Data System (ADS)
Carruthers, P.; Duong-van, Minh
1983-07-01
We analyze the Fermi-Landau statistical hydrodynamical model of hadron-hadron multiplicities in the framework of QCD, using the Pokorski-Van Hove model wherein the collision of preexisting glue dominates the multiplicity. It is noted that previous dismissal of the possibility of thermalization in the basis of nuclear "transparency" is circumvented in this picture because the valence quarks pass through, whereas the gluon clouds interact strongly. Assuming that the gluons equilibrate to a thermalized plasmoid within the Fermi-Landau (FL) Lorentz-contracted initial volume, we derive a simple formula for the multiplicity with the form Nch~2.5f14Whad12 (three flavors excited), where 1-f is the fraction of energy carried away by the leading particles and Whad=fW is the energy left behind. If f were fixed at a constant value of 1/2 , the formula would agree extremely well with data up to and including p¯p collider energies. (The widely held belief that collider multiplicities rule out the Fermi power law was based on the use of W rather than Whad.) However, using the data of Basile et al., in which multiplicities are broken down as a function of Whad for different W values, we find that the f14 dependence is ruled out. We conclude that thermalization of the colliding gluon clouds in the FL volume is also ruled out, although thermalization in the gluon fragmentation and central regions remains a possibility.
From Hermann Weyl to Yang and Mills to Quantum Chromodynamics
NASA Astrophysics Data System (ADS)
Chýla, J.
2005-03-01
This is a personal view of the developments from the invention of the concept of gauge invariance to our present understanding that it provides the fundamental principle for the construction of theories of forces between the basic blocs of matter. This journey was full of twists and turns and marked by fascinating moments. It is these aspects of the development of gauge theories that I will concentrate on. Although Yang-Mills theories provide the basic framework for both strong and electroweak interactions, my contribution concerns almost exclusively the former only. There are many excellent articles discussing various aspects of the development of Yang-Mills theories [D. Gross: Twenty five years of asymptotic freedom, Nucl. Phys. (Proc. Suppl.) 74 (1999) 426, hep-ph/98, A. de Rujula: Fifty years of Yang-Mills theories: a phenomenological point of view, hep-ph/0404215, S. Weinberg: The Making of the Standard Model, Eur. Phys. J. C 34 (2004) 5]. The contribution of Weyl toward the concept of gauge invariance is discussed in [N. Straumann: Early Histrory of Gauge Theories and Weak Interactions, Invited talk at the PSI Summer School in Physics, Zuoz, Switzerland, August 1996].
Bosonic and Baryonic String Theory in Quantum Chromodynamics
Kuti, Julius
2007-02-27
Bosonic string formation in gauge theories is reviewed with particular attention to the confining flux in lattice QCD and its effective string theory description. Recent results on the Casimir energy of the ground state and the string excitation spectrum are analyzed in the Dirichlet string limit of large separation between static sources. The closed string-soliton (torelon) with electric flux winding around a compact dimension is discussed and a new bound state tower spectrum at baryon string junctions is presented.
Charmed baryon isodoublet mass splitting in quantum chromodynamics revitalized
NASA Astrophysics Data System (ADS)
Sinha, S. N.; Sinha, S. M.; Rahman, M.; Kim, D. Y.
1989-02-01
We calculate the isodoublet mass splitting of charmed baryons in the quark model in QCD, which includes the relativistic correction and the explicit use of running QCD coupling constants with flavors. The model was applied and tested in the past for the calculations of isodoublet mass splittings of several hadrons. Our theoretical result ( Δmth( Σc++- Σc0)≅1.5±0.2 MeV) is in agteement with the recent experimental result ( Δmex( Σc++- Σc0)=1.2±0.7±0.3 MeV) by the ARGUS Collaboration at the DORIS II storage ring.
Precision tests of quantum chromodynamics and the standard model
Brodsky, S.J.; Lu, H.J.
1995-06-01
The authors discuss three topics relevant to testing the Standard Model to high precision: commensurate scale relations, which relate observables to each other in perturbation theory without renormalization scale or scheme ambiguity, the relationship of compositeness to anomalous moments, and new methods for measuring the anomalous magnetic and quadrupole moments of the W and Z.
Magnetic moments of light nuclei from lattice quantum chromodynamics
Beane, S. R.; Chang, E.; Cohen, S.; ...
2014-12-16
We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton and 3He, along with those of the neutron and proton. These calculations, performed at quark masses corresponding to mπ ~ 800 MeV, reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. We find that the magnetic moment of 3He differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired protons and a valence neutron captures itsmore » dominant structure. Similarly a shell-model-like moment is found for the triton, μ3H ~ μp. The deuteron magnetic moment is found to be equal to the nucleon isoscalar moment within the uncertainties of the calculations.« less
Magnetic moments of light nuclei from lattice quantum chromodynamics
Beane, S. R.; Chang, E.; Cohen, S.; Detmold, W.; Lin, H. W.; Orginos, K.; Parreño, A.; Savage, M. J.; Tiburzi, B. C.
2014-12-16
We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton and ^{3}He, along with those of the neutron and proton. These calculations, performed at quark masses corresponding to m_{π} ~ 800 MeV, reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. We find that the magnetic moment of ^{3}He differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired protons and a valence neutron captures its dominant structure. Similarly a shell-model-like moment is found for the triton, μ_{3H} ~ μ_{p}. The deuteron magnetic moment is found to be equal to the nucleon isoscalar moment within the uncertainties of the calculations.
Tests of quantum chromodynamics in exclusive and inclusive electroproduction
Brodsky, S.J.
1989-06-01
This paper discusses the following topics: overview of electroproduction phenomenology; hadronization of the quark and spectator systems; hadronization in nuclei; shadowing and anti- shadowing; color transparency; exclusive channels in electroproduction; hadronic wavefunction phenomenology; diffractive electroproduction; exclusive nuclear processes in QCD; and relation of electroproduction to QCD wavefunctions. 58 refs., 22 figs. (LSP)
Two-photon exclusive processes in quantum chromodynamics
Brodsky, S.J.
1986-07-01
QCD predictions for ..gamma gamma.. annihilation into single mesons, meson pairs, and baryon pairs are reviewed. Two-photon exclusive processes provide the most sensitive and practical measure of the distribution amplitudes, and thus a critical confrontation between QCD and experiment. Both the angular distribution and virtual photon mass dependence of these amplitudes are sensitive to the shapes of the phi (chi, Q). Novel effects involving the production of qq anti q anti q states at threshold are also discussed, and a new method is presented for systematically incorporating higher-order QCD corrections in ..gamma gamma.. reactions.
Low-mass solitons from fractional charges in quantum chromodynamics
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; Nair, V. P.; Panchapakesan, N.; Rajeev, S. G.
1983-12-01
Slansky, Goldman, and Shaw have proposed a model to account for the observation of fractionally charged states. We show that in this model, there are expected to be several low-mass solitons (four being in the mass range ~20-60 MeV) associated with the third homotopy group π3(SU(3)SO(3))=Z4, besides a low-mass (~30 MeV) Z2 monopole. Confirmation of these levels and hence of the model has important implications for Cabrera's results on the magnetic monopole. An efficient algorithm for the calculation of π3(GH) for a general Lie group G and a subgroup H is developed. It is pointed out that solitons associated with the third homotopy group are predicted by some grand-unified-theory scenarios.
The Conformal Template and New Perspectives for Quantum Chromodynamics
Brodsky, Stanley J.; /SLAC
2007-03-06
Conformal symmetry provides a systematic approximation to QCD in both its perturbative and nonperturbative domains. One can use the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically tractable approximation to QCD in the regime where the QCD coupling is large and constant. For example, there is an exact correspondence between the fifth-dimensional coordinate of AdS space and a specific impact variable which measures the separation of the quark constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, the fundamental entities which encode hadron properties and allow the computation of exclusive scattering amplitudes. One can also use conformal symmetry as a template for perturbative QCD predictions where the effects of the nonzero beta function can be systematically included in the scale of the QCD coupling. This leads to fixing of the renormalization scale and commensurate scale relations which relate observables without scale or scheme ambiguity. The results are consistent with the renormalization group and the analytic connection of QCD to Abelian theory at N{sub C} {yields} 0. I also discuss a number of novel phenomenological features of QCD. Initial- and .nal-state interactions from gluon-exchange, normally neglected in the parton model, have a profound effect in QCD hard-scattering reactions, leading to leading-twist single-spin asymmetries, diffractive deep inelastic scattering, di.ractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss tests of hidden color in nuclear wavefunctions, the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, nonperturbative antisymmetric sea quark distributions, anomalous heavy quark e.ects, and the unexpected effects of direct higher-twist processes.
Problems at the interface between perturbative and nonperturbative quantum chromodynamics
Brodsky, S.J.; Bodwin, G.T.; Lepage, G.P.
1983-06-01
Predictions based on perturbative QCD rest on three premises: (1) that hadronic interactions become weak in strength at small invariant separation; (2) that the perturbative expansion in ..cap alpha../sub s/(Q) is well-defined; and (3) factorization: all effects of collinear singularities, confinement, nonperturbative interactions, and bound state dynamics can be isolated at large momentum transfer in terms of structure functions, fragmentation functions, or in the case of exclusive processes, distribution amplitudes. The assumption that the perturbative expansion for hard scattering amplitudes converges has certainly not been demonstrated; in addition, there are serious ambiguities concerning the choice of renormalization scheme and scale choice Q/sup 2/ for the expansion in ..cap alpha../sub s/(Q/sup 2/). We will discuss a new procedure to at least partly rectify the latter problem. In the case of exclusive processes, the factorization of hadronic amplitudes at large momentum transfer in the form of distribution amplitudes convoluted with hard scattering quark-gluon subprocess amplitudes can be demonstrated systematically to all orders in ..cap alpha../sub s/(Q/sup 2/). In the case of inclusive reactions, factorization remains an ansatz; general all-orders proofs do not exist because of the complications of soft initial state interactions for hadron-induced processes; thus far factorization has only been verified to two loops beyond lowest order in a regime where the applicability of perturbation theory is in doubt. However, we shall show that a necessary condition for the validity of factorization in inclusive reactions is that the momentum transfer must be large compared to the (rest frame) length of the target. We review the present status of the factorization ansatz. 52 references.
Embedding nonrelativistic physics inside a gravitational wave
NASA Astrophysics Data System (ADS)
Bekaert, Xavier; Morand, Kevin
2013-09-01
Gravitational waves with parallel rays are known to have remarkable properties: their orbit space of null rays possesses the structure of a nonrelativistic spacetime of codimension-1. Their geodesics are in one-to-one correspondence with dynamical trajectories of a nonrelativistic system. Similarly, the null dimensional reduction of Klein-Gordon’s equation on this class of gravitational waves leads to a Schrödinger equation on curved space. These properties are generalized to the class of gravitational waves with a null Killing vector field, of which we propose a new geometric definition, as conformally equivalent to the previous class and such that the Killing vector field is preserved. This definition is instrumental for performing this generalization, as well as various applications. In particular, results on geodesic completeness are extended in a similar way. Moreover, the classification of the subclass with constant scalar invariants is investigated.
Superconductivity in Supersymmetric Theory in Restricted Chromodynamics
NASA Astrophysics Data System (ADS)
Rajput, B. S.; Kumar, Sandeep
2011-02-01
The study of superconductivity, dual superconductivity and color superconductivity has been undertaken through the breaking of super symmetric gauge theory in restricted chromo dynamics (RCD) which automatically incorporates the condensation of monopoles and dyons leading to confining and superconducting phases. Dyonic supermultiplets in N=1 super symmetry have been obtained quantum mechanically in RCD and it has been shown that dyon appears in RCD theory only through restricted part of the generalized potential and it is only this part of this potential which is responsible for quark confinement and the resulting superconductivity through the mechanism of dyonic condensation.
Nonrelativistic QED expansion for the electron self-energy
NASA Astrophysics Data System (ADS)
Patkóš, V.; Šimsa, D.; Zamastil, J.
2017-01-01
The recently proposed relativistic multipole expansion (RME) of the self-energy effect suggests some observations on the nonrelativistic expansion of the effect. First, the nature of the series for the one-loop self-energy of an electron bound by the Coulomb field of the nucleus is clarified. It is shown that the expansion of the energy shift caused by the self-energy effect contains terms of the form α (Zα ) 7ln(Z α ) , α (Zα ) 8ln3(Z α ) , α (Zα ) 9ln2(Z α ) , α (Zα ) 10ln4(Z α ) , and so on. Here Z is the charge of the nucleus. The origin of these terms is traced back to the logarithmic divergence of the Dirac S -wave function at the origin. These terms eventually lead to breakdown of the nonrelativistic quantum electrodynamics approach. Second, at leading order relativistic multipole expansion requires an evaluation of the "extended Bethe logarithm" (EBL). When expanded in series in Z α EBL reduces at leading order to the ordinary Bethe logarithm. However, it is argued that it is both more accurate and easier to calculate the EBL than the ordinary Bethe logarithm. Both variants of the Bethe logarithm can be calculated by means of the pseudostate method. An improvement of this method is suggested. Finally, the contribution of the combined self-energy vacuum polarization contribution to the Lamb shift in muonic hydrogen for the 1 s -4 s and 2 p -4 p states by means of the EBL is calculated. For cases that had already been calculated the results reported here are more accurate than the previous ones.
Convex Decompositions of Thermal Equilibrium for Non-interacting Non-relativistic Particles
NASA Astrophysics Data System (ADS)
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.
Poincaré invariance in low-energy EFTs for QCD
NASA Astrophysics Data System (ADS)
Hwang, Sungmin
2017-03-01
We present the calculations on deriving constraints between the Wilson coefficients in non-relativistic quantum chromodynamics and potential non-relativistic quantum chromodynamics by exploiting the symmetry of its fundamental theory, Poincaré invariance in particular. Implications of the constraints are briefly discussed in the context of the effective string theory.
New approach to nonrelativistic ideal magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Kumar, Kuldeep
2016-07-01
We provide a novel action principle for nonrelativistic ideal magnetohydrodynamics in the Eulerian scheme exploiting a Clebsch-type parametrisation. Both Lagrangian and Hamiltonian formulations have been considered. Within the Hamiltonian framework, two complementary approaches have been discussed using Dirac's constraint analysis. In one case the Hamiltonian is canonical involving only physical variables but the brackets have a noncanonical structure, while the other retains the canonical structure of brackets by enlarging the phase space. The special case of incompressible magnetohydrodynamics is also considered where, again, both the approaches are discussed in the Hamiltonian framework. The conservation of the stress tensor reveals interesting aspects of the theory.
Mass of nonrelativistic meson from leading twist distribution amplitudes
NASA Astrophysics Data System (ADS)
Braguta, V. V.
2011-01-01
In this paper distribution amplitudes of pseudoscalar and vector nonrelativistic mesons are considered. Using equations of motion for the distribution amplitudes, relations are derived which allow one to calculate the masses of nonrelativistic pseudoscalar and vector meson if the leading twist distribution amplitudes are known. These relations can be also rewritten as relations between the masses of nonrelativistic mesons and infinite series of QCD operators, what can be considered as an exact version of Gremm-Kapustin relation in NRQCD.
Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices.
Zohar, Erez; Cirac, J Ignacio; Reznik, Benni
2016-01-01
Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1 dimensions using ultracold atoms in optical lattices.
Quarkonium hybrids with nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Berwein, Matthias; Brambilla, Nora; Tarrús Castellà, Jaume; Vairo, Antonio
2015-12-01
We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass m of the heavy quark. At order 1 /m in the expansion, we obtain, at the level of potential nonrelativistic QCD, a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as Λ doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schrödinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for c c ¯, b c ¯, and b b ¯ hybrids. The Λ -doubling effect breaks the degeneracy between opposite-parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, and sum rule calculations, and discuss the relation to the Born-Oppenheimer approximation.
Holographic View of Non-relativistic Physics
NASA Astrophysics Data System (ADS)
Balasubramanian, Koushik
Motivated by the AdS/CFT correspondence for relativistic CFTs, it seems natural to generalize it to non-relativistic CFTs. Such a dual description could provide insight into strong coupling phenomena observed in condensed matter systems. Scale invariance can be realized in non-relativistic theories in many ways. One freedom is the relative scale dimension of time and space, called the dynamical exponent z. In this thesis, we will mainly focus on the case where z = 2, however gravity duals for other values of z have also been found. In the first part of the thesis, we study NRCFTs that are Galilean invariant. Discrete light cone quantization (DLCQ) of N = 4 super Yang-Mills theory is an example of such a system with z = 2 scaling symmetry. A more realistic example of a system with the same set of symmetries is a system of cold fermions at unitarity. These non-relativistic systems respect a symmetry algebra known as the Schrodinger algebra. We propose a gravity dual that realizes the symmetries of the Schrodinger algebra as isometries. An unusual feature of this duality is that the bulk geometry has two extra dimensions than the CFT, instead of the usual one. The additional direction is a compact direction and shift symmetry along this direction corresponds to the particle number transformation. This solution can be embedded into string theory by performing a set of operations (known as the Null-Melvin twist) on AdS 5 x S5 solution of type IIB supergravity. This method also provides a way of finding a black hole solution which has asymptotic Schrodinger symmetries. The field theory dual of these gravity solutions happens to be a modified version of DLCQ N = 4 super Yang-Mills theory. The thermodynamics of these theories is very different from that of cold atoms. This happens to be a consequence of realizing the entire Schrodinger group as isometries of the spacetime. We give an example of a holographic realization in which the particle number symmetry is realized as
Vortex dynamics in nonrelativistic Abelian Higgs model
NASA Astrophysics Data System (ADS)
Kozhevnikov, A. A.
2015-11-01
The dynamics of the gauge vortex with arbitrary form of a contour is considered in the framework of the nonrelativistic Abelian Higgs model, including the possibility of the gauge field interaction with the fermion asymmetric background. The equations for the time derivatives of the curvature and the torsion of the vortex contour generalizing the Betchov-Da Rios equations in hydrodynamics, are obtained. They are applied to study the conservation of helicity of the gauge field forming the vortex, twist, and writhe numbers of the vortex contour. It is shown that the conservation of helicity is broken when both terms in the equation of the vortex motion are present, the first due to the exchange of excitations of the phase and modulus of the scalar field and the second one due to the coupling of the gauge field forming the vortex, with the fermion asymmetric background.
GRB afterglows in the nonrelativistic phase
NASA Astrophysics Data System (ADS)
Huang, Y. F.; Lu, T.
2008-10-01
When discussing the afterglows of gamma-ray bursts analytically, it is usually assumed that the external shock is always ultra-relativisitc, with the bulk Lorentz factor much larger than 1. However, we show that the deceleration of the external shock is actually very quick. The afterglow may typically enter the nonrelativistic phase in several days to teens of days, and may even enter the deep Newtonian phase in tens of days to several months. One thus should be careful in using those familiar analytical expressions that are derived only under the ultra-relativistic assumption. To explain the observed afterglows that typically last for a few weeks to several months, we need to consider the dynamics and radiation in the nonrelativisitic phase.
Extended Galilean symmetries of non-relativistic strings
NASA Astrophysics Data System (ADS)
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.
Operator ordering problem of the nonrelativistic Chern-Simons theory
Park, M.; Park, Y. )
1994-12-15
The operator ordering problem due to the quantization or regularization ambiguity in the Chern-Simons theory exists. However, we show that this can be avoided if we require Galilei covariance of the nonrelativistic Abelian Chern-Simons theory even at the quantum level for the extended sources. The covariance can be recovered only by choosing some particular operator orderings for the generators of the Galilei group depending on the quantization ambiguities of the gauge-matter commutation relation. We show that the desired ordering for the unusual prescription is not the same as the well-known normal ordering but still satisfies all the necessary conditions. Furthermore we show that the equations of motion can be expressed in a similar form regardles of the regularization ambiguity. This suggests that the different regularization prescriptions do not change the physics. On the other hand, for the case of point sources the regularization prescription is uniquely determined, and only the orderings, which are equivalent to the usual one, are allowed.
Path integral polymer propagator of relativistic and nonrelativistic particles
NASA Astrophysics Data System (ADS)
Morales-Técotl, Hugo A.; Rastgoo, Saeed; Ruelas, Juan C.
2017-03-01
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 and as a new result we obtain the polymer propagator of the relativistic particle. All of them reduce to their standard form in the continuum limit for which the length scale parameter of the polymer quantization is taken to be small. Our results are robust thanks to their analytic and exact character which in turn come from the fact that presented models are solvable. They lend support to the vertex expansion scheme of the polymer path integral explored before in a formal way for cosmological models. Some possible future developments are commented upon in the discussion.
Nonrelativistic anti-Snyder model and some applications
NASA Astrophysics Data System (ADS)
Ching, C. L.; Yeo, C. X.; Ng, W. K.
2017-01-01
In this paper, we examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the nonrelativistic anti-Snyder model which is relevant to doubly/deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigensolutions 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 nmax due to the orthogonality of the polynomials and the maximum energy is truncated at nmax. 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 β → 0. By taking m → 0, we explore the motion of effective massless charged fermions in graphene-like material and obtained a maximum bound of deformed parameter βmax. Furthermore, we consider the modified energy dispersion relations and its application in describing the behavior of neutrinos oscillation under modified commutation relations.
Isotropic Landau levels of relativistic and non-relativistic fermions in 3D flat space
NASA Astrophysics Data System (ADS)
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.
Thermodynamics of the QCD[sub 1+1] nonrelativistic baryon gas
Engelhardt, M. )
1994-12-01
The nonrelativistic baryon gas of QCD[sub 1+1] for SU(2) color is studied in the low density regime using two complementary approaches: In the classical limit, the Gibbs free energy can be evaluated analytically, yielding an exact value for the second virial coefficient and a bound for the equation of state at higher densities. Certain thermodynamic observables can already be given for the entire range of densities due to simple scaling properties. On the other hand, a quantum mechanical baryon-baryon scattering calculation yields the behavior of the second virial coefficient away from the classical limit down to low temperatures.
Ab initio non-relativistic spin dynamics
Ding, Feizhi; Goings, Joshua J.; Li, Xiaosong; Frisch, Michael J.
2014-12-07
Many magnetic materials do not conform to the (anti-)ferromagnetic paradigm where all electronic spins are aligned to a global magnetization axis. Unfortunately, most electronic structure methods cannot describe such materials with noncollinear electron spin on account of formally requiring spin alignment. To overcome this limitation, it is necessary to generalize electronic structure methods and allow each electron spin to rotate freely. Here, we report the development of an ab initio time-dependent non-relativistic two-component spinor (TDN2C), which is a generalization of the time-dependent Hartree-Fock equations. Propagating the TDN2C equations in the time domain allows for the first-principles description of spin dynamics. A numerical tool based on the Hirshfeld partitioning scheme is developed to analyze the time-dependent spin magnetization. In this work, we also introduce the coupling between electron spin and a homogenous magnetic field into the TDN2C framework to simulate the response of the electronic spin degrees of freedom to an external magnetic field. This is illustrated for several model systems, including the spin-frustrated Li{sub 3} molecule. Exact agreement is found between numerical and analytic results for Larmor precession of hydrogen and lithium atoms. The TDN2C method paves the way for the ab initio description of molecular spin transport and spintronics in the time domain.
Nonrelativistic theory of heavy-ion collisions
Bertsch, G.
1984-07-17
A wide range of phenomena is observed in heavy-ion collisions, calling for a comprehensive theory based on fundamental principles of many-particle quantum mechanics. At low energies, the nuclear dynamics is controlled by the mean field, as we know from spectroscopic nuclear physics. We therefore expect the comprehensive theory of collisions to contain mean-field theory at low energies. The mean-field theory is the subject of the first lectures in this chapter. This theory can be studied quantum mechanically, in which form it is called TDHF (time-dependent Hartree-Fock), or classically, where the equation is called the Vlasov equation. 25 references, 14 figures.
NASA Astrophysics Data System (ADS)
Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen
2015-07-01
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
Massless ghost pole in chromodynamics and the solution of the U/sub 1/ problem
D'yakonov, D.I.; Eides, M.I.
1981-08-01
An analysis of the U/sub 1/ problem (which consists, in particular, in the absence of a ninth light pseudoscalar meson) from the point of view of quantum chromodynamics (QCD) leads to the conclusion that the theory should contain a massless pole in some of the gauge-invariant quantities. The nature of this pole is new to particle physics: it is connected with the periodicity of the OCD potential energy with respect to a certain ''generalized'' coordinate and to the possibility of ''free motion'' of the system with respect to a certain coordinate. Owing to the axial anomaly, mixing takes the place of the ghost with light (pseudo-Goldstone) quark-antiquark states; diagonalization gives rise to physical eta and gh' mesons, and the large mass of the latter is determined mainly by the mixing amplitude. The masses of the eta and eta' mesons are calculated, and certain amplitudes of the processes in which they take part agree well with experiment.
Physical stress, mass, and energy for non-relativistic matter
NASA Astrophysics Data System (ADS)
Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.
2017-06-01
For theories of relativistic matter fields 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.
Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories
Bagchi, Arjun
2010-10-22
We find a surprising connection between asymptotically flat spacetimes and nonrelativistic conformal systems in one lower dimension. The Bondi-Metzner-Sachs (BMS) group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is known to be infinite dimensional in three and four dimensions. We show that the BMS algebra in 3 dimensions is the same as the 2D Galilean conformal algebra (GCA) which is of relevance to nonrelativistic conformal symmetries. We further justify our proposal by looking at a Penrose limit on a radially infalling null ray inspired by nonrelativistic scaling and obtain a flat metric. The BMS{sub 4} algebra is also discussed and found to be the same as another class of GCA, called semi-GCA, in three dimensions. We propose a general BMS-GCA correspondence. Some consequences are discussed.
Spinors in non-relativistic Chern{endash}Simons electrodynamics
Duval, C.; Horvathy, P.A.; Palla, L.
1996-07-01
It is shown that the non-relativistic {open_quote}{open_quote}Dirac{close_quote}{close_quote} equation of L{acute e}vy-Leblond, we used recently to describe a spin 1/2 field interacting non-relativistically with a Chern{endash}Simons gauge field, can be obtained by lightlike reduction from 3+1 dimensions. This allows us to prove that the system is Schr{umlt o}dinger symmetric. A spinor representation of the Schr{umlt o}dinger group is presented. Static, self-dual solutions, describing spinor vortices are given and shown to be the nonrelativistic limits of the fermionic vortices found by Cho {ital et} {ital al}. The construction is extended to external harmonic and uniform magnetic fields. Copyright {copyright} 1996 Academic Press, Inc.
Nonrelativistic equations of motion for particles with arbitrary spin
Fushchich, V.I.; Nikitin, A.G.
1981-09-01
First- and second-order Galileo-invariant systems of differential equations which describe the motion of nonrelativistic particles of arbitrary spin are derived. The equations can be derived from a Lagrangian and describe the dipole, quadrupole, and spin-orbit interaction of the particles with an external field; these interactions have traditionally been regarded as purely relativistic effects. The problem of the motion of a nonrelativistic particle of arbitrary spin in a homogeneous magnetic field is solved exactly on the basis of the obtained equations. The generators of all classes of irreducible representations of the Galileo group are found.
Nonrelativistic approaches derived from point-coupling relativistic models
Lourenco, O.; Dutra, M.; Delfino, A.; Sa Martins, J. S.
2010-03-15
We construct nonrelativistic versions of relativistic nonlinear hadronic point-coupling models, based on new normalized spinor wave functions after small component reduction. These expansions give us energy density functionals that can be compared to their relativistic counterparts. We show that the agreement between the nonrelativistic limit approach and the Skyrme parametrizations becomes strongly dependent on the incompressibility of each model. We also show that the particular case A=B=0 (Walecka model) leads to the same energy density functional of the Skyrme parametrizations SV and ZR2, while the truncation scheme, up to order {rho}{sup 3}, leads to parametrizations for which {sigma}=1.
Renormalization group analysis in nonrelativistic QCD for colored scalars
Hoang, Andre H.; Ruiz-Femenia, Pedro
2006-01-01
The velocity nonrelativistic QCD Lagrangian for colored heavy scalar fields in the fundamental representation of QCD and the renormalization group analysis of the corresponding operators are presented. The results are an important ingredient for renormalization group improved computations of scalar-antiscalar bound state energies and production rates at next-to-next-to-leading-logarithmic (NNLL) order.
Spinor vortices in nonrelativistic Chern-Simons theory
Duval, C.; Horvathy, P.A.; Palla, L.
1995-10-15
The nonrelativistic ``Dirac`` equation of Levy-Leblond is used to describe a spin-1/2 particle interacting with a Chern-Simons gauge field. Static, purely magnetic, self-dual spinor vortices are constructed. The solution can be ``exported`` to a uniform magnetic background field.
Fields and fluids on curved non-relativistic spacetimes
NASA Astrophysics Data System (ADS)
Geracie, Michael; Prabhu, Kartik; Roberts, Matthew M.
2015-08-01
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 we write down the most general theory of dissipative fluids consistent with the second law in curved non-relativistic geometries and find significant differences in the allowed transport coefficients from those found previously. Kubo formulas for all response coefficients are presented. 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 relation to non-relativistic limits may be found in a companion paper.
Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
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 quantum measurement of time
NASA Technical Reports Server (NTRS)
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.
Holography of Non-relativistic String on AdS{sub 5}xS{sup 5}
Sakaguchi, Makoto; Yoshida, Kentaroh
2008-11-23
We review a holography of a non-relativistic (NR) string on AdS{sub 5}xS{sup 5}. The NR string can be regarded as a semiclassical string around an AdS{sub 2} classical solution, which corresponds to a straight Wilson line in the gauge-theory side. Non-normalizable modes of the NR string correspond to string fluctuations reaching the boundary, and cause small deformations of the Wilson line. The operator inserted on the Wilson line are found from the small deformation of the Wilson line. Normalizable modes, which exist in the Lorentzian case, are considered as wave functions in a conformal quantum mechanics.
Generalized dilatation operator method for non-relativistic holography
NASA Astrophysics Data System (ADS)
Chemissany, Wissam; Papadimitriou, Ioannis
2014-10-01
We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent z and any value of the hyperscaling violation parameter θ compatible with the null energy condition. The objective of the algorithm is the construction of the general asymptotic solution of the radial Hamilton-Jacobi equation subject to the desired boundary conditions, from which the full dictionary can be subsequently derived. Contrary to the relativistic case, we find that a fully covariant construction of the asymptotic solution for running non-relativistic theories necessitates an expansion in the eigenfunctions of two commuting operators instead of one. This provides a covariant but non-relativistic grading of the expansion, according to the number of time derivatives.
Enforcing causality in nonrelativistic equations of state at finite temperature
NASA Astrophysics Data System (ADS)
Constantinou, Constantinos; Prakash, Madappa
2017-05-01
We present a thermodynamically consistent method by which equations of state based on nonrelativistic potential models can be modified so that they respect causality at high densities, both at zero and finite temperature (entropy). We illustrate the application of the method by using the high-density phase parametrization of the well-known Akmal-Pandharipande-Ravenhall model in its pure neutron matter configuration as an example. We also show that, for models with only contact interactions, the adiabatic speed of sound is independent of the temperature in the limit of very large temperature. This feature is approximately valid for models with finite-range interactions as well, insofar as the temperature dependence they introduce to the Landau effective mass is weak. In addition, our study reveals that in first-principle nonrelativistic models of hot and dense matter, contributions from higher-than-two-body interactions must be screened at high density to preserve causality.
Unitary Fermi Gas, ɛ Expansion, and Nonrelativistic Conformal Field Theories
NASA Astrophysics Data System (ADS)
Nishida, Yusuke; Son, Dam Thanh
We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the ɛ expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle cum, and the criticl temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.
Cyclotron resonance in topological insulators: non-relativistic effects
NASA Astrophysics Data System (ADS)
Tabert, C. J.; Carbotte, J. P.
2015-09-01
The low-energy Hamiltonian used to describe the dynamics of the helical Dirac fermions on the surface of a topological insulator contains a subdominant non-relativistic (Schrödinger) contribution. This term can have an important effect on some properties while having no effect on others. The Hall plateaus retain the same relativistic quantization as the pure Dirac case. The height of the universal interband background conductivity is unaltered, but its onset is changed. However, the non-relativistic term leads directly to particle-hole asymmetry. It also splits the interband magneto-optical lines into doublets. Here, we find that, while the shape of the semiclassical cyclotron resonance line is unaltered, the cyclotron frequency and its optical spectral weight are changed. There are significant differences in both of these quantities for a fixed value of chemical potential or fixed doping away from charge neutrality depending on whether the Fermi energy lies in the valence or conduction band.
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Geracie, Michael Prabhu, Kartik Roberts, Matthew M.
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.
Are non-relativistic neutrinos the dark matter particles?
NASA Astrophysics Data System (ADS)
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
Filamentation instability in a quantum magnetized plasma
Bret, A.
2008-02-15
The filamentation instability occurring when a nonrelativistic electron beam passes through a quantum magnetized plasma is investigated by means of a cold quantum magnetohydrodynamic model. It is proved that the instability can be completely suppressed by quantum effects if and only if a finite magnetic field is present. A dimensionless parameter is identified that measures the strength of quantum effects. Strong quantum effects allow for a much smaller magnetic field to suppress the instability than in the classical regime.
Spin- and velocity-dependent nonrelativistic potentials in modified electrodynamics
NASA Astrophysics Data System (ADS)
de Brito, G. P.; Malta, P. C.; Ospedal, L. P. R.
2017-01-01
We investigate the interparticle potential between spin-0, spin-1 /2 , and spin-1 sources interacting in modified electrodynamics in the nonrelativistic regime. By keeping terms of O (|p |2/m2) in the amplitudes, we obtain spin- and velocity-dependent interaction energies. We find well-known effects such as spin-orbit couplings, as well as spin-spin (dipole-dipole) interactions. For concreteness, we consider the cases of electrodynamics with higher derivatives (Podolsky-Lee-Wick) and hidden photons.
Conservation of energy and momentum in nonrelativistic plasmas
Sugama, H.; Watanabe, T.-H.; Nunami, M.
2013-02-15
Conservation laws of energy and momentum for nonrelativistic plasmas are derived from applying Noether's theorem to the action integral for the Vlasov-Poisson-Ampere system [Sugama, Phys. Plasmas 7, 466 (2000)]. The symmetric pressure tensor is obtained from modifying the asymmetric canonical pressure tensor with using the rotational symmetry of the action integral. Differences between the resultant conservation laws and those for the Vlasov-Maxwell system including the Maxwell displacement current are clarified. These results provide a useful basis for gyrokinetic conservation laws because gyrokinetic equations are derived as an approximation of the Vlasov-Poisson-Ampere system.
Interplay of nonrelativistic and relativistic effects in neutrino oscillations
Ahluwalia, D.V.; Goldman, T.
1997-08-01
A theoretical structure that involves neutrino mass eigenstates at nonrelativistic as well as relativistic energies is presented. Using this framework, we find that if the particle X, with a mass 33.9 MeV, of the KARMEN Collaboration anomaly is identified with the third neutrino mass eigenstate, then the present limit of 23 MeV upper bound on the {tau} neutrino mass implies {vert_bar}U{sub {tau}3}{vert_bar}{lt}0.82. {copyright} {ital 1997} {ital The American Physical Society}
Non-relativistic Bondi–Metzner–Sachs algebra
NASA Astrophysics Data System (ADS)
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.
General theory for Rydberg states of atoms: The nonrelativistic case
NASA Astrophysics Data System (ADS)
Wang, Xiao-Feng; Yan, Zong-Chao
2017-02-01
We carry out a complete derivation on nonrelativistic energies of atomic Rydberg states, including finite nuclear mass corrections. Several missing terms are found and a discrepancy is confirmed in the works of Drachman [in Long Range Casimir Forces: Theory and Recent Experiments on Atomic Systems, edited by F. S. Levin and D. A. Micha (Plenum, New York, 1993)] and Drake [Adv. At., Mol., Opt. Phys. 31, 1 (1993)]., 10.1016/S1049-250X(08)60087-7 As a benchmark, we present a detailed tabulation of different energy levels.
On the dynamics of non-relativistic flavor-mixed particles
Medvedev, Mikhail V.
2014-06-01
Evolution of a system of interacting non-relativistic quantum flavor-mixed particles is considered both theoretically and numerically. It was shown that collisions of mixed particles not only scatter them elastically, but can also change their mass eigenstates thus affecting particles' flavor composition and kinetic energy. The mass eigenstate conversions and elastic scattering are related but different processes, hence the conversion S-matrix elements can be arbitrarily large even when the elastic scattering S-matrix elements vanish. The conversions are efficient when the mass eigenstates are well-separated in space but suppressed if their wave-packets overlap; the suppression is most severe for mass-degenerate eigenstates in flat space-time. The mass eigenstate conversions can lead to an interesting process, called ''quantum evaporation'', in which mixed particles, initially confined deep inside a gravitational potential well and scattering only off each other, can escape from it without extra energy supply leaving nothing behind inside the potential at t → ∞. Implications for the cosmic neutrino background and the two-component dark matter model are discussed and a prediction for the direct detection dark matter experiments is made.
NASA Astrophysics Data System (ADS)
Elbaz, Edgard
This book gives a new insight into the interpretation of quantum mechanics (stochastic, integral paths, decoherence), a completely new treatment of angular momentum (graphical spin algebra) and an introduction to Fermion fields (Dirac equation) and Boson fields (e.m. and Higgs) as well as an introduction to QED (quantum electrodynamics), supersymmetry and quantum cosmology.
Communication: Quantum mechanics without wavefunctions
Schiff, Jeremy; Poirier, Bill
2012-01-21
We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.
Decoherence of quantum states in QCD vacuum
NASA Astrophysics Data System (ADS)
Kuvshinov, V.; Bagashov, E.
2017-09-01
The stochastic vacuum of quantum chromodynamics is used as an environment for quarks considered as color state vectors. It is shown that during interaction with the stochastic vacuum information of the quark color state is lost with time (decoherence of the quark state vector occurs), which effectively means that it is impossible to observe the quark as a free color particle (confinement).
Interfacing Relativistic and Nonrelativistic Methods: A Systematic Sequence of Approximations
NASA Technical Reports Server (NTRS)
Dyall, Ken; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
A systematic sequence of approximations for the introduction of relativistic effects into nonrelativistic molecular finite-basis set calculations is described. The theoretical basis for the approximations is the normalized elimination of the small component (ESC) within the matrix representation of the modified Dirac equation. The key features of the normalized method are the retention of the relativistic metric and the ability to define a single matrix U relating the pseudo-large and large component coefficient matrices. This matrix is used to define a modified set of one- and two-electron integrals which have the same appearance as the integrals of the Breit-Pauli Hamiltonian. The first approximation fixes the ratios of the large and pseudo-large components to their atomic values, producing an expansion in atomic 4-spinors. The second approximation defines a local fine-structure constant on each atomic centre, which has the physical value for centres considered to be relativistic and zero for nonrelativistic centres. In the latter case, the 4-spinors are the positive-energy kinetic al ly-balanced solutions of the Levy-Leblond equation, and the integrals involving pseudo-large component basis functions on these centres, are set to zero. Some results are presented for test systems to illustrate the various approximations.
Extended Klein-Gordon action, gravity and nonrelativistic fluid
Hassaiene, Mokhtar
2006-03-15
We consider a scalar field action for which the Lagrangian density is a power of the massless Klein-Gordon Lagrangian. The coupling of gravity to this matter action is considered. In this case, we show the existence of nontrivial scalar field configurations with vanishing energy-momentum tensor on any static, spherically symmetric vacuum solutions of the Einstein equations. These configurations in spite of being coupled to gravity do not affect the curvature of space-time. The properties of this particular matter action are also analyzed. For a particular value of the exponent, the extended Klein-Gordon action is shown to exhibit a conformal invariance without requiring the introduction of a nonminimal coupling. We also establish a correspondence between this action and a nonrelativistic isentropic fluid in one fewer dimension. This fluid can be identified with the (generalized) Chaplygin gas for a particular value of the power. It is also shown that the nonrelativistic fluid admits, apart from the Galileo symmetry, an additional symmetry whose action is a rescaling of the time.
The relation between relativistic and non-relativistic continuum thermodynamics
NASA Astrophysics Data System (ADS)
Schellstede, G. O.; von Borzeszkowski, H.-H.; Chrobok, T.; Muschik, W.
2014-01-01
We consider the relativistic theory of irreversible processes with the aim to answer the following questions: (1) Under which conditions is this theory a relativistic generalization of the non-relativistic theory of irreversible processes (in particular, this implies to ask for the conditions under which the first law of thermodynamics can be recovered from the relativistic conservation law of total energy), and (2) how do the relativistic corrections look like? To this end, we perform a low-energy approximation for the balance equations underlying the theory, i.e., for the balances of the particle number, the energy-momentum and the entropy. It is shown that, going up to the 3rd order in the expansion series of the balances, the non-relativistic theory can be derived when one assumes that the 4-current of the particle flow is purely convective and the product of the 3-dimensional acceleration and velocity is equal to zero. Afterwards, the higher-order terms are discussed. Since our discussion mainly makes use of those balance equations that lie on the basis of most versions of continuum thermodynamics, the results do not only refer to early TIP presented by Eckart (Phys Rev 58:919,
Three-hair relations for rotating stars: Nonrelativistic limit
Stein, Leo C.; Yagi, Kent; Yunes, Nicolás
2014-06-10
The gravitational field outside of astrophysical black holes is completely described by their mass and spin frequency, as expressed by the no-hair theorems. These theorems assume vacuum spacetimes, and thus they apply only to black holes and not to stars. Despite this, we analytically find that the gravitational potential of arbitrarily rapid, rigidly rotating stars can still be described completely by only their mass, spin angular momentum, and quadrupole moment. Although these results are obtained in the nonrelativistic limit (to leading order in a weak-field expansion of general relativity, GR), they are also consistent with fully relativistic numerical calculations of rotating neutron stars. This description of the gravitational potential outside the source in terms of just three quantities is approximately universal (independent of equation of state). Such universality may be used to break degeneracies in pulsar and future gravitational wave observations to extract more physics and test GR in the strong-field regime.
Ultrahigh energy cosmic rays from nonrelativistic quasar outflows
NASA Astrophysics Data System (ADS)
Wang, Xiawei; Loeb, Abraham
2017-03-01
It has been suggested that nonrelativistic outflows from quasars can naturally account for the missing component of the extragalactic γ -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 ˜1020 eV during the early phase of their propagation. The overall quasar population is expected to produce a cumulative ultrahigh energy cosmic-ray flux of ˜10-7 GeV cm-2 s-1 sr-1 at ECR≳1018 eV . The spectral shape and amplitude are consistent with recent observations for outflow parameters constrained to fit secondary γ rays and neutrinos without any additional parameter tuning. This indicates that quasar outflows simultaneously account for all three messengers at their observed levels.
Cheat sensitive quantum bit commitment.
Hardy, Lucien; Kent, Adrian
2004-04-16
We define cheat sensitive cryptographic protocols between mistrustful parties as protocols which guarantee that, if either cheats, the other has some nonzero probability of detecting the cheating. We describe an unconditionally secure cheat sensitive nonrelativistic bit commitment protocol which uses quantum information to implement a task which is classically impossible; we also describe a simple relativistic protocol.
Continuity properties of the semi-group and its integral kernel in non-relativistic QED
NASA Astrophysics Data System (ADS)
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.
Values of dimensional quantities from Monte Carlo calculations in quantum chromodynamics
Makeenko, Y.M.; Polikarpov, M.I.
1983-10-25
An expression is derived for ..lambda../sub L/(..beta..) to describe the behavior of the Monte Carlo data on the string tension coefficient in the transition region in the SU(3) lattice gauge theory. This expression leads to a 25% increase in ..lambda../sub mom/, while there are no changes in the other dimensional quantities (the deconfinement temperature, for example) found by the Monte Carlo method.
The BlueGene/L Supercomputer and Quantum ChromoDynamics
Vranas, P; Soltz, R
2006-10-19
In summary our update contains: (1) Perfect speedup sustaining 19.3% of peak for the Wilson D D-slash Dirac operator. (2) Measurements of the full Conjugate Gradient (CG) inverter that inverts the Dirac operator. The CG inverter contains two global sums over the entire machine. Nevertheless, our measurements retain perfect speedup scaling demonstrating the robustness of our methods. (3) We ran on the largest BG/L system, the LLNL 64 rack BG/L supercomputer, and obtained a sustained speed of 59.1 TFlops. Furthermore, the speedup scaling of the Dirac operator and of the CG inverter are perfect all the way up to the full size of the machine, 131,072 cores (please see Figure II). The local lattice is rather small (4 x 4 x 4 x 16) while the total lattice has been a lattice QCD vision for thermodynamic studies (a total of 128 x 128 x 256 x 32 lattice sites). This speed is about five times larger compared to the speed we quoted in our submission. As we have pointed out in our paper QCD is notoriously sensitive to network and memory latencies, has a relatively high communication to computation ratio which can not be overlapped in BGL in virtual node mode, and as an application is in a class of its own. The above results are thrilling to us and a 30 year long dream for lattice QCD.
Inclusive jet production at the tevatron collider in the Regge limit of quantum chromodynamics
NASA Astrophysics Data System (ADS)
Saleev, V. A.; Shipilova, A. V.; Yatsenko, E. V.
2012-03-01
We consider the inclusive hadroproduction of jets, prompt photons, and b-quark jets in the quasimulti-Regge kinematics approach based on the hypothesis of gluon and quark reggeization in t-channel exchanges at high energies. The data taken by CDF and D0 collaborations at the Fermilab Tevatron collider are well described in the region of x_T = 2p_T /sqrt s lesssim 0.1 without the introduction of any free parameters. In numeric calculations we use the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark distribution functions with Martin-Roberts-Stirling-Thorne collinear parton distribution functions taken as input.
NASA Technical Reports Server (NTRS)
Applegate, J. H.; Hogan, Craig J.; Scherrer, R. J.
1988-01-01
A simple one-dimensional model is used to describe the evolution of neutron density before and during nucleosynthesis in a high-entropy bubble left over from the cosmic quark-hadron phase transition. It is shown why cosmic nucleosynthesis in such a neutron-rich environment produces a surfeit of elements heavier than lithium. Analytical and numerical techniques are used to estimate the abundances of carbon, nitrogen, and heavier elements up to Ne-22. A high-density neutron-rich region produces enough primordial N-14 to be observed in stellar atmospheres. It shown that very heavy elements may be created in a cosmological r-process; the neutron exposure in the neutron-rich regions is large enough for the Ne-22 to trigger a catastrophic r-process runaway in which the quantity of heavy elements doubles in much less than an expansion time due to fission cycling. A primordial abundance of r-process elements is predicted to appear as an excess of rare earth elements in extremely metal-poor stars.
Hyperon-Nucleon Interactions and the Composition of Dense Matter from Quantum Chromodynamics
Konstantinos Orginos, Silas Beane, Emmanuel Chang, Saul Cohen, Huey-Wen Lin, Tom Luu, Assumpta Parreno, Martin Savage, Andre Walker-Loud, William Detmold
2012-10-01
The low-energy n{Sigma}{sup -} interactions determine, in part, the role of the strange quark in dense matter, such as that found in astrophysical environments. The scattering phase-shifts for this system are determined from a numerical evaluation of the QCD path integral using the technique of Lattice QCD. Our results, performed at a pion mass of m{sub {pi}} ~ 389 MeV in two large lattice volumes, and at one lattice spacing, are extrapolated to the physical pion mass using effective field theory. The calculated interactions indicate that the strange quark plays an important role in dense matter.
NASA Technical Reports Server (NTRS)
Applegate, J. H.; Hogan, Craig J.; Scherrer, R. J.
1988-01-01
A simple one-dimensional model is used to describe the evolution of neutron density before and during nucleosynthesis in a high-entropy bubble left over from the cosmic quark-hadron phase transition. It is shown why cosmic nucleosynthesis in such a neutron-rich environment produces a surfeit of elements heavier than lithium. Analytical and numerical techniques are used to estimate the abundances of carbon, nitrogen, and heavier elements up to Ne-22. A high-density neutron-rich region produces enough primordial N-14 to be observed in stellar atmospheres. It shown that very heavy elements may be created in a cosmological r-process; the neutron exposure in the neutron-rich regions is large enough for the Ne-22 to trigger a catastrophic r-process runaway in which the quantity of heavy elements doubles in much less than an expansion time due to fission cycling. A primordial abundance of r-process elements is predicted to appear as an excess of rare earth elements in extremely metal-poor stars.
Tests of quantum chromodynamics in exclusive e sup + e sup minus and. gamma. gamma. processes
Brodsky, S.J.
1989-09-01
This paper discusses the following topics: Factorization theorem for exclusive processes; Electromagnetic form factors of baryons; Suppression of final state interactions; The {gamma}{pi}{sub 0} Transition form factor; Exclusive charmonium decays; The {pi}-{rho} puzzle; Time-like compton processes; Multi-hadron production; Heavy Quark exclusive states and form factor zeros in QCD; Exclusive {gamma}{gamma} reactions; Higher twist effects; and Tauonium and threshold {tau}{sup +}{tau}{sup {minus}} production. 41 refs., 15 figs. (LSP)
Experimental results on QCD (Quantum Chromodynamics) from e/sup +/e/sup -/ annihilation
de Boer, W.
1987-09-01
A review is given on QCD results from studying e/sup +/e/sup -/ annihilation with the PEP and PETRA storage rings with special emphasis on jet physics and the determination of the strong coupling constant ..cap alpha../sub s/. 92 refs., 28 figs., 3 tabs.
Large-angle two-photon exclusive channels in quantum chromodynamics
Brodsky, S.J.; Lepage, G.P.
1981-05-01
Detailed leading order QCD predictions are given for the scaling, angular, and helicity dependence of the reactions ..gamma gamma.. ..-->.. M anti M (M = ..pi.., K, rho, etc.) at large momentum transfer. In addition to providing a basic test of QCD at short distances, measurements can be used to determine the process-independent meson distribution amplitudes phi/sub M/(x,Q). Other related two-photon channels such as ..gamma gamma.. ..-->.. ..gamma..rho, ..gamma..*..gamma.. ..-->.. ..pi../sup 0/, eta/sup 0/, eta' and eta/sub c/ ..-->.. ..gamma gamma.. are also discussed. The existence of a fixed Regge singularity at J = 0 which couples to ..gamma..rho ..-->.. ..gamma..rho in the t-channel but not ..gamma pi.. ..-->.. ..gamma pi.. is also proved.
Gubser, Steven S.; Nellore, Abhinav; Pufu, Silviu S.; Rocha, Fabio D.
2008-09-26
We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio {zeta}/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first-order transition, we observe a sharp rise in {zeta}/s near T{sub c}. For constructions that exhibit a smooth crossover, like QCD does, the rise in {zeta}/s is more modest. We conjecture that divergences in {zeta}/s for black hole horizons are related to extrema of the entropy density as a function of temperature.
NASA Astrophysics Data System (ADS)
Atkinson, D.; Drohm, J. K.; Johnson, P. W.; Stam, K.
1981-11-01
An approximated form of the Dyson-Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that these have a double pole at the origin of the square of the propagator momentum, together with an accumulation of soft branch points. This analytic structure is strongly suggestive of confinement by infrared slavery.
Exclusive Processes in Quantum Chromodynamics and the Light-Cone Fock Representation
Brodsky, Stanley J.
2000-12-07
Exclusive processes provide a window into the bound state structure of hadrons in QCD as well as the fundamental processes which control hadron dynamics at the amplitude level. The natural calculus for describing bound state structure of relativistic composite systems needed for describing exclusive amplitudes is the light-cone Fock expansion which encodes the multi-quark, gluonic, and color correlations of a hadron in terms of frame-independent wavefunctions. In hard exclusive processes in which hadrons receive a large momentum transfer, perturbative QCD leads to factorization theorems which separate the physics of bound state structure from that of the relevant quark and gluonic hard-scattering reactions which underlie these reactions. At leading twist, the bound state physics is encoded in terms of universal ''distribution amplitudes,'' the fundamental theoretical quantities which describe the valence quark substructure of hadrons as well as nuclei. The combination of discretized light-cone quantization and transverse lattice methods are now providing nonperturbative predictions for the pion distribution amplitude. A basic feature of the gauge theory formalism is ''color transparency,'' the absence of initial and final state interactions of rapidly-moving compact color-singlet states. Other applications of the factorization formalism are briefly discussed, including semileptonic B decays, deeply virtual Compton scattering, and dynamical higher twist effects in inclusive reactions. A new type of jet production reaction, ''self-resolving diffractive interactions'' provide empirical constraints on the light-cone wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom.
Danilov, Viatcheslav; Nagaitsev, Sergei; /Fermilab
2011-11-01
Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case. In this paper we have described an extension of the Ermakov-like transformation to the Schroedinger and Pauli equations. It is shown that these newly found transformations create a vast variety of time dependent quantum equations that can be solved in analytic functions, or, at least, can be reduced to time-independent ones.
Semi-classical Locality for the Non-relativistic Path Integral in Configuration Space
NASA Astrophysics Data System (ADS)
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.
Semi-classical Locality for the Non-relativistic Path Integral in Configuration Space
NASA Astrophysics Data System (ADS)
Gomes, Henrique
2017-06-01
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}° prO= prO° 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.
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
Commins, Eugene D.
2014-10-01
Preface; 1. Introduction; 2. Mathematical preliminaries; 3. The rules of quantum mechanics; 4. The connection between the fundamental rules and wave mechanics; 5. Further illustrations of the rules of quantum mechanics; 6. Further developments in one-dimensional wave mechanics; 7. The theory of angular momentum; 8. Wave mechanics in three dimensions: hydrogenic atoms; 9. Time-independent approximations for bound state problems; 10. Applications of static perturbation theory; 11. Identical particles; 12. Atomic structure; 13. Molecules; 14. The stability of matter; 15. Photons; 16. Interaction of non-relativistic charged particles and radiation; 17. Further topics in perturbation theory; 18. Scattering; 19. Special relativity and quantum mechanics: the Klein-Gordon equation; 20. The Dirac equation; 21. Interaction of a relativistic spin 1/2 particle with an external electromagnetic field; 22. The Dirac field; 23. Interaction between relativistic electrons, positrons, and photons; 24. The quantum mechanics of weak interactions; 25. The quantum measurement problem; Appendix A: useful inequalities for quantum mechanics; Appendix B: Bell's inequality; Appendix C: spin of the photon: vector spherical waves; Works cited; Bibliography; Index.
NASA Astrophysics Data System (ADS)
De, Sanchari; Ghosh, Sutapa; Chakrabarty, Somenath
2015-11-01
In the conventional scenario, the Hawking radiation is believed to be a tunneling process at the event horizon of the black hole. In the quantum field theoretic approach the Schwinger's mechanism is generally used to give an explanation of this tunneling process. It is the decay of quantum vacuum into particle anti-particle pairs near the black hole surface. However, in a reference frame undergoing a uniform accelerated motion in an otherwise flat Minkowski space-time geometry, in the non-relativistic approximation, the particle production near the event horizon of a black hole may be treated as a kind of Fowler-Nordheim field emission, which is the typical electron emission process from a metal surface under the action of an external electrostatic field. This type of emission from metal surface is allowed even at extremely low temperature. It has been noticed that in one-dimensional scenario, the Schrödinger equation satisfied by the created particle (anti-particle) near the event horizon, can be reduced to a differential form which is exactly identical with that obeyed by an electron immediately after the emission from the metal surface under the action of a strong electrostatic field. The mechanism of particle production near the event horizon of a black hole is therefore identified with Schwinger process in relativistic quantum field theory, whereas in the non-relativistic scenario it may be interpreted as Fowler-Nordheim emission process, when observed from a uniformly accelerated frame.
Holographic energy loss in non-relativistic backgrounds
NASA Astrophysics Data System (ADS)
Atashi, Mahdi; Fadafan, Kazem Bitaghsir; Farahbodnia, Mitra
2017-03-01
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 ω in theories with general dynamical exponent z and hyperscaling violation exponent θ . 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 how the total energy loss rate depends non-trivially on two characteristic exponents (z,θ ). We find that at zero temperature there is a special radius l_c where the energy loss is independent of different values of (θ ,z). Also at zero temperature, 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 find that the energy loss of the particle decreases by increasing θ and z. We note that, unlike in the zero temperature, there is no special radius l_c at finite temperature case.
Orbitally Excited States of Quarkonia in a Nonrelativistic Model
NASA Astrophysics Data System (ADS)
Bhaghyesh; Vijaya Kumar, K. B.; Ma, Yong-Liang
Having succeeded in predicting the S wave spectra and decays of cbar {c} and bbar {b} mesons, Bhaghyesh, K. B. Vijaya Kumar and A. P. Monteiro, J. Phys. G: Nucl. Part. Phys. 38, 085001 (2011), in this article, we apply our nonrelativistic quark model to calculate the spectra and decays of the orbitally excited states (P- and D-waves) of heavy quarkonia. The full Qbar {Q} potential used in our model consists of a Hulthen potential and a confining linear potential. The spin hyperfine, spin-orbit and tensor interactions are introduced to obtain the masses of the P- and D-wave states. The three-dimensional harmonic oscillator wave function is employed as a trial wave function to obtain the mass spectra. The model parameters and the wave function that reproduce the mass spectra of cbar {c} and bbar {b} mesons are used to investigate their decay properties. The two-photon decay widths, two-gluon decay widths and E1 radiative decay widths are calculated. The obtained values are compared with the experimental results and those obtained from other theoretical models.
Bosonization of nonrelativistic fermions on a circle: Tomonaga's problem revisited
NASA Astrophysics Data System (ADS)
Dhar, Avinash; Mandal, Gautam
2006-11-01
We use the recently developed tools for an exact bosonization of a finite number N of nonrelativistic fermions to discuss the classic Tomonaga problem. In the case of noninteracting fermions, the bosonized Hamiltonian naturally splits into an O(N) piece and an O(1) piece. We show that in the large-N and low-energy limit, the O(N) piece in the Hamiltonian describes a massless relativistic boson, while the O(1) piece gives rise to cubic self-interactions of the boson. At finite N and high energies, the low-energy effective description breaks down and the exact bosonized Hamiltonian must be used. We also comment on the connection between the Tomonaga problem and pure Yang-Mills theory on a cylinder. In the dual context of baby universes and multiple black holes in string theory, we point out that the O(N) piece in our bosonized Hamiltonian provides a simple understanding of the origin of two different kinds of nonperturbative O(e-N) corrections to the black hole partition function.
Brodsky, S.J.
1983-11-01
A number of novel features of QCD are reviewed, including the consequences of formation zone and color transparency phenomena in hadronic collisions, the use of automatic scale setting for perturbative predictions, null-zone phenomena as a fundamental test of gauge theory, and the relationship of intrinsic heavy colored particle Fock state components to new particle production. We conclude with a review of the applications of QCD to nuclear multiquark systems. 74 references.
The Thomas–Fermi quark model: Non-relativistic aspects
Liu, Quan Wilcox, Walter
2014-02-15
The first numerical investigation of non-relativistic aspects of the Thomas–Fermi (TF) statistical multi-quark model is given. We begin with a review of the traditional TF model without an explicit spin interaction and find that the spin splittings are too small in this approach. An explicit spin interaction is then introduced which entails the definition of a generalized spin “flavor”. We investigate baryonic states in this approach which can be described with two inequivalent wave functions; such states can however apply to multiple degenerate flavors. We find that the model requires a spatial separation of quark flavors, even if completely degenerate. Although the TF model is designed to investigate the possibility of many-quark states, we find surprisingly that it may be used to fit the low energy spectrum of almost all ground state octet and decuplet baryons. The charge radii of such states are determined and compared with lattice calculations and other models. The low energy fit obtained allows us to extrapolate to the six-quark doubly strange H-dibaryon state, flavor symmetric strange states of higher quark content and possible six quark nucleon–nucleon resonances. The emphasis here is on the systematics revealed in this approach. We view our model as a versatile and convenient tool for quickly assessing the characteristics of new, possibly bound, particle states of higher quark number content. -- Highlights: • First application of the statistical Thomas–Fermi quark model to baryonic systems. • Novel aspects: spin as generalized flavor; spatial separation of quark flavor phases. • The model is statistical, but the low energy baryonic spectrum is successfully fit. • Numerical applications include the H-dibaryon, strange states and nucleon resonances. • The statistical point of view does not encourage the idea of bound many-quark baryons.
Quasi-Nambu-Goldstone modes in nonrelativistic systems
NASA Astrophysics Data System (ADS)
Nitta, Muneto; Takahashi, Daisuke A.
2015-01-01
When a continuous symmetry is spontaneously broken in nonrelativistic systems, there appear either type-I or type-II Nambu-Goldstone modes (NGMs) with linear or quadratic dispersion relations, respectively. When the equation of motion or the potential term has an enhanced symmetry larger than that of Lagrangian or Hamiltonian, there can appear quasi-NGMs if it is spontaneously broken. We construct a theory to count the numbers of type-I and type-II quasi-NGMs and NGMs, when the potential term has a symmetry of a noncompact group. We show that the counting rule based on the Watanabe-Brauner matrix is valid only in the absence of quasi-NGMs because of non-Hermitian generators, while that based on the Gram matrix [D. A. Takahashi and M. Nitta, Ann. Phys. (Amsterdam) 354, 101 (2015)] is still valid in the presence of quasi-NGMs. We show that there exist two types of type-II gapless modes, a genuine NGM generated by two conventional zero modes (ZMs) originated from the Lagrangian symmetry, and quasi-NGM generated by a coupling of one conventional ZM and one quasi-ZM, which is originated from the enhanced symmetry, or two quasi-ZMs. We find that, depending on the moduli, some NGMs can change to quasi-NGMs and vice versa with preserving the total number of gapless modes. The dispersion relations are systematically calculated by a perturbation theory. The general result is illustrated by the complex linear O (N ) model, containing the two types of type-II gapless modes and exhibiting the change between NGMs and quasi-NGMs.
NASA Astrophysics Data System (ADS)
Jafarizadeh, M. A.; Sufiani, R.
2008-01-01
Two kinds of Bell-state diagonal (BSD) entanglement witnesses (EWs) are constructed by using the algebra of Dirac γ matrices in a space-time of arbitrary dimension d , where the first kind can detect some BSD relativistic and nonrelativistic m -partite multispinor bound entangled states in a Hilbert space of dimension 2m⌊d/2⌋ , including the bipartite Bell-type and isoconcurrence-type states in four-dimensional space-time (d=4) . By using the connection between the Hilbert-Schmidt measure and the optimal EWs associated with the states, it is shown that, as far as the spin quantum correlations are concerned, the amount of entanglement is not a relativistic scalar and has no invariant meaning. The introduced EWs are manipulated via linear programming (LP) and can be solved exactly by using the simplex method. The decomposability or nondecomposability of these EWs is investigated, the region of nondecomposable EWs of the first kind is partially determined and it is shown that, all of the EWs of the second kind are decomposable. These EWs have the property that in bipartite systems they can determine the region of separable states, i.e., bipartite nondetectable density matrices of the same type as the EWs of the first kind are necessarily separable. Also, multispinor EWs with nonpolygon feasible regions are provided, where the problem is solved by approximate LP, and in contrast to the exactly manipulatable EWs, both the first and second kinds of the optimal approximate EWs can detect some bound entangled states.
NASA Astrophysics Data System (ADS)
Persico, F.; Power, E. A.
1988-01-01
Various papers concerning vacuum in nonrelativistic matter-radiation systems are presented. Among the topics discussed are: squeezing the vacuum in atom-field interactions, unequal time electromagnetic (EM) field commutators in quantum optics, vacuum confinement effects on molecular dynamics in a microscope cavity, canonical state renormalization in photoexcitation, vacuum fluctuations and spontaneous emission in quantum optics, and the role of vacuum fluctuations and spontaneous emission in the laser linewidth. Also considered are: QED of atoms between parallel mirrors, QED based on self-energy, nonlinear structure of the EM vacuum, dressed and half-dressed neutral sources in nonrelativistic QED, detection of half-dressed sources in QED, virtual cloud effects in perturbed atoms, vacuum fluctuations in radiation and matter fields, corrections to the electron-spin magnetic moment near mirrors, the Lamb shift in hydrogen, gauge transformations in semiclassical radiation theory, different ways of looking at the EM vacuum, perturbation of the EM vacuum by atoms and molecules, and vacuum fluctuations and intermolecular interactions.
Relativistic and non-relativistic solitons in plasmas
NASA Astrophysics Data System (ADS)
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
Dirac oscillator and nonrelativistic Snyder-de Sitter algebra
Stetsko, M. M. E-mail: mykola@ktf.franko.lviv.ua
2015-01-15
Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.
A Non-Relativistic Look at the Compton Effect
ERIC Educational Resources Information Center
Feller, Steve; Giri, Sandeep; Zakrasek, Nicholas; Affatigato, Mario
2014-01-01
In a usual modern physics class the Compton effect is used as the pedagogical model for introducing relativity into quantum effects. The shift in photon wavelengths is usually introduced and derived using special relativity. Indeed, this works well for explaining the effect. However, in the senior author's class one of the student coauthors…
A Non-Relativistic Look at the Compton Effect
ERIC Educational Resources Information Center
Feller, Steve; Giri, Sandeep; Zakrasek, Nicholas; Affatigato, Mario
2014-01-01
In a usual modern physics class the Compton effect is used as the pedagogical model for introducing relativity into quantum effects. The shift in photon wavelengths is usually introduced and derived using special relativity. Indeed, this works well for explaining the effect. However, in the senior author's class one of the student coauthors…
A trigonometric sum relevant to the nonrelativistic theory of atoms.
Córdoba, A; Fefferman, C; Seco, L
1994-01-01
We extend Van der Corput's method for exponential sums to study an oscillatory term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations. PMID:11607477
Quantum tasks in Minkowski space
NASA Astrophysics Data System (ADS)
Kent, Adrian
2012-11-01
The fundamental properties of quantum information and its applications to computing and cryptography have been greatly illuminated by considering information-theoretic tasks that are provably possible or impossible within non-relativistic quantum mechanics. I describe here a general framework for defining tasks within (special) relativistic quantum theory and illustrate it with examples from relativistic quantum cryptography and relativistic distributed quantum computation. The framework gives a unified description of all tasks previously considered and also defines a large class of new questions about the properties of quantum information in relation to Minkowski causality. It offers a way of exploring interesting new fundamental tasks and applications, and also highlights the scope for a more systematic understanding of the fundamental information-theoretic properties of relativistic quantum theory.
Correspondence of I- and Q-balls as non-relativistic condensates
Mukaida, Kyohei; Takimoto, Masahiro E-mail: takimoto@hep-th.phys.s.u-tokyo.ac.jp
2014-08-01
If a real scalar field is dominated by non-relativistic modes, then it approximately conserves its particle number and obeys an equation that governs a complex scalar field theory with a conserved global U(1) symmetry. From this fact, it is shown that the I-ball (oscillon) can be naturally understood as a projection (e.g., real part) of the non-relativistic Q-ball solution. In particular, we clarify that the stability of the I-ball is guaranteed by the U(1) symmetry in the corresponding complex scalar field theory as long as the non-relativistic condition holds. We also discuss the longevity of I-ball from the perspective of the complex scalar field in terms of U(1) charge violating processes.
NASA Astrophysics Data System (ADS)
Lai, Sheng-Hong; Lee, Jen-Chi; Yang, Yi
2016-05-01
We review and extend high energy four point string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s- t and t- u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one higher spin string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.
Sadiq, Safeer; Mahmood, S.; Haque, Q.; Ali, Munazza Zulfiqar
2014-09-20
The propagation of electrostatic waves in a dense magnetized electron-positron-ion (EPI) plasma with nonrelativistic and ultrarelativistic degenerate electrons and positrons is investigated. The linear dispersion relation is obtained for slow and fast electrostatic waves in the EPI plasma. The limiting cases for ion acoustic wave (slow) and ion cyclotron wave (fast) are also discussed. Using the reductive perturbation method, two-dimensional propagation of ion acoustic solitons is found for both the nonrelativistic and ultrarelativistic degenerate electrons and positrons. The effects of positron concentration, magnetic field, and mass of ions on ion acoustic solitons are shown in numerical plots. The proper form of Fermi temperature for nonrelativistic and ultrarelativistic degenerate electrons and positrons is employed, which has not been used in earlier published work. The present investigation is useful for the understanding of linear and nonlinear electrostatic wave propagation in the dense magnetized EPI plasma of compact stars. For illustration purposes, we have applied our results to a pulsar magnetosphere.
Remote State Preparation for Quantum Fields
NASA Astrophysics Data System (ADS)
Ber, Ran; Zohar, Erez
2016-07-01
Remote state preparation is generation of a desired state by a remote observer. In spite of causality, it is well known, according to the Reeh-Schlieder theorem, that it is possible for relativistic quantum field theories, and a "physical" process achieving this task, involving superoscillatory functions, has recently been introduced. In this work we deal with non-relativistic fields, and show that remote state preparation is also possible for them, hence obtaining a Reeh-Schlieder-like result for general fields. Interestingly, in the nonrelativistic case, the process may rely on completely different resources than the ones used in the relativistic case.
On the question of symmetries in nonrelativistic diffeomorphism-invariant theories
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Gangopadhyay, Sunandan; Mukherjee, Pradip
2017-07-01
A novel algorithm is provided to couple a Galilean-invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and canonical transformation of the original fields. That the twin requirements are fulfilled is ensured by a new field, the existence of which was demonstrated recently from Galilean gauge theory. The ambiguities and anomalies concerning the recovery of Galilean symmetry in the flat limit of spatial nonrelativistic diffeomorphic theories, reported in the literature, are focused and resolved from a new angle.
Breathers and nonlinear waves on open vortex filaments in the nonrelativistic Abelian Higgs model
NASA Astrophysics Data System (ADS)
Van Gorder, Robert A.
2017-05-01
We demonstrate the existence of various nonlinear waves along open vortex filaments in the nonrelativistic Abelian Higgs model. These include nonlinear waves, which give the birth and death of helical filaments, as well breathers, which modify the amplitude of helical filaments periodically in time. Importantly, we demonstrate that some of the dynamics are quite particular to the equation of motion for vortex filaments under the nonrelativistic Abelian Higgs model, giving rise to vortex filament solutions not possible under the hydrodynamic vortex filament equation of motion (the local induction approximation) or generalizations used to study the dynamics of quantized vortex filaments in He4 .
Galilei invariant technique for quantum system description
Kamuntavičius, Gintautas P.
2014-04-15
Problems with quantum systems models, violating Galilei invariance are examined. The method for arbitrary non-relativistic quantum system Galilei invariant wave function construction, applying a modified basis where center-of-mass excitations have been removed before Hamiltonian matrix diagonalization, is developed. For identical fermion system, the Galilei invariant wave function can be obtained while applying conventional antisymmetrization methods of wave functions, dependent on single particle spatial variables.
Eavesdropping of quantum communication from a noninertial frame
Bradler, K.
2007-02-15
We introduce a relativistic version of the quantum encryption protocol by considering two inertial observers who wish to securely transmit quantum information encoded in a free scalar quantum field state forming Minkowski particles. In a nonrelativistic setting a certain amount of shared classical resources is necessary to perfectly encrypt the state. We show that in the case of a uniformly accelerated eavesdropper the communicating parties need to share (asymptotically in the limit of infinite acceleration) just half of the classical resources.
World Sheet Commuting beta-gamma CFT and Non-Relativistic StringTheories
Kim, Bom Soo
2007-08-30
We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri[1] and Danielsson et. al.[2, 3]. Our theory is much simpler than their theory and does not assume a compact coordinate. This non-relativistic string theory has a bosonic matter {beta}{gamma} CFT with the conformal weight of {beta} as 1. It is natural to identify time as a linear combination of {gamma} and {bar {gamma}} through an explicit realization of the Galilean boost symmetry. The angle between {gamma} and {bar {gamma}} parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a non-relativistic dispersion relation without a nontrivial topology in the non-relativistic setup, which is one of the major differences from the previous works[1, 2, 3]. This simple theory is the non-relativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the {beta}{gamma} CFT. We also mention supersymmetric generalizations of these theories.
World sheet commuting {beta}{gamma} conformal field theory and nonrelativistic string theories
Kim, Bom Soo
2007-11-15
We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri [J. Math. Phys. (N.Y.) 42, 3127 (2001)] and Danielsson et al. [J. High Energy Phys. 10 (2000) 020; J. High Energy Phys. 03 (2001) 041.]. Our theory is much simpler than their theory and does not assume a compact coordinate. This nonrelativistic string theory has a bosonic matter {beta}{gamma} conformal field theory with the conformal weight of {beta} as 1. It is natural to identify time as a linear combination of {gamma} and {gamma} through an explicit realization of the Galilean boost symmetry. The angle between {gamma} and {gamma} parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a nonrelativistic dispersion relation without a nontrivial topology in the nonrelativistic setup, which is one of the major differences from the previous works of Gomis and Ooguri and of Danielsson and co-workers. This simple theory is the nonrelativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the {beta}{gamma} conformal field theory. We also mention supersymmetric generalizations of these theories.
The non-relativistic cow experiment in the uniformly accelerated reference frame
NASA Astrophysics Data System (ADS)
Beyer, Horst; Nitsch, Jürgen
1986-12-01
In consideration of the more realistic experimental circumstances in the theoretical treatment of the COW experiment, the non-relativistic phase shift of the COW experiment performed in a uniformly accelerated reference system is derived. Thereby a new contribution of the phase shift is obtained, second order in the acceleration constant, which might be measurable in the near future by using ultra cold neutrons.
Semi-nonrelativistic limit of the Chern-Simons-Higgs system
Chae, Myeongju; Huh, Hyungjin
2009-07-15
The semi-nonrelativistic limit of Chern-Simons-Higgs system is considered. We obtain several uniform estimates with respect to the light speed c and show the convergence of the solution of Chern-Simons-Higgs system to the solution of Chern-Simons-Schroedinger equations.
Spin-Zero Particles must be Bosons: A New Proof within Nonrelativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Peshkin, Murray
2006-01-01
The key assumption is that of Leinaas and Myrheim and of Berry and Robbins, here specialized to spin zero: for n particles, the argument of the wave function should be the unordered multiplet { r 1, r 2,..., r n }. I also make use of the requirement that wave functions in the domain of the Hamiltonian must be continuous functions of the spatial variables. The new proof presented here has advantages of simplicity and transparency in comparison with earlier work based on the same two principles and it uses weaker assumptions, especially avoiding the use of rotations of the relative coordinate of identical particles.
Reginatto, M.
1998-09-01
The many-particle time-dependent Schr{umlt o}dinger equation is derived using the principle of minimum Fisher information. This application of information theory leads to a physically well motivated derivation of the Schr{umlt o}dinger equation, which distinguishes between subjective and objective elements of the theory.
Gravity-darkening exponents for neutron and non-relativistic stars
NASA Astrophysics Data System (ADS)
Claret, A.
2015-05-01
Context. Rotation affects various aspects of the stellar structure and evolution. For example, it distorts the star and causes the energy flow to be dependent on the local gravity (von Zeipel effect). Recent advances in the semi-empirical derivation of the gravity-darkening exponents in eclipsing binaries and very fast rotators require new theoretical calculations so that the results can be compared with these observations. Aims: Using an analytical alternative method, we studied how the temperature is distributed over distorted neutron star (NS) surfaces through the gravity-darkening exponent (GDE). We also extended these investigations to non-relativistic stars. Methods: The envelopes of NS, whose properties are necessary to derive the GDE, were computed using routines of the code mesa. The non-relativistic stellar models were computed following the code granada. Results: We use a perturbation theory to derive an equation for the GDE for neutron and non-relativistic stars as a function of the rotation law, of the colatitude, and of the logarithmic derivatives of the opacity. Significant deviations from the von Zeipel's theorem were found for differentially rotating NS as well as for non-relativistic stars. This equation is also capable of predicting the transition zone in the GDE around log Teff = 3.9 for non-relativistic stars, in good agreement with observational data. We use this equation to explore the effects of differential rotation to explain the anomalous values of semi-empirical GDE found in some early-type eclipsing binaries. We also analysed the role of convection and of the change of the main thermonuclear energy source in the GDE calculations for late-type stars.
The quantum mechanics of cosmology.
NASA Astrophysics Data System (ADS)
Hartle, James B.
to the Quantum Mechanics of a Non-Relativistic Particle * Semiclassical Prediction in Quantum Cosmology * ACKNOWLEDGEMENTS * REFERENCES * APPENDIX: BUZZWORDS
Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations
Gevorkyan, A. S.; Burdik, C.; Oganesyan, K. B.
2010-05-04
Spontaneous transitions between bound states of an atomic system, 'Lamb Shift' of energy level, as well as many other phenomena in real nonrelativistic quantum systems are connected with the influence of quantum vacuum fluctuations which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system 'quantum harmonic oscillator (QHO)+ environment' is described in terms of complex probabilistic processes (CPP) which satisfies a stochastic differential equation (SDE) of Langevin-Schroedinger (L-Sch) type. On the basis of orthogonal CPP, the method of stochastic density matrix (SDM) is developed. The energy spectrum of QHO and a possibility of infringement of detailed balance of transitions between quantum levels including spontaneous decay of <
Nontrivial systems and the necessity of the scalar quantum mechanics axioms
Kotulek, Jan
2009-06-15
We discuss the necessity of the axioms of scalar quantum mechanics introduced by Paschke and clearly demonstrate their geometric and/or physical meaning. We show that reasonable nonrelativistic quantum mechanics is exactly specified by the axioms. A system describing the electric Aharonov-Bohm effect is presented. It illustrates the topological obstructions for the existence of a Hamiltonian.
NASA Astrophysics Data System (ADS)
Hobson, Art
2011-10-01
An earlier paper2 introduces quantum physics by means of four experiments: Youngs double-slit interference experiment using (1) a light beam, (2) a low-intensity light beam with time-lapse photography, (3) an electron beam, and (4) a low-intensity electron beam with time-lapse photography. It's ironic that, although these experiments demonstrate most of the quantum fundamentals, conventional pedagogy stresses their difficult and paradoxical nature. These paradoxes (i.e., logical contradictions) vanish, and understanding becomes simpler, if one takes seriously the fact that quantum mechanics is the nonrelativistic limit of our most accurate physical theory, namely quantum field theory, and treats the Schroedinger wave function, as well as the electromagnetic field, as quantized fields.2 Both the Schroedinger field, or "matter field," and the EM field are made of "quanta"—spatially extended but energetically discrete chunks or bundles of energy. Each quantum comes nonlocally from the entire space-filling field and interacts with macroscopic systems such as the viewing screen by collapsing into an atom instantaneously and randomly in accordance with the probability amplitude specified by the field. Thus, uncertainty and nonlocality are inherent in quantum physics. This paper is about quantum uncertainty. A planned later paper will take up quantum nonlocality.
Magnetically driven quantum heat engine
NASA Astrophysics Data System (ADS)
Muñoz, Enrique; Peña, Francisco J.
2014-05-01
We studied the efficiency of two different schemes for a magnetically driven quantum heat engine, by considering as the "working substance" a single nonrelativistic particle trapped in a cylindrical potential well, in the presence of an external magnetic field. 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 modulation of the external magnetic-field intensity. The second scheme is a variant of the former, where the 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.
Quantum Tunneling Time: Relativistic Extensions
NASA Astrophysics Data System (ADS)
Xu, Dai-Yu; Wang, Towe; Xue, Xun
2013-11-01
Several years ago, in quantum mechanics, Davies proposed a method to calculate particle's traveling time with the phase difference of wave function. The method is convenient for calculating the sojourn time inside a potential step and the tunneling time through a potential hill. We extend Davies' non-relativistic calculation to relativistic quantum mechanics, with and without particle-antiparticle creation, using Klein-Gordon equation and Dirac Equation, for different forms of energy-momentum relation. The extension is successful only when the particle and antiparticle creation/annihilation effect is negligible.
Magnetically driven quantum heat engine.
Muñoz, Enrique; Peña, Francisco J
2014-05-01
We studied the efficiency of two different schemes for a magnetically driven quantum heat engine, by considering as the "working substance" a single nonrelativistic particle trapped in a cylindrical potential well, in the presence of an external magnetic field. 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 modulation of the external magnetic-field intensity. The second scheme is a variant of the former, where the 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.
Cavity loss factors of non-relativistic beams for Project X
Lunin, A.; Yakovlev, V.; Kazakov, S.; /Fermilab
2011-03-01
Cavity loss factor calculation is an important part of the total cryolosses estimation for the super conductive (SC) accelerating structures. There are two approaches how to calculate cavity loss factors, the integration of a wake potential over the bunch profile and the addition of loss factors for individual cavity modes. We applied both methods in order to get reliable results for non-relativistic beam. The time domain CST solver was used for a wake potential calculation and the frequency domain HFSS code was used for the cavity eigenmodes spectrum findings. Finally we present the results of cavity loss factors simulations for a non-relativistic part of the ProjectX and analyze it for various beam parameters.
General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
Son, D.T.; Wingate, M. . E-mail: wingate@phys.washington.edu
2006-01-15
We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.
NASA Astrophysics Data System (ADS)
Kanazawa, Takuya; Yamamoto, Arata
2016-01-01
We apply QCD-inspired techniques to study nonrelativistic N -component degenerate fermions with attractive interactions. By analyzing the singular-value spectrum of the fermion matrix in the Lagrangian, we derive several exact relations that characterize spontaneous symmetry breaking U (1 )×SU (N )→Sp (N ) through bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Nonlocal order parameters are also introduced and their spectral representations are derived, from which a nontrivial constraint on the phase diagram is obtained. The effective theory of soft collective excitations is derived, and its equivalence to random matrix theory is demonstrated in the ɛ regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.
Screening Effects on Nonrelativistic Bremsstrahlung in the Scattering of Electrons by Neutral Atoms
NASA Technical Reports Server (NTRS)
Jung, Young-Dae; Lee, Kun-Sang
1995-01-01
Atomic screening effects on nonrelativistic electron-atom bremsstrahlung radiation are investigated using a simple analytic solution of the Thomas-Fermi model for many-electron atoms. The Born approximation is assumed for the initial and final states of the projectile electron. The results show that the screening effect is important in the soft radiation region and is decreasing with increasing radiation. These results help provide correct information about the behavior of bound electrons in the target atom in bremsstrahlung processes.
NASA Astrophysics Data System (ADS)
Griffiths, Robert B.
2001-11-01
Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics. Comprehensive account Written by one of the main figures in the field Paperback edition of successful work on philosophy of quantum mechanics
About the non-relativistic limit of the phase velocity of matter waves
NASA Astrophysics Data System (ADS)
Mundarain, Douglas
2017-07-01
This work revisits the apparent paradox that emerges from some results found in many basic textbooks which address the problem of calculating the phase velocity of free particles in the relativistic regime and its relation with the same quantity in the non-relativistic regime. Because some books use the Newtonian kinetic energy and others use the total relativistic energy (including the rest energy), the non-relativistic limit of the relativistic phase velocity differs from the Newtonian phase velocity, which can be confusing for many students. This paper proposes expressing the phase velocity by first subtracting the rest energy from the relativistic energy before imposing the usual de Broglie relations. In addition to providing the corresponding Newtonian phase velocity, it also provides a relativistic Schrödinger equation which intuitively reduces to the non-relativistic Schrödinger equation in the appropriate regime. The problem of the equivalence between the relativistic Schrödinger equation and the Klein-Gordon equation is also addressed by using arguments which can be understood by undergraduate students.
Hussain, S.; Mahmood, S.; Rehman, Aman-ur-
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.
Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar
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 spectral dimension in quantum field theory
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
2016-03-01
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators.
Belenchia, Alessio; Benincasa, Dionigi M T; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-22
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators
NASA Astrophysics Data System (ADS)
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-01
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Energy transmission using recyclable quantum entanglement.
Ye, Ming-Yong; Lin, Xiu-Min
2016-07-28
It is known that faster-than-light (FTL) transmission of energy could be achieved if the transmission were considered in the framework of non-relativistic classical mechanics. Here we show that FTL transmission of energy could also be achieved if the transmission were considered in the framework of non-relativistic quantum mechanics. In our transmission protocol a two-spin Heisenberg model is considered and the energy is transmitted by two successive local unitary operations on the initially entangled spins. Our protocol does not mean that FTL transmission can be achieved in reality when the theory of relativity is considered, but it shows that quantum entanglement can be used in a recyclable way in energy transmission.
Energy transmission using recyclable quantum entanglement
Ye, Ming-Yong; Lin, Xiu-Min
2016-01-01
It is known that faster-than-light (FTL) transmission of energy could be achieved if the transmission were considered in the framework of non-relativistic classical mechanics. Here we show that FTL transmission of energy could also be achieved if the transmission were considered in the framework of non-relativistic quantum mechanics. In our transmission protocol a two-spin Heisenberg model is considered and the energy is transmitted by two successive local unitary operations on the initially entangled spins. Our protocol does not mean that FTL transmission can be achieved in reality when the theory of relativity is considered, but it shows that quantum entanglement can be used in a recyclable way in energy transmission. PMID:27465431
Mueller, B.; Springer, R.P.
1995-05-15
A brief summary of the progress made for the year is given for each of the following areas: (1) quark-gluon plasma and relativistic heavy ion collisions (nine contributions); (2) effective theories for hadrons and nuclei (four contributions); (4) renormalization group approach to field theory at finite temperature; (5) symmetry-preserving regularization; and (6) an effective field theory approach to the cosmological constant problem.
NASA Astrophysics Data System (ADS)
Bedir, Islam
The methods are developed of two-loop calculation of spectral density for the 3-point correlation function of an electromagnetic current and two axial currents which are the basis of the pion form factor analysis within the framework of QCD sum rules and local quark-hadron duality approach. The nature of various types of contributions is established which are related to particular regions of momentum integrations inside Feynman integrals. The trace factors accompanying all six two-loop diagrams are calculated and classified. To regularize particular loop integrals, the dimensional regularization technique has been used. The calculation involves such methods as infinite-momentum frame approach, alpha-representation method, Sudakov parametrization of the integration momentum and covariant calculation in momentum space. It is shown that final results of integration are given by logarithms and di-logarithm functions. For the diagram with the gluon correction to the electromagnetic vertex, it is shown that its large momentum transfer behavior is dominated by the Feynman mechanism, in which the active quark carries the bulk of the hadron momentum both before and after collision with virtual photon. For this diagram, the Sudakov double logarithmic terms were obtained that are known to convert into the Sudakov form factor after summation over all orders. Another type of double-logarithmic term was found in the contribution of the diagrams with the gluon correction to the axial-current vertices. This term appears as a power correction to the leading power behavior of this diagram governed by a short-distance re-scattering subprocess in which the exchanged gluon has large virtuality. This subprocess corresponds to the asymptotic perturbative QCD contribution. This observation shows that the two double-logarithmic terms have different nature. The methods developed in this dissertation may be applied to other two-loop calculations within the QCD sum rule method.
A closed formula for the barrier transmission coefficient in quaternionic quantum mechanics
De Leo, Stefano; Leonardi, Vinicius; Pereira, Kenia; Ducati, Gisele
2010-11-15
In this paper, we analyze, by using a matrix approach, the dynamics of a nonrelativistic particle in presence of a quaternionic potential barrier. The matrix method used to solve the quaternionic Schroedinger equation allows us to obtain a closed formula for the transmission coefficient. Up to now, in quaternionic quantum mechanics, almost every discussion on the dynamics of nonrelativistic particle was motivated by or evolved from numerical studies. A closed formula for the transmission coefficient stimulates an analysis of qualitative differences between complex and quaternionic quantum mechanics and by using the stationary phase method, gives the possibility to discuss transmission times.
Intermediate quantum statistics for identical objects
Kuryshkin, V.V.
1988-11-01
Methods to construct various algebras of creation and annihilation operators of physical objects in complex quantum state spaces with a nonnegative metric are proposed. All allowed algebras for the cases of identical nonrelativistic systems in the second quantization of the Schrodinger equation, of identical quanta of relativistic tensor fields, and of identical quanta of relativistic spinor fields are constructed. A comparison of the obtained algebras with the well-known algebras of this type (Fermi, Bose, para-Fermi, and superalgebras) is given.
Bound State Problems and Study of Symmetry in Quantum Field Theory.
NASA Astrophysics Data System (ADS)
Levine, Robert Yale
This dissertation has four independent parts. The first part is a study of heavy quark-antiquark bound states. After a review of early nonrelativistic potential models an analytic potential form is derived based on the quantum chromodynamic running coupling constant and the string model. Various methods of fixing parameters in the potential lead to descriptions of (psi)/J, (UPSILON) and (t(')t) resonances. Energy levels, leptonic decay and E1 transition rates are calculated. Speculations on the mass dependence of leptonic decay rates, and on effects of spin-spin interactions on leptonic decay rates, are given. In the second part a theory of positron desorption from metal surfaces is derived and applied to surface positron conversion to positronium. Angular distribution and energy dependence of positronium from Al(100) are calculated as well as the polarization of pickup electrons from ferromagnetic nickel. Part three is a study of the supersymmetry algebra resulting with commuting (not nilpotent) parameters. The extended algebra is an infinite dimensional Kac-Moody type algebra with momentum in the role of the geometrical parameter. Representations of the resulting fixed momentum finite algebra are analyzed in the massive and massless case. The Klein transformation is introduced to accommodate the generator's fermionic statistics. Field theory representations which modify the Wess-Zumino model with abnormal statistics are shown to satisfy the infinite Lie algebra. The final part is a study of generalized parastatistics motivated by the identification of the Green index with an internal symmetry index. Generalized double commutation relations are introduced which are covariant rather than invariant under internal symmetry transformations. A study is made of local invariant interaction terms and types of normal Higgs mechanisms which are allowed by generalized statistics. Symmetry transmutation, a modification of normal isospin relations due to general statistics, is
Accioly, Antonio; Dias, Marco
2004-11-15
The problem of computing the effective nonrelativistic potential U{sub D} for the interaction of charged-scalar bosons, within the context of D-dimensional electromagnetism with a cutoff, is reduced to quadratures. It is shown that U{sub 3} cannot bind a pair of identical charged-scalar bosons; nevertheless, numerical calculations indicate that boson-boson bound states do exist in the framework of three-dimensional higher-derivative electromagnetism augmented by a topological Chern-Simons term.
Propagation of a nonrelativistic electron beam in a plasma in a magnetic field
Okuda, H.; Horton, R.; Ono, M.; Ashour-Abdalla, M.
1986-10-01
Propagation of a nonrelativistic electron beam in a plasma in a strong magnetic field has been studied using electrostatic one-dimensional particle simulation models. Electron beams of finite pulse length and of continuous injection are followed in time to study the effects of beam-plasma interaction on the beam propagation. For the case of pulsed beam propagation, it is found that the beam distribution rapidly spreads in velocity space generating a plateaulike distribution with a high energy tail extending beyond the initial beam velocity.
Radiation of non-relativistic particle on a conducting sphere and a string of spheres
NASA Astrophysics Data System (ADS)
Shul'ga, N. F.; Syshchenko, V. V.; Larikova, E. A.
2017-07-01
The radiation resulting from the uniform motion of a charged particle by (or through) metal sphere is considered. The simple but rigorous description of the radiation process is developed for the case of non-relativistic particle and perfectly conducting sphere by the way of the method of images known from electrostatics. The spectral-angular and spectral densities of the diffraction and transition radiation on the single sphere are computed. The Smith-Purcell radiation caused by motion of the particle parallel to the periodic string of spheres is also considered.
Supersymmetry of the planar Dirac-Deser-Jackiw-Templeton system and of its nonrelativistic limit
Horvathy, Peter A.; Valenzuela, Mauricio; Plyushchay, Mikhail S.
2010-09-15
The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The super-Poincare symmetry emerges from the osp(1|2) supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The nonrelativistic limit yields spin 1/2 as well as new, spin 1 ''Levy-Leblond-type'' equations which, together, carry an N=2 super-Schroedinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the super-Poincare algebra.
η(c) production at the LHC challenges nonrelativistic QCD factorization.
Butenschoen, Mathias; He, Zhi-Guo; Kniehl, Bernd A
2015-03-06
We analyze the first measurement of η_{c} production, performed by the LHCb Collaboration, in the nonrelativistic QCD (NRQCD) factorization framework at next-to-leading order (NLO) in the strong-coupling constant α_{s} and the relative velocity v of the bound quarks including the feeddown from h_{c} mesons. Converting the long-distance matrix elements extracted by various groups from J/ψ yield and polarization data to the η_{c} case using heavy-quark spin symmetry, we find that the resulting NLO NRQCD predictions greatly overshoot the LHCb data, while the color-singlet model provides an excellent description.
NASA Astrophysics Data System (ADS)
Schlickeiser, R.; Yoon, P. H.
2012-02-01
Using the system of the Klimontovich and Maxwell equations, general expressions for the electromagnetic fluctuation spectra (electric and magnetic field, charge and current densities) from uncorrelated plasma particles are derived, which are covariantly correct within the theory of special relativity. The general expressions hold for arbitrary momentum dependences of the plasma particle distribution functions and for collective and non-collective fluctuations. In this first paper of a series, the results are illustrated for the important special case of nonrelativistic isotropic Maxwellian particle distribution functions providing in particular the thermal fluctuations of weakly amplified modes and aperiodic modes.
SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS
Caprioli, Damiano; Pop, Ana-Roxana; Spitkovsky, Anatoly
2015-01-10
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.
Park, Jaehong; Caprioli, Damiano; Spitkovsky, Anatoly
2015-02-27
We study diffusive shock acceleration (DSA) of protons and electrons at nonrelativistic, high Mach number, quasiparallel, collisionless shocks by means of self-consistent 1D particle-in-cell simulations. For the first time, both species are found to develop power-law distributions with the universal spectral index -4 in momentum space, in agreement with the prediction of DSA. We find that scattering of both protons and electrons is mediated by right-handed circularly polarized waves excited by the current of energetic protons via nonresonant hybrid (Bell) instability. Protons are injected into DSA after a few gyrocycles of shock drift acceleration (SDA), while electrons are first preheated via SDA, then energized via a hybrid acceleration process that involves both SDA and Fermi-like acceleration mediated by Bell waves, before eventual injection into DSA. Using the simulations we can measure the electron-proton ratio in accelerated particles, which is of paramount importance for explaining the cosmic ray fluxes measured on Earth and the multiwavelength emission of astrophysical objects such as supernova remnants, radio supernovae, and galaxy clusters. We find the normalization of the electron power law is ≲10^{-2} of the protons for strong nonrelativistic shocks.
Mahmood, S.; Sadiq, Safeer; Haque, Q.
2013-12-15
Linear and nonlinear electrostatic waves in magnetized dense electron-ion plasmas are studied with nonrelativistic and ultra-relativistic degenerate and singly, doubly charged helium (He{sup +}, He{sup ++}) and hydrogen (H{sup +}) ions, respectively. The dispersion relation of electrostatic waves in magnetized dense plasmas is obtained under both the energy limits of degenerate electrons. Using reductive perturbation method, the Zakharov-Kuznetsov equation for nonlinear propagation of electrostatic solitons in magnetized dense plasmas is derived for both nonrelativistic and ultra-relativistic degenerate electrons. It is found that variations in plasma density, magnetic field intensity, different mass, and charge number of ions play significant role in the formation of electrostatic solitons in magnetized dense plasmas. The numerical plots are also presented for illustration using the parameters of dense astrophysical plasma situations such as white dwarfs and neutron stars exist in the literature. The present investigation is important for understanding the electrostatic waves propagation in the outer periphery of compact stars which mostly consists of hydrogen and helium ions with degenerate electrons in dense magnetized plasmas.
Fundamentals of collisionless shocks for astrophysical application, 1. Non-relativistic shocks
NASA Astrophysics Data System (ADS)
Treumann, R. A.
2009-12-01
A comprehensive review is given of the theory and properties of nonrelativistic shocks in hot collisionless plasmas—in view of their possible application in astrophysics. Understanding non-relativistic collisionless shocks is an indispensable step towards a general account of collisionless astrophysical shocks of high Mach number and of their effects in dissipating flow-energy, in heating matter, in accelerating particles to high—presumably cosmic-ray—energies, and in generating detectable radiation from radio to X-rays. Non-relativistic shocks have Alfvénic Mach numbers {{fancyscript{M}}_A≪ sqrt{m_i/m_e}(ω_{pe}/ω_{ce})}, where m i / m e is the ion-to-electron mass ratio, and ω pe , ω ce are the electron plasma and cyclotron frequencies, respectively. Though high, the temperatures of such shocks are limited (in energy units) to T < m e c 2. This means that particle creation is inhibited, classical theory is applicable, and reaction of radiation on the dynamics of the shock can be neglected. The majority of such shocks are supercritical, meaning that non-relativistic shocks are unable to self-consistently produce sufficient dissipation and, thus, to sustain a stationary shock transition. As a consequence, supercritical shocks act as efficient particle reflectors. All these shocks are microscopically thin, with shock-transition width of the order of the ion inertial length λ i = c/ ω pi (with ω pi the ion plasma frequency). The full theory of such shocks is developed, and the different possible types of shocks are defined. Since all collisionless shocks are magnetised, the most important distinction is between quasi-perpendicular and quasi-parallel shocks. The former propagate about perpendicularly, the latter roughly parallel to the upstream magnetic field. Their manifestly different behaviours are described in detail. In particular, although both types of shocks are non-stationary, they have completely different reformation cycles. From numerical
On the geometrization of quantum mechanics
Tavernelli, Ivano
2016-08-15
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.
On the geometrization of quantum mechanics
NASA Astrophysics Data System (ADS)
Tavernelli, Ivano
2016-08-01
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave-particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie-Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space-time, as it is the case for gravitation in the general relativity.
The equation of motion of an electron : a debate in classical and quantum physics.
Kim, K.-J.
1999-01-27
The current status of understanding of the equation of motion of an electron is summarized. Classically, a consistent, linearized theory exists for an electron of finite extent, as long as the size of the electron is larger than the classical electron radius. Nonrelativistic quantum mechanics seems to offer a tine theory even in the point-particle limit.
Energy modulation of nonrelativistic electrons in an optical near field on a metal microslit
NASA Astrophysics Data System (ADS)
Ishikawa, R.; Bae, J.; Mizuno, K.
2001-04-01
Energy modulation of nonrelativistic electrons with a laser beam using a metal microslit as an interaction circuit has been investigated. An optical near field is induced in the proximity of the microslit by illumination of the laser beam. The electrons passing close to the slit are accelerated or decelerated by an evanescent wave contained in the near field whose phase velocity is equal to the velocity of the electrons. The electron-evanescent wave interaction in the microslit has been analyzed theoretically and experimentally. The theory has predicted that electron energy can be modulated at optical frequencies. Experiments performed in the infrared region have verified theoretical predictions. The electron-energy changes of more than ±5 eV with a 10 kW CO2 laser pulse at the wavelength of 10.6 μm has been successfully observed for an electron beam with an energy of less than 80 keV.
Injection and propagation of a nonrelativistic electron beam and spacecraft charging
Okuda, H.; Berchem, J.
1987-05-01
Two-dimensional numerical simulations have been carried out in order to study the injection and propagation of a nonrelativistic electron beam from a spacecraft into a fully ionized plasma in a magnetic field. Contrary to the earlier results in one-dimension, a high density electron beam whose density is comparable to the ambient density can propagate into a plasma. A strong radial electric field resulting from the net charges in the beam causes the beam electrons to spread radially reducing the beam density. When the injection current exceeds the return current, significant charging of the spacecraft is observed along with the reflection of the injected electrons back to the spacecraft. Recent data on the electron beam injection from the Spacelab 1 (SEPAC) are discussed.
NASA Astrophysics Data System (ADS)
Cardall, Christian Y.; Budiardja, Reuben D.; Endeve, Eirik; Mezzacappa, Anthony
2014-02-01
GenASiS (General Astrophysical Simulation System) is a new code being developed initially and primarily, though by no means exclusively, for the simulation of core-collapse supernovae on the world's leading capability supercomputers. This paper—the first in a series—demonstrates a centrally refined coordinate patch suitable for gravitational collapse and documents methods for compressible nonrelativistic hydrodynamics. We benchmark the hydrodynamics capabilities of GenASiS against many standard test problems; the results illustrate the basic competence of our implementation, demonstrate the strengths and limitations of the HLLC relative to the HLL Riemann solver in a number of interesting cases, and provide preliminary indications of the code's ability to scale and to function with cell-by-cell fixed-mesh refinement.
Can Nonrelativistic QCD Explain the γγ^{*}→η_{c} Transition Form Factor Data?
Feng, Feng; Jia, Yu; Sang, Wen-Long
2015-11-27
Unlike the bewildering situation in the γγ^{*}→π form factor, a widespread view is that perturbative QCD can decently account for the recent BABAR measurement of the γγ^{*}→η_{c} transition form factor. The next-to-next-to-leading-order perturbative correction to the γγ^{*}→η_{c,b} form factor, is investigated in the nonrelativistic QCD (NRQCD) factorization framework for the first time. As a byproduct, we obtain, by far, the most precise order-α_{s}^{2} NRQCD matching coefficient for the η_{c,b}→γγ process. After including the substantial negative order-α_{s}^{2} correction, the good agreement between NRQCD prediction and the measured γγ^{*}→η_{c} form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of the NRQCD approach to hard exclusive reactions involving charmonium.
Solar He-3-rich events and nonrelativistic electron events - A new association
NASA Technical Reports Server (NTRS)
Reames, D. V.; Von Rosenvinge, T. T.; Lin, R. P.
1985-01-01
In 15 months of observation by the ISEE-e spacecraft, it was found that virtually all solar greater than or approximately equal to 1.3 MeV/nucleon He-3-rich events are associated with impulsive 2 to approximately 100 keV electron events, although many electron events were not accompanied by detectable He-3 increases. Both the He-3 and the electrons exhibit nearly scatter-free propagation in the interplanetary medium, and the times of onset and maximum for the He-3 and electron increases are closely related by velocity dispersion. The electron events and their related type III solar radio bursts provide, for the first time, identification of the flares which produce the He-3-rich events. He-3 appears to be accelerated at the flash phase of solar flares along with nonrelativistic electrons.
Solar He-3-rich events and non-relativistic electron events: A new association
NASA Technical Reports Server (NTRS)
Reames, D. V.; Vonrosenvinge, T. T.; Lin, R. P.
1984-01-01
In 15 months of observation by the ISEE-e spacecraft, it was found that virtually all solar greater than or approximately equal to 1.3 MeV/nucleon He-3-rich events are associated with impulsive 2 to approximately 100 keV electron events, although many electron events were not accompanied by detectable He-3 increases. Both the He-3 and the electrons exhibit nearly scatter-free propagation in the interplanetary medium, and the times of onset and maximum for the He-3 and electron increases are closely related by velocity dispertion. The electron events and their related type III solar radio bursts provide, for the first time, identification of the flares which produce He-3-rich events. He-3 appears to be accelerated at the flash phase of solar flares along with nonrelativistic electrons.
Complete Nonrelativistic-QCD Prediction for Prompt Double J /ψ Hadroproduction
NASA Astrophysics Data System (ADS)
He, Zhi-Guo; Kniehl, Bernd A.
2015-07-01
We perform a complete study of prompt double J /ψ hadroproduction at leading order in the nonrelativistic-QCD factorization framework by including all possible pairings of the c c ¯ Fock states 1S0[8] , 3S1[1,8] , and 3PJ[1,8] with J =0 ,1 ,2 . We find that the 1S0[8] and 3PJ[8] channels of J /ψ and ψ' production and the 3PJ[1] and 3S1[8] channels of χc J production, which have been overlooked so far, greatly dominate at large invariant masses and rapidity separations of the J /ψ pair, and that their inclusion nearly fills the large gap between previous incomplete predictions within the color-singlet model and the recent measurement by the CMS Collaboration at the CERN LHC, leaving room for next-to-leading-order corrections of typical size.
Holographic non-relativistic fermionic fixed point and bulk dipole coupling
NASA Astrophysics Data System (ADS)
Li, Wei-Jia; Zhang, Hongbao
2011-11-01
Inspired by the recently discovered non-relativistic fermionic fixed points, we investigate how the presence of bulk dipole coupling modifies the spectral function at one of these novel fixed points. As a result, although the infinite flat band is always visible in the presence of the bulk dipole coupling as well as chemical potential, the band is modified in a remarkable way at small momenta up to the order of magnitude of bulk dipole coupling. On the other hand, like a phoenix, a new Fermi surface sprouts from the formed gap when the bulk dipole coupling is pushed up further such as to overshadow the charge parameter, which is obviously different from what is found at the relativistic fixed points.
NASA Astrophysics Data System (ADS)
Cotner, Eric
2016-09-01
Scalar particles are a common prediction of many beyond the Standard Model theories. If they are light and cold enough, there is a possibility they may form Bose-Einstein condensates, which will then become gravitationally bound. These boson stars are solitonic solutions to the Einstein-Klein-Gordon equations but may be approximated in the nonrelativistic regime with a coupled Schrödinger-Poisson system. General properties of single soliton states are derived, including the possibility of quartic self-interactions. Binary collisions between two solitons are then studied, and the effects of different mass ratios, relative phases, self-couplings, and separation distances are characterized, leading to an easy conceptual understanding of how these parameters affect the collision outcome in terms of conservation of energy. Applications to dark matter are discussed.
Time Operator in Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Khorasani, Sina
2017-07-01
It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.
Theory and Applications of Non-relativistic and Relativistic Turbulent Reconnection
NASA Astrophysics Data System (ADS)
Lazarian, A.; Kowal, G.; Takamoto, M.; de Gouveia Dal Pino, E. M.; Cho, J.
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers of the flows. Therefore, the theories intended for describing astrophysical reconnection should not ignore the effects of turbulence. 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 the outflows from magnetic reconnection induce turbulence affecting the rate of turbulent reconnection. Thus turbulence must be accounted for any realistic astrophysical reconnection set up. 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, including the situations when turbulent reconnection is self-driven, i.e. the turbulence in the system is generated by the reconnection process itself. In addition, we consider observational testing of turbulent reconnection as well as numerous implications of the theory. The former includes the Sun and solar wind reconnection, while the latter include the process of reconnection diffusion induced by turbulent reconnection, the acceleration of energetic particles, bursts of turbulent reconnection related to black hole sources and gamma ray bursts. Finally, we explain why turbulent reconnection cannot be explained by turbulent resistivity or derived through the mean field approach. We also argue that the tearing reconnection transfers to fully turbulent reconnection in 3D astrophysically relevant settings with realistically high Reynolds numbers.
Simulations of ion acceleration at non-relativistic shocks. II. Magnetic field amplification
Caprioli, D.; Spitkovsky, A.
2014-10-10
We use large hybrid simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient, we find that the upstream magnetic field is significantly amplified. The total amplification factor is larger than 10 for shocks with Alfvénic Mach number M = 100, and scales with the square root of M. The spectral energy density of excited magnetic turbulence is determined by the energy distribution of accelerated particles, and for moderately strong shocks (M ≲ 30) agrees well with the prediction of resonant streaming instability, in the framework of quasilinear theory of diffusive shock acceleration. For M ≳ 30, instead, Bell's non-resonant hybrid (NRH) instability is predicted and found to grow faster than resonant instability. NRH modes are excited far upstream by escaping particles, and initially grow without disrupting the current, their typical wavelengths being much shorter than the current ions' gyroradii. Then, in the nonlinear stage, most unstable modes migrate to larger and larger wavelengths, eventually becoming resonant in wavelength with the driving ions, which start diffuse. Ahead of strong shocks we distinguish two regions, separated by the free-escape boundary: the far upstream, where field amplification is provided by the current of escaping ions via NRH instability, and the shock precursor, where energetic particles are effectively magnetized, and field amplification is provided by the current in diffusing ions. The presented scalings of magnetic field amplification enable the inclusion of self-consistent microphysics into phenomenological models of ion acceleration at non-relativistic shocks.
Mass spectra and decays of ground and orbitally excited cb¯ states in nonrelativistic quark model
NASA Astrophysics Data System (ADS)
Monteiro, Antony Prakash; Bhat, Manjunath; Vijaya Kumar, K. B.
2017-02-01
The complete spectrum of cb¯ states is obtained in a phenomenological nonrelativistic quark model (NRQM), which consists of a confinement potential and one gluon exchange potential (OGEP) as effective quark-antiquark potential. We make predictions for the radiative decay (E1 and M1) widths and weak decay widths of cb¯ states in the framework of NRQM formalism.
Grinberg, H.; Maranon, J.; Vucetich, H.
1983-01-15
The Kustaanheimo--Stiefel transformation together with the well-known expansion of the kernel of an isotropic harmonic oscillator is used to generate the atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism. Group theoretical implications of the present problem are briefly discussed.
Knecht, Stefan; Jensen, Hans Jorgen Aa; Fleig, Timo
2008-01-07
We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.
NASA Astrophysics Data System (ADS)
Knecht, Stefan; Jensen, Hans Jørgen Aa.; Fleig, Timo
2008-01-01
We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5×109 Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10days to less than 1day.
Cheng, Lan
2015-08-14
Quantum-chemical computations of nuclear quadrupole-coupling parameters for 24 open-shell states of small molecules based on non-relativistic and spin-free exact two-component (SFX2C) relativistic equation-of-motion coupled-cluster (EOM-CC) as well as spin-orbital-based restricted open-shell Hartree-Fock coupled-cluster (ROHF-CC) methods are reported. Relativistic effects, the performance of the EOM-CC and ROHF-CC methods for treating electron correlation, as well as basis-set convergence have been carefully analyzed. Consideration of relativistic effects is necessary for accurate calculations on systems containing third-row (K-Kr) and heavier elements, as expected, and the SFX2C approach is shown to be a useful cost-effective option here. Further, it is demonstrated that the EOM-CC methods constitute flexible and accurate alternatives to the ROHF-CC methods in the calculations of nuclear quadrupole-coupling parameters for open-shell states.
Electromagnetic wave equations for relativistically degenerate quantum magnetoplasmas.
Masood, Waqas; Eliasson, Bengt; Shukla, Padma K
2010-06-01
A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin- 1/2, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin- 1/2 contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.
Electromagnetic wave equations for relativistically degenerate quantum magnetoplasmas
Masood, Waqas; Eliasson, Bengt; Shukla, Padma K.
2010-06-15
A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin-(1/2), and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin-(1/2) contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.
Magnetically driven quantum heat engine
NASA Astrophysics Data System (ADS)
Munoz, Enrique; Pena, Francisco
2015-03-01
In analogy with classical thermodynamics, a quantum heat engine generates useful mechanical work from heat, by means of a reversible sequence of transformations (trajectories), where the ``working substance'' is of quantum mechanical nature. Several theoretical implementations for a quantum heat engine have been discussed in the literature, such as entangled states in a qubit, quantum mechanical versions of the Otto cycle, and photocells. In this work, we propose yet a different alternative by introducing the concept of a magnetically driven quantum heat engine. We studied the efficiency of such system, by considering as the ``working substance'' a single nonrelativistic particle trapped in a cylindrical potential well, as a model for a semiconductor quantum dot, in the presence of an external magnetic field. The trajectories are driven by a quasistatic modulation of the external magnetic-field intensity, while the system is in contact with macroscopic thermostats. The external magnetic field modulation allows to modify the effective geometric confinement, in analogy with a piston in a classical gas. E. Munoz acknowledges financial support from Fondecyt under Contract 1141146.
Polymer quantum mechanics some examples using path integrals
Parra, Lorena; Vergara, J. David
2014-01-14
In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems.
Yannouleas, Constantine; Romanovsky, Igor; Landman, Uzi
2015-01-20
Graphene's isolation launched explorations of fundamental relativistic physics originating from the planar honeycomb lattice arrangement of the carbon atoms, and of potential technological applications in nanoscale electronics. Bottom-up fabricated atomically-precise segmented graphene nanoribbons, SGNRs, open avenues for studies of electrical transport, coherence, and interference effects in metallic, semiconducting, and mixed GNRs, with different edge terminations. Conceptual and practical understanding of electric transport through SGNRs is gained through nonequilibrium Green's function (NEGF) conductance calculations and a Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. The continuum model reproduces the NEGF results, including optical Dirac Fabry-Prot (FP) equidistant oscillations for massless relativistic carriers in metallic armchair SGNRs, and an unequally-spaced FP pattern for mixed armchair-zigzag SGNRs where carriers transit from a relativistic (armchair) to a nonrelativistic (zigzag) regime. This provides a unifying framework for analysis of coherent transport phenomena and interpretation of forthcoming experiments in SGNRs.
NASA Astrophysics Data System (ADS)
Yannouleas, Constantine; Romanovsky, Igor; Landman, Uzi
2015-01-01
Graphene's isolation launched explorations of fundamental relativistic physics originating from the planar honeycomb lattice arrangement of the carbon atoms, and of potential technological applications in nanoscale electronics. Bottom-up fabricated atomically-precise segmented graphene nanoribbons, SGNRs, open avenues for studies of electrical transport, coherence, and interference effects in metallic, semiconducting, and mixed GNRs, with different edge terminations. Conceptual and practical understanding of electric transport through SGNRs is gained through nonequilibrium Green's function (NEGF) conductance calculations and a Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. The continuum model reproduces the NEGF results, including optical Dirac Fabry-Prot (FP) equidistant oscillations for massless relativistic carriers in metallic armchair SGNRs, and an unequally-spaced FP pattern for mixed armchair-zigzag SGNRs where carriers transit from a relativistic (armchair) to a nonrelativistic (zigzag) regime. This provides a unifying framework for analysis of coherent transport phenomena and interpretation of forthcoming experiments in SGNRs.
NASA Astrophysics Data System (ADS)
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.
Yannouleas, Constantine; Romanovsky, Igor; Landman, Uzi
2015-01-20
Graphene's isolation launched explorations of fundamental relativistic physics originating from the planar honeycomb lattice arrangement of the carbon atoms, and of potential technological applications in nanoscale electronics. Bottom-up fabricated atomically-precise segmented graphene nanoribbons, SGNRs, open avenues for studies of electrical transport, coherence, and interference effects in metallic, semiconducting, and mixed GNRs, with different edge terminations. Conceptual and practical understanding of electric transport through SGNRs is gained through nonequilibrium Green's function (NEGF) conductance calculations and a Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. The continuum model reproduces themore » NEGF results, including optical Dirac Fabry-Pérot (FP) equidistant oscillations for massless relativistic carriers in metallic armchair SGNRs, and an unequally-spaced FP pattern for mixed armchair-zigzag SGNRs where carriers transit from a relativistic (armchair) to a nonrelativistic (zigzag) regime. This provides a unifying framework for analysis of coherent transport phenomena and interpretation of forthcoming experiments in SGNRs.« less
Yannouleas, Constantine; Romanovsky, Igor; Landman, Uzi
2015-01-20
Graphene's isolation launched explorations of fundamental relativistic physics originating from the planar honeycomb lattice arrangement of the carbon atoms, and of potential technological applications in nanoscale electronics. Bottom-up fabricated atomically-precise segmented graphene nanoribbons, SGNRs, open avenues for studies of electrical transport, coherence, and interference effects in metallic, semiconducting, and mixed GNRs, with different edge terminations. Conceptual and practical understanding of electric transport through SGNRs is gained through nonequilibrium Green's function (NEGF) conductance calculations and a Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. The continuum model reproduces the NEGF results, including optical Dirac Fabry-Pérot (FP) equidistant oscillations for massless relativistic carriers in metallic armchair SGNRs, and an unequally-spaced FP pattern for mixed armchair-zigzag SGNRs where carriers transit from a relativistic (armchair) to a nonrelativistic (zigzag) regime. This provides a unifying framework for analysis of coherent transport phenomena and interpretation of forthcoming experiments in SGNRs.
Effective field theory and dispersion law of the phonons of a nonrelativistic superfluid
Escobedo, Miguel Angel; Manuel, Cristina
2010-08-15
We study the recently proposed effective-field theory for the phonon of an arbitrary nonrelativistic superfluid. After computing the one-loop phonon self-energy, we obtain the low-temperature T contributions to the phonon dispersion law at low momentum and see that the real part of those can be parametrized as a thermal correction to the phonon velocity. Because the phonons are the quanta of the sound waves, at low momentum their velocity should agree with the speed of sound. We find that our results match at order T{sup 4}lnT with those predicted by Andreev and Khalatnikov for the speed of sound, derived from the superfluid hydrodynamical equations and the phonon kinetic theory. We get also higher-order corrections of order T{sup 4}, which are not reproduced pushing naively the kinetic theory computation. Finally, as an application, we consider the cold Fermi gas in the unitarity limit and find a universal expression for the low-T relative correction to the speed of sound for these systems.
Yannouleas, Constantine; Romanovsky, Igor; Landman, Uzi
2015-01-01
Graphene's isolation launched explorations of fundamental relativistic physics originating from the planar honeycomb lattice arrangement of the carbon atoms, and of potential technological applications in nanoscale electronics. Bottom-up fabricated atomically-precise segmented graphene nanoribbons, SGNRs, open avenues for studies of electrical transport, coherence, and interference effects in metallic, semiconducting, and mixed GNRs, with different edge terminations. Conceptual and practical understanding of electric transport through SGNRs is gained through nonequilibrium Green's function (NEGF) conductance calculations and a Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass-barriers at the contacts between segments. The continuum model reproduces the NEGF results, including optical Dirac Fabry-Prot (FP) equidistant oscillations for massless relativistic carriers in metallic armchair SGNRs, and an unequally-spaced FP pattern for mixed armchair-zigzag SGNRs where carriers transit from a relativistic (armchair) to a nonrelativistic (zigzag) regime. This provides a unifying framework for analysis of coherent transport phenomena and interpretation of forthcoming experiments in SGNRs. PMID:25599915
Solution of the nonrelativistic wave equation using the tridiagonal representation approach
NASA Astrophysics Data System (ADS)
Alhaidari, A. D.
2017-07-01
We choose a complete set of square integrable functions as a basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent linear wave operator is tridiagonal and symmetric. Consequently, the matrix wave equation becomes a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. The recursion relation is then solved exactly in terms of orthogonal polynomials in the energy. Some of these polynomials are not found in the mathematics literature. The asymptotics of these polynomials give the phase shift for the continuous energy scattering states and the spectrum for the discrete energy bound states. Depending on the space and boundary conditions, the basis functions are written in terms of either the Laguerre or Jacobi polynomials. The tridiagonal requirement limits the number of potential functions that yield exact solutions of the wave equation. Nonetheless, the class of exactly solvable problems in this approach is larger than the conventional class (see, for example, Table XII in the text). We also give very accurate results for cases where the wave operator matrix is not tridiagonal but its elements could be evaluated either exactly or numerically with high precision.
Complete Nonrelativistic-QCD Prediction for Prompt Double J/ψ Hadroproduction.
He, Zhi-Guo; Kniehl, Bernd A
2015-07-10
We perform a complete study of prompt double J/ψ hadroproduction at leading order in the nonrelativistic-QCD factorization framework by including all possible pairings of the cc̅ Fock states (1)S(0)([8]), (3)S(1)([1,8]), and (3)P(J)([1,8]) with J=0,1,2. We find that the (1)S(0)([8]) and (3)P(J)([8]) channels of J/ψ and ψ'} production and the (3)P(J)([1]) and (3)S(1)([8]) channels of χ(cJ) production, which have been overlooked so far, greatly dominate at large invariant masses and rapidity separations of the J/ψ pair, and that their inclusion nearly fills the large gap between previous incomplete predictions within the color-singlet model and the recent measurement by the CMS Collaboration at the CERN LHC, leaving room for next-to-leading-order corrections of typical size.
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
NASA Astrophysics Data System (ADS)
Ko, Sung Moon; Melby-Thompson, Charles M.; Meyer, René; Park, Jeong-Hyuck
2015-12-01
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 [1] 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 [2] 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.
NASA Astrophysics Data System (ADS)
Stepanov, Nikolay S.; Zelekson, Lev A.
2017-03-01
The exact stationary solution of one-dimensional non-relativistic Vlasov equation is obtained in the article. It is shown that in the energy exchange with the self-consistent longitudinal electric field, both wave trapped charged particles and the passing ones take part. It is proved that the trapped electron distribution is fundamentally different from distribution functions described by other authors, which used the Bernstein, Greene, and Kruskal method. So, the correct distribution function is characterized by its sudden change at the equality of wave and electrons' velocity but not on the edges of the potential well. This jump occurs for any arbitrary small value of wave potential. It was also found that the energy density of fast electrons trapped by the wave is less than the energy density of slow trapped electrons. This leads to the fact that the energy of the self-consistent electric field may both increase and decrease due to the nonlinear Landau damping. The conditions under which a similar effect can be observed are defined. Also for the first time, it is shown that the self-generated strong electric field always produces antitropic electron beams.
Potential-model calculation of an order-v2 nonrelativistic QCD matrix element
NASA Astrophysics Data System (ADS)
Bodwin, Geoffrey T.; Kang, Daekyoung; Lee, Jungil
2006-07-01
We present two methods for computing dimensionally regulated nonrelativistic QCD heavy-quarkonium matrix elements that are related to the second derivative of the heavy-quarkonium wave function at the origin. The first method makes use of a hard-cutoff regulator as an intermediate step and requires knowledge only of the heavy-quarkonium wave function. It involves a significant cancellation that is an obstacle to achieving high numerical accuracy. The second method is more direct and yields a result that is identical to the Gremm-Kapustin relation, but it is limited to use in potential models. It can be generalized to the computation of matrix elements of higher order in the heavy-quark velocity and can be used to resum the contributions to decay and production rates that are associated with those matrix elements. We apply these methods to the Cornell potential model and compute a matrix element for the J/ψ state that appears in the leading relativistic correction to the production and decay of that state through the color-singlet quark-antiquark channel.
Electron Acceleration in a Nonrelativistic Shock with Very High Alfvén Mach Number
NASA Astrophysics Data System (ADS)
Matsumoto, Y.; Amano, T.; Hoshino, M.
2013-11-01
Electron acceleration associated with various plasma kinetic instabilities in a nonrelativistic shock with very high Alfvén Mach number (MA˜45) is revealed by means of a two-dimensional fully kinetic particle-in-cell simulation. Electromagnetic (ion Weibel) and electrostatic (ion-acoustic and Buneman) instabilities are strongly activated at the same time in different regions of the two-dimensional shock structure. Relativistic electrons are quickly produced predominantly by the shock surfing mechanism with the Buneman instability at the leading edge of the foot. The energy spectrum has a high-energy tail exceeding the upstream ion kinetic energy accompanying the main thermal population. This gives a favorable condition for the ion-acoustic instability at the shock front, which in turn results in additional energization. The large-amplitude ion Weibel instability generates current sheets in the foot, implying another dissipation mechanism via magnetic reconnection in a three-dimensional shock structure in the very-high-MA regime.
Sims, James S.; Hagstrom, Stanley A.
2014-06-14
In a previous work, Sims and Hagstrom [“Hylleraas-configuration-interaction study of the 1 {sup 1}S ground state of neutral beryllium,” Phys. Rev. A 83, 032518 (2011)] reported Hylleraas-configuration-interaction (Hy-CI) method variational calculations for the {sup 1}S ground state of neutral beryllium with an estimated accuracy of a tenth of a microhartree. In this work, the calculations have been extended to higher accuracy and, by simple scaling of the orbital exponents, to the entire Be 2 {sup 1}S isoelectronic sequence. The best nonrelativistic energies for Be, B{sup +}, and C{sup ++} obtained are −14.6673 5649 269, −24.3488 8446 36, and −36.5348 5236 25 hartree, respectively. Except for Be, all computed nonrelativistic energies are superior to the known reference energies for these states.
Aucar, Ignacio A; Gómez, Sergio S; Ruiz de Azúa, Martín C; Giribet, Claudia G
2012-05-28
A theoretical study of the relation between the relativistic formulation of the nuclear magnetic shielding and spin-rotation tensors is presented. To this end a theoretical expression of the relativistic spin-rotation tensor is formulated, considering a molecular Hamiltonian of relativistic electrons and non-relativistic nuclei. Molecular rotation effects are introduced considering the terms of the Born-Oppenheimer decomposition, which couple the electrons and nuclei dynamics. The loss of the simple relation linking both spectral parameters in the non-relativistic formulation is further analyzed carrying out a perturbative expansion of relativistic effects by means of the linear response within the elimination of the small component approach. It is concluded that relativistic effects on the spin-rotation tensor are less important than those of the nuclear magnetic shielding tensor.
NASA Astrophysics Data System (ADS)
Keenan, Brett D.; Ford, Alexander L.; Medvedev, Mikhail V.
2015-09-01
Plasmas with electromagnetic fields turbulent at sub-Larmor scales are a feature of a wide variety of high-energy-density environments and are essential to the description of many astrophysical and laboratory plasma phenomena. Radiation from particles, whether they are relativistic or nonrelativistic, moving through small-scale magnetic turbulence has spectral characteristics distinct from both synchrotron and cyclotron radiation. The radiation, carrying information on the statistical properties of the magnetic turbulence, is also intimately related to the particle diffusive transport. We have investigated, both theoretically and numerically, the transport of nonrelativistic and trans-relativistic particles in plasmas with high-amplitude isotropic sub-Larmor-scale magnetic turbulence, and its relation to the spectra of radiation simultaneously produced by these particles. Consequently, the diffusive and radiative properties of plasmas turbulent on sub-Larmor scales may serve as a powerful tool to diagnosis laboratory and astrophysical plasmas.
Sims, James S; Hagstrom, Stanley A
2014-06-14
In a previous work, Sims and Hagstrom ["Hylleraas-configuration-interaction study of the 1 (1)S ground state of neutral beryllium," Phys. Rev. A 83, 032518 (2011)] reported Hylleraas-configuration-interaction (Hy-CI) method variational calculations for the (1)S ground state of neutral beryllium with an estimated accuracy of a tenth of a microhartree. In this work, the calculations have been extended to higher accuracy and, by simple scaling of the orbital exponents, to the entire Be 2 (1)S isoelectronic sequence. The best nonrelativistic energies for Be, B(+), and C(++) obtained are -14.6673 5649 269, -24.3488 8446 36, and -36.5348 5236 25 hartree, respectively. Except for Be, all computed nonrelativistic energies are superior to the known reference energies for these states.
Quark-gluon plasma and topological quantum field theory
NASA Astrophysics Data System (ADS)
Luo, M. J.
2017-03-01
Based on an analogy with topologically ordered new state of matter in condensed matter systems, we propose a low energy effective field theory for a parity conserving liquid-like quark-gluon plasma (QGP) around critical temperature in quantum chromodynamics (QCD) system. It shows that below a QCD gap which is expected several times of the critical temperature, the QGP behaves like topological fluid. Many exotic phenomena of QGP near the critical temperature discovered at Relativistic Heavy Ion Collision (RHIC) are more readily understood by the suggestion that QGP is a topologically ordered state.
Loop quantum cosmology and singularities.
Struyve, Ward
2017-08-15
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
Hu, Bin; Petela, Naomi; Kurze, Alexander; Chan, Kok-Lung; Chapard, Christophe; Nasmyth, Kim
2015-01-01
Sequencing DNA fragments associated with proteins following in vivo cross-linking with formaldehyde (known as ChIP-seq) has been used extensively to describe the distribution of proteins across genomes. It is not widely appreciated that this method merely estimates a protein's distribution and cannot reveal changes in occupancy between samples. To do this, we tagged with the same epitope orthologous proteins in Saccharomyces cerevisiae and Candida glabrata, whose sequences have diverged to a degree that most DNA fragments longer than 50 bp are unique to just one species. By mixing defined numbers of C. glabrata cells (the calibration genome) with S. cerevisiae samples (the experimental genomes) prior to chromatin fragmentation and immunoprecipitation, it is possible to derive a quantitative measure of occupancy (the occupancy ratio – OR) that enables a comparison of occupancies not only within but also between genomes. We demonstrate for the first time that this ‘internal standard’ calibration method satisfies the sine qua non for quantifying ChIP-seq profiles, namely linearity over a wide range. Crucially, by employing functional tagged proteins, our calibration process describes a method that distinguishes genuine association within ChIP-seq profiles from background noise. Our method is applicable to any protein, not merely highly conserved ones, and obviates the need for the time consuming, expensive, and technically demanding quantification of ChIP using qPCR, which can only be performed on individual loci. As we demonstrate for the first time in this paper, calibrated ChIP-seq represents a major step towards documenting the quantitative distributions of proteins along chromosomes in different cell states, which we term biological chromodynamics. PMID:26130708
Quantum theory and chemistry: Two propositions
NASA Technical Reports Server (NTRS)
Aronowitz, S.
1980-01-01
Two propositions concerning quantum chemistry are proposed. First, it is proposed that the nonrelativistic Schroedinger equation, where the Hamiltonian operator is associated with an assemblage of nuclei and electrons, can never be arranged to yield specific molecules in the chemists' sense. It is argued that this result is a necessary condition if the Schroedinger has relevancy to chemistry. Second, once a system is in a particular state with regard to interactions among its components (the assemblage of nuclei and electrons), it cannot spontaneously eliminate any of those interactions. This leads to a subtle form of irreversibility.
Simulations of ion acceleration at non-relativistic shocks. I. Acceleration efficiency
Caprioli, D.; Spitkovsky, A.
2014-03-10
We use two-dimensional and three-dimensional 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 Alfvénic Mach numbers, produces universal power-law spectra ∝p {sup –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 shock drift acceleration, but they only gain a factor of a few in momentum and their maximum energy does not increase with time. These findings are consistent with the degree of polarization and the morphology of the radio and X-ray synchrotron emission observed, for instance, in the remnant of SN 1006. We also discuss the transition from thermal to non-thermal particles in the ion spectrum (supra-thermal region) and we identify two dynamical signatures peculiar of efficient particle acceleration, namely, the formation of an upstream precursor and the alteration of standard shock jump conditions.
Electron Pre-acceleration at Nonrelativistic High-Mach-number Perpendicular Shocks
NASA Astrophysics Data System (ADS)
Bohdan, Artem; Niemiec, Jacek; Kobzar, Oleh; Pohl, Martin
2017-09-01
We perform particle-in-cell simulations of perpendicular nonrelativistic collisionless shocks to study electron heating and pre-acceleration for parameters that permit the extrapolation to the conditions at young supernova remnants. Our high-resolution large-scale numerical experiments sample a representative portion of the shock surface and demonstrate that the efficiency of electron injection is strongly modulated with the phase of the shock reformation. For plasmas with low and moderate temperature (plasma beta {β }{{p}}=5\\cdot {10}-4 and {β }{{p}}=0.5), we explore the nonlinear shock structure and electron pre-acceleration for various orientations of the large-scale magnetic field with respect to the simulation plane, while keeping it at 90° to the shock normal. Ion reflection off of the shock leads to the formation of magnetic filaments in the shock ramp, resulting from Weibel-type instabilities, and electrostatic Buneman modes in the shock foot. In all of the cases under study, the latter provides first-stage electron energization through the shock-surfing acceleration mechanism. The subsequent energization strongly depends on the field orientation and proceeds through adiabatic or second-order Fermi acceleration processes for configurations with the out-of-plane and in-plane field components, respectively. For strictly out-of-plane field, the fraction of suprathermal electrons is much higher than for other configurations, because only in this case are the Buneman modes fully captured by the 2D simulation grid. Shocks in plasma with moderate {β }{{p}} provide more efficient pre-acceleration. The relevance of our results to the physics of fully 3D systems is discussed.
NASA Astrophysics Data System (ADS)
Long, Andrew J.; Lunardini, Cecilia; Sabancilar, Eray
2014-08-01
We study the physics potential of the detection of the Cosmic Neutrino Background via neutrino capture on tritium, taking the proposed PTOLEMY experiment as a case study. With the projected energy resolution of Δ ~ 0.15 eV, the experiment will be sensitive to neutrino masses with degenerate spectrum, m1 simeq m2 simeq m3 = mν gtrsim 0.1 eV. These neutrinos are non-relativistic today; detecting them would be a unique opportunity to probe this unexplored kinematical regime. The signature of neutrino capture is a peak in the electron spectrum that is displaced by 2 mν above the beta decay endpoint. The signal would exceed the background from beta decay if the energy resolution is Δ lesssim 0.7 mν . Interestingly, the total capture rate depends on the origin of the neutrino mass, being ΓD simeq 4 and ΓM simeq 8 events per year (for a 100 g tritium target) for unclustered Dirac and Majorana neutrinos, respectively. An enhancement of the rate of up to Script O(1) is expected due to gravitational clustering, with the unique potential to probe the local overdensity of neutrinos. Turning to more exotic neutrino physics, PTOLEMY could be sensitive to a lepton asymmetry, and reveal the eV-scale sterile neutrino that is favored by short baseline oscillation searches. The experiment would also be sensitive to a neutrino lifetime on the order of the age of the universe and break the degeneracy between neutrino mass and lifetime which affects existing bounds.
Long, Andrew J.; Lunardini, Cecilia; Sabancilar, Eray E-mail: Cecilia.Lunardini@asu.edu
2014-08-01
We study the physics potential of the detection of the Cosmic Neutrino Background via neutrino capture on tritium, taking the proposed PTOLEMY experiment as a case study. With the projected energy resolution of Δ ∼ 0.15 eV, the experiment will be sensitive to neutrino masses with degenerate spectrum, m{sub 1} ≅ m{sub 2} ≅ m{sub 3} = m{sub ν} ∼> 0.1 eV. These neutrinos are non-relativistic today; detecting them would be a unique opportunity to probe this unexplored kinematical regime. The signature of neutrino capture is a peak in the electron spectrum that is displaced by 2 m{sub ν} above the beta decay endpoint. The signal would exceed the background from beta decay if the energy resolution is Δ ∼< 0.7 m{sub ν} . Interestingly, the total capture rate depends on the origin of the neutrino mass, being Γ{sup D} ≅ 4 and Γ{sup M} ≅ 8 events per year (for a 100 g tritium target) for unclustered Dirac and Majorana neutrinos, respectively. An enhancement of the rate of up to O(1) is expected due to gravitational clustering, with the unique potential to probe the local overdensity of neutrinos. Turning to more exotic neutrino physics, PTOLEMY could be sensitive to a lepton asymmetry, and reveal the eV-scale sterile neutrino that is favored by short baseline oscillation searches. The experiment would also be sensitive to a neutrino lifetime on the order of the age of the universe and break the degeneracy between neutrino mass and lifetime which affects existing bounds.
Effects of the generalised uncertainty principle on quantum tunnelling
NASA Astrophysics Data System (ADS)
Blado, Gardo; Prescott, Trevor; Jennings, James; Ceyanes, Joshuah; Sepulveda, Rafael
2016-03-01
In a previous paper (Blado et al 2014 Eur. J. Phys. 35 065011), we showed that quantum gravity effects can be discussed with only a background in non-relativistic quantum mechanics at the undergraduate level by looking at the effect of the generalised uncertainty principle (GUP) on the finite and infinite square wells. In this paper, we derive the GUP corrections to the tunnelling probability of simple quantum mechanical systems which are accessible to undergraduates (alpha decay, simple models of quantum cosmogenesis and gravitational tunnelling radiation) and which employ the WKB approximation, a topic discussed in undergraduate quantum mechanics classes. It is shown that the GUP correction increases the tunnelling probability in each of the examples discussed.
Robust state preparation in quantum simulations of Dirac dynamics
NASA Astrophysics Data System (ADS)
Song, Xue-Ke; Deng, Fu-Guo; Lamata, Lucas; Muga, J. G.
2017-02-01
A nonrelativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between momentum and internal levels poses some difficulties to manipulate the internal states accurately in wave packets. We use invariants of motion to inverse engineer robust population inversion processes with a homogeneous, time-dependent simulated electric field. This exemplifies the usefulness of inverse-engineering techniques to improve the performance of quantum simulation protocols.
A hydrodynamical model for relativistic spin quantum plasmas
Asenjo, Felipe A.; Munoz, Victor; Valdivia, J. Alejandro; Mahajan, Swadesh M.
2011-01-15
Based on the one-body particle-antiparticle Dirac theory of electrons, a set of relativistic quantum fluid equations for a spin half plasma is derived. The particle-antiparticle nature of the relativistic particles is explicit in this fluid theory, which also includes quantum effects such as spin. The nonrelativistic limit is shown to be in agreement with previous attempts to develop a spin plasma theory derived from the Pauli Hamiltonian. Harnessing the formalism to the study of electromagnetic mode propagation, conceptually new phenomena are revealed; the particle-antiparticle effects increase the fluid opacity to these waves, while the spin effects tend to make the fluid more transparent.
NASA Astrophysics Data System (ADS)
Hagar, Amit
Among the alternatives of non-relativistic quantum mechanics (NRQM) there are those that give different predictions than quantum mechanics in yet-untested circumstances, while remaining compatible with current empirical findings. In order to test these predictions, one must isolate one's system from environmental induced decoherence, which, on the standard view of NRQM, is the dynamical mechanism that is responsible for the 'apparent' collapse in open quantum systems. But while recent advances in condensed-matter physics may lead in the near future to experimental setups that will allow one to test the two hypotheses, namely genuine collapse vs. decoherence, hence make progress toward a solution to the quantum measurement problem, those philosophers and physicists who are advocating an information-theoretic approach to the foundations of quantum mechanics are still unwilling to acknowledge the empirical character of the issue at stake. Here I argue that in doing so they are displaying an unwarranted double standard.
Quantum phases of Yang-Mills matrix model coupled to fundamental fermions
NASA Astrophysics Data System (ADS)
Pandey, Mahul; Vaidya, Sachindeo
2017-02-01
By investigating the SU(2) Yang-Mills matrix model coupled to fundamental fermions in the adiabatic limit, we demonstrate quantum critical behaviour at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. As a consequence of our analysis, we show that 2-color quantum chromodynamics coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase.
Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems
NASA Technical Reports Server (NTRS)
Zylka, Christian; Vojta, Guenter
1993-01-01
The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.
Sapir, Nir; Waxman, Eli; Katz, Boaz
2013-09-01
The spectrum of radiation emitted following shock breakout from a star's surface with a power-law density profile {rho}{proportional_to}x{sup n} is investigated. Assuming planar geometry, local Compton equilibrium, and bremsstrahlung emission as the dominant photon production mechanism, numerical solutions are obtained for the photon number density and temperature profiles as a function of time for hydrogen-helium envelopes. The temperature solutions are determined by the breakout shock velocity v{sub 0} and the pre-shock breakout density {rho}{sub 0} and depend weakly on the value of n. Fitting formulae for the peak surface temperature at breakout as a function of v{sub 0} and {rho}{sub 0} are provided, with T{sub peak} approx. 9.44 exp [12.63(v{sub 0}/c){sup 1/2}] eV, and the time dependence of the surface temperature is tabulated. The time integrated emitted spectrum is a robust prediction of the model, determined by T{sub peak} and v{sub 0} alone and insensitive to details of light travel time or slight deviations from spherical symmetry. Adopting commonly assumed progenitor parameters, breakout luminosities of Almost-Equal-To 10{sup 45} erg s{sup -1} and Almost-Equal-To 10{sup 44} erg s{sup -1} in the 0.3-10 keV band are expected for blue supergiant (BSG) and red supergiant (RSG)/He-WR progenitors, respectively (T{sub peak} is well below the band for RSGs, unless their radius is {approx}10{sup 13} cm). >30 detections of SN 1987A-like (BSG) breakouts are expected over the lifetime of ROSAT and XMM-Newton. An absence of such detections would imply either that the typical parameters assumed for BSG progenitors are grossly incorrect or that their envelopes are not hydrostatic. The observed spectrum and duration of XRF 080109/SN 2008D are in tension with a non-relativistic breakout from a stellar surface interpretation.
Decay widths of ground-state and excited {Xi}{sub b} baryons in a nonrelativistic quark model
Limphirat, Ayut; Kobdaj, Chinorat; Suebka, Prasart; Yan, Yupeng
2010-11-15
Decay processes of ground and excited bottom baryons are studied in the {sup 3}P{sub 0} nonrelativistic quark model with all model parameters fixed in the sector of light quarks. Using as an input the recent mass of {Xi}{sub b} and the theoretical masses of {Xi}{sub b}{sup *} and {Xi}{sub b}{sup '}, narrow decay widths are predicted for the ground-state bottom baryons {Xi}{sub b}{sup *} and {Xi}{sub b}{sup '}. The work predicts large decay widths, about 100 MeV for the {rho}-type orbital excitation states of {Xi}{sub b}.
NASA Astrophysics Data System (ADS)
Haider, Md. Masum
2016-12-01
An attempt has been taken to find a general equation for degenerate pressure of Chandrasekhar and constants, by using which one can study nonrelativistic as well as ultra-relativistic cases instead of two different equations and constants. Using the general equation, ion-acoustic solitary and shock waves have been studied and compared, numerically and graphically, the two cases in same situation of electron-positron-ion plasmas. Korteweg-de Vries (KdV) and KdV-Barger equations have been derived as well as their solution to study the soliton and shock profiles, respectively.
NASA Astrophysics Data System (ADS)
Ding, Min; Li, Yachun
2017-08-01
We consider the 1-D piston problem for the isentropic relativistic Euler equations when the total variations of the initial data and the speed of the piston are both 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 study the convergence of the entropy solutions to the corresponding entropy solutions of the classical non-relativistic isentropic Euler equations as the light speed c →+∞ .
NASA Astrophysics Data System (ADS)
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→ +∞.
Minic, Djordje; Pleimling, Michel
2008-12-01
We point out that the recent discussion of nonrelativistic anti-de Sitter space and conformal field theory correspondence has a direct application in nonequilibrium statistical physics, a fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent z=2 and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.
The Non-linear Schrödinger Equation and the Conformal Properties of Non-relativistic Space-Time
NASA Astrophysics Data System (ADS)
Horváthy, P. A.; Yera, J.-C.
2009-08-01
The cubic non-linear Schrödinger equation where the coefficient of the nonlinear term is a function F(t,x) only passes the Painlevé test of Weiss, Tabor, and Carnevale only for F=(a+bt)-1, where a and b are constants. This is explained by transforming the time-dependent system into the constant-coefficient NLS by means of a time-dependent non-linear transformation, related to the conformal properties of non-relativistic space-time. A similar argument explains the integrability of the NLS in a uniform force field or in an oscillator background.
Probability and Quantum Symmetries. II. The Theorem of Noether in quantum mechanics
Albeverio, S.; Rezende, J.; Zambrini, J.-C.
2006-06-15
For the largest class of physical systems having a classical analog, a new rigorous, but not probabilistic, Lagrangian version of nonrelativistic quantum mechanics is given, in terms of a notion of regularized action function. As a consequence of the study of the symmetries of this action, an associated Noether theorem is obtained. All the quantum symmetries resulting from the canonical quantization procedure follow in this way, as well as a number of symmetries which are new even for the case of the simplest systems. The method is based on the study of a corresponding Lie algebra and an analytical continuation in the time parameter of the probabilistic construction given in paper I of this work. Generically, the associated quantum first integrals are time dependent and the probabilistic model provides a natural interpretation of the new symmetries. Various examples illustrate the physical relevance of our results.
Freitag, Mark A.
2001-12-31
The major title of this dissertation, 'From first principles,' is a phase often heard in the study of thermodynamics and quantum mechanics. These words embody a powerful idea in the physical sciences; namely, that it is possible to distill the complexities of nature into a set of simple, well defined mathematical laws from which specific relations can then be derived . In thermodynamics, these fundamental laws are immediately familiar to the physical scientist by their numerical order: the First, Second and Third Laws. However, the subject of the present volume is quantum mechanics-specifically, non-relativistic quantum mechanics, which is appropriate for most systems of chemical interest.
The many facets of the (non-relativistic) Nuclear Equation of State
NASA Astrophysics Data System (ADS)
Giuliani, G.; Zheng, H.; Bonasera, A.
2014-05-01
A nucleus is a quantum many body system made of strongly interacting Fermions, protons and neutrons (nucleons). This produces a rich Nuclear Equation of State whose knowledge is crucial to our understanding of the composition and evolution of celestial objects. The nuclear equation of state displays many different features; first neutrons and protons might be treated as identical particles or nucleons, but when the differences between protons and neutrons are spelled out, we can have completely different scenarios, just by changing slightly their interactions. At zero temperature and for neutron rich matter, a quantum liquid-gas phase transition at low densities or a quark-gluon plasma at high densities might occur. Furthermore, the large binding energy of the α particle, a Boson, might also open the possibility of studying a system made of a mixture of Bosons and Fermions, which adds to the open problems of the nuclear equation of state.
NASA Astrophysics Data System (ADS)
Kaur, Gurpreet; Mittal, Raj
2014-11-01
Average M shell fluorescence yield (ϖM) have been calculated from non-relativistic data of McGuire (Phys Rev A 1972;5:1043-47) in the region Z=60-90 and relativistic data of Chen, Crasemann and Mark (Phys Rev A 1980;21:449-53) and (Phys Rev A 1983;27:2989-94) in the region Z=70-90 on M sub-shell fluorescence yield (ωMi, i=1-5) and Coster-Kronig yield (fMij, i=1-4, j=2-5) procured from our earlier work (a computer software code MFCKYLD) using Scofield's data (Lawrence Livermore Laboratory Report UCRL 51326; 1973) on M sub-shell photo-ionization cross-sections. Subsequently, a computer software code AMSFYLD was developed to generate the yield values on computer terminal or in file for both non-relativistic and relativistic data just by entering the atomic number Z of the element through keyboard or file. The values were compared with available theoretical and experimental values in the literature. The agreement between the present data and the other supports the present values.
Li, Shu-Shen; Long, Gui-Lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi
2001-01-01
Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization. PMID:11562459
NASA Astrophysics Data System (ADS)
Sulejmanpasic, Tin; Shao, Hui; Sandvik, Anders W.; Ünsal, Mithat
2017-09-01
In a spontaneously dimerized quantum antiferromagnet, spin-1 /2 excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-Abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between particle physics and condensed-matter physics. The analogy opens doors to improving our understanding of particle confinement and deconfinement by computational and experimental studies in quantum magnetism.
Sulejmanpasic, Tin; Shao, Hui; Sandvik, Anders W; Ünsal, Mithat
2017-09-01
In a spontaneously dimerized quantum antiferromagnet, spin-1/2 excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-Abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between particle physics and condensed-matter physics. The analogy opens doors to improving our understanding of particle confinement and deconfinement by computational and experimental studies in quantum magnetism.
Relativistic quantum dynamics on a double cone
NASA Astrophysics Data System (ADS)
Gomes, F. A.; Silva, Edilberto O.; Lima, Jonas R. F.; Filgueiras, C.; Moraes, F.
2017-02-01
In this paper, we study the relativistic quantum problem of a particle constrained to a double cone surface. For this purpose, we build the Dirac equation in a curved space using the tetrads formalism. Two cases are analysed. First, we consider a free particle on the conical surface, and then we add an uniform magnetic field. In the first case, the exact energy spectrum is obtained and its non-relativistic limit compared to previously published results. In the second case, the spectrum is also exactly obtained and a detailed analysis considering all possible combinations of signs of the quantum numbers reveals the occurrence of highly degenerate zero energy modes. The results obtained here can be applied, for instance, in the investigation of the electronic and transport properties of condensed matter systems that can be described by an effective Dirac equation, such as graphene and topological insulators.
Scattering States of HULTHÉN Interaction in Minimal Length Quantum Mechanics
NASA Astrophysics Data System (ADS)
Hassanabadi, H.; Zarrinkamar, S.; Maghsoodi, E.
2013-05-01
We first revisit the nonrelativistic minimal length quantum mechanics and reveal an interesting symmetry of the problem. In fact, we will show that the cumbersome problem can be cast into the ordinary Schrödinger equation with a new effective potential. Next, as a typical example, we show the minimal length Schrödinger equation in the presence of a nonminimal Hulthén vector interaction. The transmission and reflection coefficients are reported as well.
Transforming quantum operations: Quantum supermaps
NASA Astrophysics Data System (ADS)
Chiribella, G.; D'Ariano, G. M.; Perinotti, P.
2008-08-01
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.
NASA Astrophysics Data System (ADS)
Goldstein, Sheldon; Struyve, Ward
2015-01-01
Non-relativistic de Broglie-Bohm theory describes particles moving under the guidance of the wave function. In de Broglie's original formulation, the particle dynamics is given by a first-order differential equation. In Bohm's reformulation, it is given by Newton's law of motion with an extra potential that depends on the wave function—the quantum potential—together with a constraint on the possible velocities. It was recently argued, mainly by numerical simulations, that relaxing this velocity constraint leads to a physically untenable theory. We provide further evidence for this by showing that for various wave functions the particles tend to escape the wave packet. In particular, we show that for a central classical potential and bound energy eigenstates the particle motion is often unbounded. This work seems particularly relevant for ways of simulating wave function evolution based on Bohm's formulation of the de Broglie-Bohm theory. Namely, the simulations may become unstable due to deviations from the velocity constraint.
Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy
NASA Astrophysics Data System (ADS)
Hasebe, Kazuki
2017-07-01
We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S 2 k - 1 in the SO (2 k - 1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S 2 k - 1 to the one-dimension higher SO (2 k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Dowdall, R J; Davies, C T H; Horgan, R R; Monahan, C J; Shigemitsu, J
2013-05-31
We present the first lattice QCD calculation of the decay constants f(B) and f(B(s)) with physical light quark masses. We use configurations generated by the MILC Collaboration including the effect of u, d, s, and c highly improved staggered quarks in the sea at three lattice spacings and with three u/d quark mass values going down to the physical value. We use improved nonrelativistic QCD (NRQCD) for the valence b quarks. Our results are f(B)=0.186(4) GeV, f(B(s))=0.224(4) GeV, f(B(s))/f(B)=1.205(7), and M(B(s))-M(B)=85(2) MeV, superseding earlier results with NRQCD b quarks. We discuss the implications of our results for the standard model rates for B((s))→μ(+)μ(-) and B→τν.
R Aqr: a prototype for non-relativistic astrophysical jets and a key for understanding jet formation
NASA Astrophysics Data System (ADS)
Stute, Matthias
2013-10-01
R Aqr is a well-known prototype for non-relativistic astrophysical jets. The R Aqr jet has been extensively observed in the ultraviolet, optical, and radio regimes. We propose to re-visit this enigmatic object with HST after twelve years, in order to measure the proper motions of its inner knots with unprecedented accuracy, to derive emission lines ratios for these knots, and to investigate the width of the jet at several distances from the jet source. We will compare the results with numerical models of radiative shocks in propagating jets and of jet formation models and will determine the kinematics of the jet, the history of ejection events and basic parameters of the jet engine as e.g. the launching radius of the jet-ejecting accretion disk.
NASA Astrophysics Data System (ADS)
Li, A.; Hu, J. N.; Shang, X. L.; Zuo, W.
2016-01-01
The density and isospin dependencies of nonrelativistic nucleon effective mass (mN*) are studied, which is a measure of the nonlocality of the single particle (s.p.) potential. It can be decoupled as the so-called k mass (mk*, i.e., the nonlocality in space) and E mass (mE*, i.e., the nonlocality in time). Both k mass and E mass are determined and compared by using the latest versions of the nonrelativistic Brueckner-Hartree-Fock (BHF) model and the relativistic Hartree-Fock (RHF) model. The latter is achieved based on the corresponding Schrödinger equivalent s.p. potential in a relativistic framework. We demonstrate the origins of different effective masses and discuss also their neutron-proton splitting in the asymmetric matter in different models. We find that the neutron-proton splittings of both the k mass and the E mass have the same asymmetry dependencies at the densities considered; namely, mk,n *>mk,p * and mE,p *>mE,n * . However, the resulting splittings of nucleon effective masses could have different asymmetry dependencies in these two models because they could be dominated either by the k mass (then we have mn*>mp* in the BHF model), or by the E mass (then we have mp*>mn* in the RHF model). The isospin splitting in the BHF model is more consistent with the recent analysis from the nucleon-nucleus-scattering data, while the small E mass mE* in the RHF case as a result of the missing ladder summation finally leads to an opposite splitting behavior.
The impact of QCD and light-cone quantum mechanics on nuclear physics
Brodsky, S.J.; Schlumpf, F.
1994-12-01
We discuss a number of novel applications of Quantum Chromodynamics to nuclear structure and dynamics, such as the reduced amplitude formalism for exclusive nuclear amplitudes. We particularly emphasize the importance of light-cone Hamiltonian and Fock State methods as a tool for describing the wavefunctions of composite relativistic many-body systems and their interactions. We also show that the use of covariant kinematics leads to nontrivial corrections to the standard formulae for the axial, magnetic, and quadrupole moments of nucleons and nuclei.
Quantum gravitational decoherence of light and matter
NASA Astrophysics Data System (ADS)
Oniga, Teodora; Wang, Charles H.-T.
2016-02-01
Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms of energy and matter causing decoherence. This may have subtle implications on precision laboratory experiments and astronomical observations and could limit the ultimate capacities for quantum technologies prone to decoherence. To establish the essential physical mechanism of decoherence under weak spacetime fluctuations, we carry out a sequence of analytical steps utilizing the Dirac constraint quantization and gauge invariant influence functional techniques resulting in a general master equation of a compact form that describes an open quantum gravitational system with arbitrary bosonic fields. An initial application of the theory is illustrated by the implied quantum gravitational dissipation of light as well as (non)relativistic massive or massless scalar particles. Related effects could eventually lead to important physical consequences including those on a cosmological scale and for a large number of correlated particles.
NASA Astrophysics Data System (ADS)
Procopio, Lorenzo M.; Rozema, Lee A.; Dakić, Borivoje; Walther, Philip
2017-09-01
In his recent article [Phys. Rev. A 95, 060101(R) (2017), 10.1103/PhysRevA.95.060101], Adler questions the usefulness of the bound found in our experimental search for genuine effects of hypercomplex quantum mechanics [Nat. Commun. 8, 15044 (2017), 10.1038/ncomms15044]. Our experiment was performed using a black-box (instrumentalist) approach to generalized probabilistic theories; therefore, it does not assume a priori any particular underlying mechanism. From that point of view our experimental results do indeed place meaningful bounds on the possible effects of "postquantum theories," including quaternionic quantum mechanics. In his article, Adler compares our experiment to nonrelativistic and Möller formal scattering theories within quaternionic quantum mechanics. With a particular set of assumptions, he finds that quaternionic effects would likely not manifest themselves in general. Although these assumptions are justified in the nonrelativistic case, a proper calculation for relativistic particles is still missing. Here, we provide a concrete relativistic example of Klein-Gordon scattering wherein the quaternionic effects persist. We note that when the Klein-Gordon equation is formulated using a Hamiltonian formalism it displays a so-called "indefinite metric," a characteristic feature of relativistic quantum wave equations. In Adler's example this is directly forbidden by his assumptions, and therefore our present example is not in contradiction to his work. In complex quantum mechanics this problem of an indefinite metric is solved in a second quantization. Unfortunately, there is no known algorithm for canonical field quantization in quaternionic quantum mechanics.
Effects of Number Scaling on Entangled States in Quantum Mechanics
Benioff, Paul
2016-05-19
A summary of number structure scaling is followed by a description of the effects of number scaling in nonrelativistic quantum mechanics. The description extends earlier work to include the effects on the states of two or more interacting particles. Emphasis is placed on the effects on entangled states. The resulting scaling field is generalized to describe the effects on these states. It is also seen that one can use fiber bundles with fibers associated with single locations of the underlying space to describe the effects of scaling on arbitrary numbers of particles.
Quantum power functional theory for many-body dynamics
Schmidt, Matthias
2015-11-07
We construct a one-body variational theory for the time evolution of nonrelativistic quantum many-body systems. The position- and time-dependent one-body density, particle current, and time derivative of the current act as three variational fields. The generating (power rate) functional is minimized by the true current time derivative. The corresponding Euler-Lagrange equation, together with the continuity equation for the density, forms a closed set of one-body equations of motion. Space- and time-nonlocal one-body forces are generated by the superadiabatic contribution to the functional. The theory applies to many-electron systems.
Operational dynamic modeling transcending quantum and classical mechanics.
Bondar, Denys I; Cabrera, Renan; Lompay, Robert R; Ivanov, Misha Yu; Rabitz, Herschel A
2012-11-09
We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.
Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
NASA Astrophysics Data System (ADS)
Bondar, Denys I.; Cabrera, Renan; Lompay, Robert R.; Ivanov, Misha Yu.; Rabitz, Herschel A.
2012-11-01
We introduce a general and systematic theoretical framework for operational dynamic modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide-ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.
Finite-time measurement of quantum particle's mean position
NASA Astrophysics Data System (ADS)
Liu, Y.; Sokolovski, D.
2001-01-01
We analyze nonrelativistic quantum measurement of the time average of the particle's coordinate, X≡t- 1∫t0x(t')dt'. The measurement amplitude is constructed by restricting the Feynman path integral to paths with the required value of X. The resulting decomposition of the Schrödinger wave function determines the type of meter needed to measure X. We show that such meter can be realized as a magnetic moment traveling with the particle in a magnetic field whose magnitude linearly changes with x. Weak and strong measurement regimes are discussed.
Entanglement renormalization for quantum fields in real space.
Haegeman, Jutho; Osborne, Tobias J; Verschelde, Henri; Verstraete, Frank
2013-03-08
We show how to construct renormalization group (RG) flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space. This is achieved by generalizing the multiscale entanglement renormalization ansatz to continuum theories. The variational class of wave functions arising from this RG flow are translation invariant and exhibits an entropy-area law. We illustrate the construction for a free nonrelativistic boson model, and argue that the full power of the construction should emerge in the case of interacting theories.
Murguia, Gabriela; Moreno, Matias; Torres, Manuel
2009-04-20
A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non-relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non-perturbative methodology should be applied.
How do quantum numbers generally vary in the adiabatic transformation of an ideal gas?
NASA Astrophysics Data System (ADS)
Yarman, T.; L. Kholmetskii, A.
2011-10-01
We continue to analyse the known law of adiabatic transformation for an ideal gas PV5/3 = Constant, where P is the pressure and V is the volume, and following the approach of non-relativistic quantum mechanics which we suggested in a previous work (Yarman et al. 2010 Int. J. Phys. Sci. 5 1524). We explicitly determine the constant for the general parallelepiped geometry of a container. We also disclose how the quantum numbers associated with molecules of an ideal gas vary through an arbitrary adiabatic transformation. Physical implications of the results obtained are discussed.
Manakov, N. L. Krylovetsky, A. A.; Marmo, S. I.
2015-11-15
Compact analytic expressions have been derived by a direct expansion in ħ → 0 for the nonrelativistic amplitude of Coulomb bremsstrahlung radiation (BR), the differential (in frequency and angles of the scattered electron) BR cross section, and the triply differential BR cross section that takes into account the bremsstrahlung photon direction and polarization and the scattered electron direction. They contain the classical limit and a quantum correction of the order of ħ at an arbitrary BR frequency ω. An explicit expression has been found for the quantum correction of the order of ħ to the classical BR spectrum.
NASA Astrophysics Data System (ADS)
Dragan, Andrzej; Fuentes, Ivette; Louko, Jorma
2011-04-01
A single quantum system, such as the Unruh-DeWitt detector, can be used to determine absolute acceleration by local measurements on a quantum field. To show this, we consider two kinematically indistinguishable scenarios: an inertial observer, Bob, measuring the field of a uniformly accelerated cavity, and his noninertial twin, Rob, accelerating and making measurements in a stationary cavity. We find that these scenarios can be distinguished in the nonrelativistic regime only by measurements on highly excited massive fields, allowing one to detect the noninertialness of the reference frame.
An Efficient and Accurate Quantum Lattice-Gas Model for the Many-Body Schroedinger Wave Equation
2002-01-01
CONTRACT NUMBER AN EFFICIENT AND ACCURATE QUANTUM LATTICE-GAS MODEL FOR THE MANY-BODY SCHROEDINGER WAVE EQUATION 5b. GRANT NUMBER SC. PROGRAM ELEMENT...for simulating the time-dependent evolution of a many-body jiiantum mechanical system of particles governed by the non-relativistic Schroedinger " wave...the numerical dispersion of the simulated wave packets is compared with the analytical solutions. 15. SUBJECT TERM: Schroedinger wave equation
Quantum correlations which imply causation
Fitzsimons, Joseph F.; Jones, Jonathan A.; Vedral, Vlatko
2015-01-01
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously, motivating us to define a measure of causality that discriminates between spatial and temporal correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements. PMID:26675807
NASA Astrophysics Data System (ADS)
Ducharme, R.; da Paz, I. G.
2016-08-01
In two recent papers exact Hermite-Gaussian solutions to relativistic wave equations were obtained for both electromagnetic and particle beams. The solutions for particle beams correspond to those of the Schrödinger equation in the nonrelativistic limit. Here, it will be shown that each beam particle has additional 4-momentum resulting from transverse localization compared to a free particle traveling in the same direction as the beam with the same speed. This will be referred to as the quantum 4-potential term since it will be shown to play an analogous role in relativistic Hamiltonian quantum mechanics as the Bohm potential in the nonrelativistic quantum Hamilton-Jacobi equation. Low-order localization effects include orbital angular momentum, Gouy phase, and beam spreading. Toward a more systematic approach for calculating localization effects at all orders, it will be shown that both the electromagnetic and quantum 4-potentials couple into the canonical 4-momentum of a particle in a similar way. This offers the prospect that traditional methods used to calculate the affect of an electromagnetic field on a particle can now be adapted to take localization effects into account. The prospects for measuring higher order quantum 4-potential related effects experimentally are also discussed alongside some questions to challenge the quantum information and quantum field theorists.
Entanglement spectrum and Rényi entropies of nonrelativistic conformal fermions
NASA Astrophysics Data System (ADS)
Porter, William J.; Drut, Joaquín E.
2016-10-01
We characterize nonperturbatively the Rényi entropies of degree n =2 ,3 ,4 , and 5 of three-dimensional, strongly coupled many-fermion systems in the scale-invariant regime of short interaction range and large scattering length, i.e., in the unitary limit. We carry out our calculations using lattice methods devised recently by us. Our results show the effect of strong pairing correlations on the entanglement entropy, which modify the subleading behavior for large subsystem sizes (as characterized by the dimensionless parameter x =kFLA , where kF is the Fermi momentum and LA the linear subsystem size), but leave the leading order unchanged relative to the noninteracting case. Moreover, we find that the onset of the subleading asymptotic regime is at surprisingly small x ≃2 -4 . We provide further insight into the entanglement properties of this system by analyzing the spectrum of the entanglement Hamiltonian of the two-body problem from weak to strong coupling. The low-lying entanglement spectrum displays clear features as the strength of the coupling is varied, such as eigenvalue crossing and merging, a sharp change in the Schmidt gap, and scale invariance at unitarity. Beyond the low-lying component, the spectrum appears as a quasicontinuum distribution, for which we present a statistical characterization; we find, in particular, that the mean shifts to infinity as the coupling is turned off, which indicates that that part of the spectrum represents nonperturbative contributions to the entanglement Hamiltonian. In contrast, the low-lying entanglement spectrum evolves to finite values in the noninteracting limit. The scale invariance of the unitary regime guarantees that our results are universal features intrinsic to three-dimensional quantum mechanics and represent a well-defined prediction for ultracold atom experiments, which were recently shown to have direct access to the entanglement entropy.
Spin Matrix theory: a quantum mechanical model of the AdS/CFT correspondence
NASA Astrophysics Data System (ADS)
Harmark, Troels; Orselli, Marta
2014-11-01
We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U( N). We show that SMT describes super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the g → ∞ limit of SMT can be mapped to the supersymmetric sector of string theory on AdS5 × S 5. We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite- N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g. Setting g = 0 it is a theory of N 2 + 1 harmonic oscillators while for large g it becomes 2 N harmonic oscillators.
Composition in the Quantum World
NASA Astrophysics Data System (ADS)
Hall, Edward Jonathan
This thesis presents a problem for the foundations of quantum mechanics. It arises from the way that theory describes the composition of larger systems in terms of smaller ones, and renders untenable a wide range of interpretations of quantum mechanics. That quantum mechanics is difficult to interpret is old news, given the well-known Measurement Problem. But the problem I raise is quite different, and in important respects more fundamental. In brief: The physical world exhibits mereological structure: physical objects have parts, which in turn have parts, and so on. A natural way to try to represent this structure is by means of a particle theory, according to which the physical world consists entirely enduring physical objects which themselves have no proper parts, but aggregates of which are, or compose, all physical objects. Elementary, non-relativistic quantum mechanics can be cast in this mold--at least, according to the usual expositions of that theory. But herein lies the problem: the standard attempt to give a systematic particle interpretation to elementary quantum mechanics results in nonsense, thanks to the well-established principle of Permutation Invariance, which constrains the quantum -mechanical description of systems containing identical particles. Specifically, it follows from the most minimal principles of a particle interpretation (much weaker than those needed to generate the Measurement Problem), together with Permutation Invariance, that systems identical in composition must have the same physical state. In other words, systems which merely have the same numbers of the same types of particles are therefore, at all times, perfect physical duplicates. This conclusion is absurd: e.g., it is quite plausible that some of those particles which compose my body make up a system identical in composition to some pepperoni pizza. Yet no part of me is a qualitative physical duplicate of any pepperoni pizza. Perhaps "you are what you eat" --but not in
Alba, David; Crater, Horace W.; Lusanna, Luca
2011-06-15
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics, where the world-lines of the particles are parametrized in terms of the Fokker-Pryce center of inertia and of Wigner-covariant relative 3-coordinates inside the instantaneous Wigner 3-spaces, and where there is a decoupled (non-covariant and non-local) canonical relativistic center of mass. This approach: (a) allows us to make a consistent quantization in every inertial frame; (b) leads to a description of both bound and scattering states; (c) offers new insights on the relativistic localization problem; (d) leads to a non-relativistic limit with a Hamilton-Jacobi treatment of the Newton center of mass; (e) clarifies non-local aspects (spatial non-separability) of relativistic entanglement connected with Lorentz signature and not present in its non-relativistic treatment.
Braun, Jens; Chen, Jiunn-Wei; Deng, Jian; Drut, Joaquín E; Friman, Bengt; Ma, Chen-Te; Tsai, Yu-Dai
2013-03-29
From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.
Stapp, H.P.
1988-12-01
Quantum ontologies are conceptions of the constitution of the universe that are compatible with quantum theory. The ontological orientation is contrasted to the pragmatic orientation of science, and reasons are given for considering quantum ontologies both within science, and in broader contexts. The principal quantum ontologies are described and evaluated. Invited paper at conference: Bell's Theorem, Quantum Theory, and Conceptions of the Universe, George Mason University, October 20-21, 1988. 16 refs.
Salbi, Pegah; Matzner, Christopher D.; Ro, Stephen; Levin, Yuri
2014-07-20
Non-spherical explosions develop non-radial flows as the pattern of shock emergence progresses across the stellar surface. In supernovae, these flows can limit ejecta speeds, stifle shock breakout emission, and cause collisions outside the star. Similar phenomena occur in stellar and planetary collisions, tidal disruption events, accretion-induced collapses, and propagating detonations. We present two-dimensional, nested-grid Athena simulations of non-radial shock emergence in a frame comoving with the breakout pattern, focusing on the adiabatic, non-relativistic limit in a plane stratified envelope. We set boundary conditions using a known self-similar solution and explore the role of box size and resolution on the result. The shock front curves toward the stellar surface, and exhibits a kink from which weak discontinuities originate. Flow around the point of shock emergence is neither perfectly steady nor self-similar. Waves and vortices, which are not predominantly due to grid effects, emanate from this region. The post-shock flow is deflected along the stellar surface and its pressure disturbs the stellar atmosphere upstream of the emerging shock. We use the numerical results and their analytical limits to predict the effects of radiation transfer and gravity, which are not included in our simulations.
NASA Astrophysics Data System (ADS)
Grinevich, P. G.; Mironov, A. E.; Novikov, S. P.
2010-09-01
We study the manifold of complex Bloch-Floquet eigenfunctions for the zero level of a two-dimensional nonrelativistic Pauli operator describing the propagation of a charged particle in a periodic magnetic field with zero flux through the elementary cell and a zero electric field. We study this manifold in full detail for a wide class of algebraic-geometric operators. In the nonzero flux case, the Pauli operator ground state was found by Aharonov and Casher for fields rapidly decreasing at infinity and by Dubrovin and Novikov for periodic fields. Algebraic-geometric operators were not previously known for fields with nonzero flux because the complex continuation of "magnetic" Bloch-Floquet eigenfunctions behaves wildly at infinity. We construct several nonsingular algebraic-geometric periodic fields (with zero flux through the elementary cell) corresponding to complex Riemann surfaces of genus zero. For higher genera, we construct periodic operators with interesting magnetic fields and with the Aharonov-Bohm phenomenon. Algebraic-geometric solutions of genus zero also generate soliton-like nonsingular magnetic fields whose flux through a disc of radius R is proportional to R (and diverges slowly as R → ∞). In this case, we find the most interesting ground states in the Hilbert space L 2 (ℝ 2 ).
Riconda, C.; Weber, S.; Tikhonchuk, V. T.; Adam, J.-C.; Heron, A.
2006-08-15
Two-dimensional particle-in-cell simulations of laser-plasma interaction using a plane-wave geometry show strong bursty stimulated Brillouin backscattering, rapid filamentation, and subsequent plasma cavitation. It is shown that the cavitation is not induced by self-focusing. The electromagnetic fields below the plasma frequency that are excited are related to transient soliton-like structures. At the origin of these solitons is a three-wave decay process exciting new modes in the plasma. The cavitation is responsible for a strong local reduction of the reflectivity and goes along with an efficient but transient heating of the electrons. Once heating ceases, transmission starts to increase. Local as well as global average reflectivities attain a very low value due to strong plasma density variations brought about by the cavitation process. On the one hand, the simulations confirm the existence of a new mechanism of cavity and soliton formation in nonrelativistic laser-plasma interaction in two dimensions, which was shown to exist in one-dimensional simulations [S. Weber, C. Riconda, and V. T. Tikhonchuk, Phys. Rev. Lett. 94, 055005 (2005)]. On the other hand, new aspects are introduced inherently related to the additional degree of freedom.
Greenwald, Jared; Satheeshkumar, V.H.; Wang, Anzhong E-mail: VHSatheeshkumar@baylor.edu
2010-12-01
We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in terms of the U(1) gauge field A. When solar system tests are considered, severe constraints on A are obtained, which seemingly pick up the Schwarzschild solution uniquely. In contrast to other versions of the Horava-Lifshitz theory, non-singular static stars made of a perfect fluid without heat flow can be constructed, due to the coupling of the fluid with the gauge field. These include the solutions with a constant pressure. We also study the general junction conditions across the surface of a star. In general, the conditions allow the existence of a thin matter shell on the surface. When applying these conditions to the perfect fluid solutions with the vacuum ones as describing their external spacetimes, we find explicitly the matching conditions in terms of the parameters appearing in the solutions. Such matching is possible even without the presence of a thin matter shell.
NASA Astrophysics Data System (ADS)
Le Yaouanc, A.; Melikhov, D.; Morénas, V.; Oliver, L.; Pène, O.; Raynal, J.-C.
2000-10-01
The quark-hadron duality in the inclusive semileptonic decay B-->Xclν in the Shifman-Voloshin limit Λ<<δm=mb-mc<
Quantum Computer Games: Quantum Minesweeper
ERIC Educational Resources Information Center
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Quantum Computer Games: Quantum Minesweeper
ERIC Educational Resources Information Center
Gordon, Michal; Gordon, Goren
2010-01-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…
Quantum computation for quantum chemistry
NASA Astrophysics Data System (ADS)
Aspuru-Guzik, Alan
2010-03-01
Numerically exact simulation of quantum systems on classical computers is in general, an intractable computational problem. Computational chemists have made progress in the development of approximate methods to tackle complex chemical problems. The downside of these approximate methods is that their failure for certain important cases such as long-range charge transfer states in the case of traditional density functional theory. In 1982, Richard Feynman suggested that a quantum device should be able to simulate quantum systems (in our case, molecules) exactly using quantum computers in a tractable fashion. Our group has been working in the development of quantum chemistry algorithms for quantum devices. In this talk, I will describe how quantum computers can be employed to carry out numerically exact quantum chemistry and chemical reaction dynamics calculations, as well as molecular properties. Finally, I will describe our recent experimental quantum computation of the energy of the hydrogen molecule using an optical quantum computer.
NASA Astrophysics Data System (ADS)
Degen, C. L.; Reinhard, F.; Cappellaro, P.
2017-07-01
"Quantum sensing" describes the use of a quantum system, quantum properties, or quantum phenomena to perform a measurement of a physical quantity. Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors or atomic clocks. More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions, and flux qubits. The field is expected to provide new opportunities—especially with regard to high sensitivity and precision—in applied physics and other areas of science. This review provides an introduction to the basic principles, methods, and concepts of quantum sensing from the viewpoint of the interested experimentalist.
Pfeiffer, P.; Sanz, M.
2016-07-06
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. As a result, the proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.
NASA Astrophysics Data System (ADS)
Pfeiffer, P.; Egusquiza, I. L.; di Ventra, M.; Sanz, M.; Solano, E.
2016-07-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.
Pfeiffer, P.; Egusquiza, I. L.; Di Ventra, M.; Sanz, M.; Solano, E.
2016-01-01
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems. PMID:27381511
Transit time of a freely falling quantum particle in a background gravitational field
NASA Astrophysics Data System (ADS)
Davies, P. C. W.
2004-12-01
Using a model quantum clock, I evaluate an expression for the time of a non-relativistic quantum particle to transit a piecewise geodesic path in a background gravitational field with small spacetime curvature (gravity gradient), in the case in which the apparatus is in free fall. This calculation complements and extends an earlier one (Davies 2004) in which the apparatus is fixed to the surface of the Earth. The result confirms that, for particle velocities not too low, the quantum and classical transit times coincide, in conformity with the principle of equivalence. I also calculate the quantum corrections to the transit time when the de Broglie wavelengths are long enough to probe the spacetime curvature. The results are compared with the calculation of Chiao and Speliotopoulos (2003), who propose an experiment to measure the foregoing effects.
Wake potential with exchange-correlation effects in semiconductor quantum plasmas
Khan, Arroj A.; Jamil, M.; Hussain, A.
2015-09-15
Using the non-relativistic quantum hydrodynamic model, wake potential has been studied in a magnetized semiconductor quantum plasma in the presence of upper hybrid wave which is excited via externally injected electron beam. The quantum effect contains electron exchange and correlation potential, Fermi degenerate pressure, and Bohm potential. It is found that the contribution of quantum mechanical electron exchange and correlation potential significantly modifies the amplitude and the effective length of the oscillatory wake potential. In the electron-hole plasma systems, electron exchange-correlation effects tend to increase the magnitude of the wake potential and are much effective at the distances of the order of Debye-length. The application of the work in context of the semiconductor plasmas have also been analyzed graphically.
Security of quantum bit string commitment depends on the information measure.
Buhrman, Harry; Christandl, Matthias; Hayden, Patrick; Lo, Hoi-Kwong; Wehner, Stephanie
2006-12-22
Unconditionally secure nonrelativistic bit commitment is known to be impossible in both the classical and the quantum world. However, when committing to a string of n bits at once, how far can we stretch the quantum limits? In this Letter, we introduce a framework of quantum schemes where Alice commits a string of n bits to Bob, in such a way that she can only cheat on a bits and Bob can learn at most b bits of information before the reveal phase. Our results are twofold: we show by an explicit construction that in the traditional approach, where the reveal and guess probabilities form the security criteria, no good schemes can exist: a + b is at least n. If, however, we use a more liberal criterion of security, the accessible information, we construct schemes where a = 4log2(n) + O(1) and b = 4, which is impossible classically. Our findings significantly extend known no-go results for quantum bit commitment.
NASA Astrophysics Data System (ADS)
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.
Bakke, K.; Furtado, C.; Belich, H.
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.
Solving the nonlocality riddle by conformal quantum geometrodynamics
NASA Astrophysics Data System (ADS)
Santamato, Enrico; De Martini, Francesco
2013-06-01
A rigorous ab initio derivation of the quantum mechanics of a single particle with spin is presented starting by conformally Weyl-gauge-invariant principle. The particle is described as a relativistic top with six Euler's angles and quantum effects are introduced by assuming that the Weyl's curvature of the particle configuration space acts on it as an external scalar potential. Weyl's conformal covariance is made explicit in all steps of the theory. It is shown that metric of the configuration space accounts for non-quantum relativistic effects, while the affine connections account for quantum relativistic effects. In this way, classical and quantum features acquire well distinguished geometrical origin. A scalar wave function is also introduced to recover the connection with the standard quantum description based on Dirac's four-component spinors. Finally, the case of two entangled spins is considered in the nonrelativistic limit and it is found that the nonlocality rests on the entanglement of the spin internal orientational variables, playing the role of "hidden variables". The theory was carried out in the Minkowski space-time, but it can be easily extended to a space with nonzero Riemann curvature.
General relativistic effects in quantum interference of photons
NASA Astrophysics Data System (ADS)
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Ralph, Timothy C.; Brukner, Časlav
2012-11-01
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon’s coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.
NASA Astrophysics Data System (ADS)
Wieland, Volkmar; Pohl, Martin; Niemiec, Jacek; Rafighi, Iman; Nishikawa, Ken-Ichi
2016-03-01
For parameters that are applicable to the conditions at young supernova remnants, we present results of two-dimensional, three-vector (2D3V) particle-in-cell simulations of a non-relativistic plasma shock with a large-scale perpendicular magnetic field inclined at a 45^\\circ angle to the simulation plane to approximate three-dimensional (3D) physics. We developed an improved clean setup that uses the collision of two plasma slabs with different densities and velocities, leading to the development of two distinctive shocks and a contact discontinuity. The shock formation is mediated by Weibel-type filamentation instabilities that generate magnetic turbulence. Cyclic reformation is observed in both shocks with similar period, for which we note global variations due to shock rippling and local variations arising from turbulent current filaments. The shock rippling occurs on spatial and temporal scales produced by the gyro-motions of shock-reflected ions. The drift motion of electrons and ions is not a gradient drift, but is commensurate with {\\boldsymbol{E}}× {\\boldsymbol{B}} drift. We observe a stable supra-thermal tail in the ion spectra, but no electron acceleration because the amplitude of the Buneman modes in the shock foot is insufficient for trapping relativistic electrons. We see no evidence of turbulent reconnection. A comparison with other two-dimensional (2D) simulation results suggests that the plasma beta and the ion-to-electron mass ratio are not decisive for efficient electron acceleration, but the pre-acceleration efficacy might be reduced with respect to the 2D results once 3D effects are fully accounted for. Other microphysical factors may also play a part in limiting the amplitude of the Buneman waves or preventing the return of electrons to the foot region.
NASA Astrophysics Data System (ADS)
Alba, David; Lusanna, Luca; Pauri, Massimo
2002-01-01
After the separation of the center-of-mass motion, a new privileged class of canonical Darboux bases is proposed for the nonrelativistic N-body problem by exploiting a geometrical and group theoretical approach to the definition of body frame for deformable bodies. This basis is adapted to the rotation group SO(3), whose canonical realization is associated with a symmetry Hamiltonian left action. The analysis of the SO(3) coadjoint orbits contained in the N-body phase space implies the existence of a spin frame for the N-body system. Then, the existence of appropriate nonsymmetry Hamiltonian right actions for nonrigid systems leads to the construction of an N-dependent discrete number of dynamical body frames for the N-body system, hence to the associated notions of dynamical and measurable orientation and shape variables, angular velocity, rotational and vibrational configurations. For N=3 the dynamical body frame turns out to be unique and our approach reproduces the xxzz gauge of the gauge theory associated with the orientation-shape SO(3) principal bundle approach of Littlejohn and Reinsch. For N>=4 our description is different, since the dynamical body frames turn out to be momentum dependent. The resulting Darboux bases for N>=4 are connected to the coupling of the spins of particle clusters rather than the coupling of the centers of mass (based on Jacobi relative normal coordinates). One of the advantages of the spin coupling is that, unlike the center-of-mass coupling, it admits a relativistic generalization.
NASA Astrophysics Data System (ADS)
Bashir, Muhammad Fraz; Murtaza, G.
2012-12-01
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 modes whose magnetic-field perturbations are perpendicular to the ambient magnetic field, i.e., B 1 bot B 0, 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 (i.e., the whistler mode, pure Alfvén mode, firehose instability, and whistler instability), and the O-mode are affected by thermal anisotropies, since they satisfy the required condition {B}1bot {B}0. By contrast, the perpendicularly propagating X-mode and the modes derived from it (the pure transverse X-mode and Bernstein mode) show no such effect. In general, we note that the thermal anisotropy modifies the parallel propagating modes via the parallel acoustic effect, while it modifies the perpendicular propagating modes via the Larmor-radius effect. In oblique propagation for kinetic Alfvén waves, the thermal anisotropy affects the kinetic regime more than it affects the inertial regime. The generalized fast mode exhibits two distinct acoustic effects, one in the direction parallel to the ambient magnetic field and the other in the direction perpendicular to it. In the fast-mode instability, the magneto-sonic wave causes suppression of the firehose instability. We discuss all these propagation characteristics and present graphic illustrations. The threshold conditions for different instabilities are
Tests of quantum-gravity-induced nonlocality via optomechanical experiments
NASA Astrophysics Data System (ADS)
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2017-01-01
The nonrelativistic limit of nonlocal modifications to the Klein-Gordon operator is studied, and the experimental possibilities of casting stringent constraints on the nonlocality scale via planned and/or current optomechanical experiments are discussed. Details of the perturbative analysis and semianalytical simulations leading to the dynamic evolution of a quantum harmonic oscillator in the presence of nonlocality reported in [A. Belenchia, D. M. T. Benincasa, S. Liberati, F. Marin, F. Marino, and A. Ortolan, Phys. Rev. Lett. 116, 161303 (2016), 10.1103/PhysRevLett.116.161303] are given, together with a comprehensive account of the experimental methodology with particular regard to sensitivity limitations related to thermal decoherence time and active cooling of the oscillator. Finally, a strategy for detecting nonlocality scales of the order of 10-22÷10-26 m by means of the spontaneous time-periodic squeezing of quantum-coherent states is provided.
Geometric quantum phase in the spacetime of topological defects
NASA Astrophysics Data System (ADS)
Bakke, K.; Furtado, C.; Nascimento, J. R.
2011-07-01
In this contribution, we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of a neutral particle which possesses permanent magnetic and electric dipole moments in the presence of an electromagnetic field in this curved background. We also study the influence of noninertial effects of a rotating frame and and obtain several contributions to the relativistic geometric phase due to the noninertial effects and the topology of spacetime. The analogous Aharonov-Casher and He-Mckellar-Wilkens effects are investigated in the nonrelativistic dynamics with the presence of a topological defect and under the influence of noninertial effects. We also obtain effects analogous to the Sagnac effect and Mashhoon effect due to the presence of the topological defect.
Tartarus: A relativistic Green's function quantum average atom code
NASA Astrophysics Data System (ADS)
Gill, N. M.; Starrett, C. E.
2017-09-01
A relativistic Green's Function quantum average atom model is implemented in the Tartarus code for the calculation of equation of state data in dense plasmas. We first present the relativistic extension of the quantum Green's Function average atom model described by Starrett [1]. The Green's Function approach addresses the numerical challenges arising from resonances in the continuum density of states without the need for resonance tracking algorithms or adaptive meshes, though there are still numerical challenges inherent to this algorithm. We discuss how these challenges are addressed in the Tartarus algorithm. The outputs of the calculation are shown in comparison to PIMC/DFT-MD simulations of the Principal Shock Hugoniot in Silicon. We also present the calculation of the Hugoniot for Silver coming from both the relativistic and nonrelativistic modes of the Tartarus code.
Tartarus: A relativistic Green's function quantum average atom code
Gill, Nathanael Matthew; Starrett, Charles Edward
2017-06-28
A relativistic Green’s Function quantum average atom model is implemented in the Tartarus code for the calculation of equation of state data in dense plasmas. We first present the relativistic extension of the quantum Green’s Function average atom model described by Starrett [1]. The Green’s Function approach addresses the numerical challenges arising from resonances in the continuum density of states without the need for resonance tracking algorithms or adaptive meshes, though there are still numerical challenges inherent to this algorithm. We discuss how these challenges are addressed in the Tartarus algorithm. The outputs of the calculation are shown in comparisonmore » to PIMC/DFT-MD simulations of the Principal Shock Hugoniot in Silicon. Finally, we also present the calculation of the Hugoniot for Silver coming from both the relativistic and nonrelativistic modes of the Tartarus code.« less
Quantum robots and quantum computers
Benioff, P.
1998-07-01
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.
Zurek, Wojciech H
2008-01-01
Quantum Darwinism - proliferation, in the environment, of multiple records of selected states of the system (its information-theoretic progeny) - explains how quantum fragility of individual state can lead to classical robustness of their multitude.
Pfeiffer, P.; Egusquiza, I. L.; Di Ventra, M.; ...
2016-07-06
Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor is still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantummore » regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. As a result, the proposed quantum memristor is then a building block for neuromorphic quantum computation and quantum simulations of non-Markovian systems.« less
NASA Astrophysics Data System (ADS)
Crease, Robert P.
2012-06-01
Fresh from his appearance on the latest Physics World podcast, which examined the enduring popularity of books about quantum mechanics, Robert P Crease surveys the many tour guides to the quantum world.
1994-08-15
Notre Dame was concerned with a variety of quantum transport in mesoscopic structures. This research was funded by the Air Force Office of Scientific...Research under Grant No. AFOSR-91-0211. The major issues examined included quantum transport in high magnetic fields and modulated channels, Coulomb...lifetimes in quasi-1D structures, quantum transport experiments in metals, the mesoscopic photovoltaic effect, and new techniques for fabricating quantum structures in semiconductors.
Quantum mechanics with coordinate dependent noncommutativity
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.
2013-11-01
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
A Process Algebra Approach to Quantum Electrodynamics
NASA Astrophysics Data System (ADS)
Sulis, William
2017-04-01
The process algebra program is directed towards developing a realist model of quantum mechanics free of paradoxes, divergences and conceptual confusions. From this perspective, fundamental phenomena are viewed as emerging from primitive informational elements generated by processes. The process algebra has been shown to successfully reproduce scalar non-relativistic quantum mechanics (NRQM) without the usual paradoxes and dualities. NRQM appears as an effective theory which emerges under specific asymptotic limits. Space-time, scalar particle wave functions and the Born rule are all emergent in this framework. In this paper, the process algebra model is reviewed, extended to the relativistic setting, and then applied to the problem of electrodynamics. A semiclassical version is presented in which a Minkowski-like space-time emerges as well as a vector potential that is discrete and photon-like at small scales and near-continuous and wave-like at large scales. QED is viewed as an effective theory at small scales while Maxwell theory becomes an effective theory at large scales. The process algebra version of quantum electrodynamics is intuitive and realist, free from divergences and eliminates the distinction between particle, field and wave. Computations are carried out using the configuration space process covering map, although the connection to second quantization has not been fully explored.
Quantum mechanics with coordinate dependent noncommutativity
Kupriyanov, V. G.
2013-11-15
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this paper we discuss the mathematical framework of such a theory. The noncommutativity is treated as an external antisymmetric field satisfying the Jacobi identity. First, we propose a symplectic realization of a given Poisson manifold and construct the Darboux coordinates on the obtained symplectic manifold. Then we define the star product on a Poisson manifold and obtain the expression for the trace functional. The above ingredients are used to formulate a nonrelativistic quantum mechanics on noncommutative spaces of general form. All considered constructions are obtained as a formal series in the parameter of noncommutativity. In particular, the complete algebra of commutation relations between coordinates and conjugated momenta is a deformation of the standard Heisenberg algebra. As examples we consider a free particle and an isotropic harmonic oscillator on the rotational invariant noncommutative space.
An approach to nonstandard quantum mechanics
NASA Astrophysics Data System (ADS)
Raab, A.
2004-12-01
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to nonrelativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the Mo/ller wave operators and the S-matrix.
Orientable Objects in Relativistic Quantum Theory
NASA Astrophysics Data System (ADS)
Gitman, D. M.; Shelepin, A. L.
2017-03-01
An approach to the quantum description of the orientation of relativistic particles, generalizing the approach to nonrelativistic objects possessing orientation (in particular, a rotator) is proposed, based on the self-consistent use of two reference frames. The realization of such an approach is connected with the introduction of wave functions f (x, z) on the Poincaré group M(3,1), which depend on the coordinates x μ of the Minkowski space M(3,1)/Spin(3,1) and orientational variables assigned by the elements z {β/α} of the matrix Z ∈Spin(3,1).The field f (x, z) is the generating function for ordinary spin-tensor fields and admits a number of symmetries. Besides the Lorentz transformations (corresponding to the action of the Poincaré group from the left and interpretable as external symmetries), transformations of a reference frame associated with an orientable object (corresponding to the action of the Poincaré group from the right and interpretable as internal symmetries) are applicable to orientable objects. In addition to the six quantum numbers assigned by the Casimir operators and the left generators, quantum numbers arise here that are assigned by the right generators and are associated with internal symmetries. The assumption that the internal symmetries of the theory of orientable objects are local leads to gauge theories describing the electroweak and gravitational interactions.
NASA Astrophysics Data System (ADS)
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.
Quantum theory of Thomson scattering
NASA Astrophysics Data System (ADS)
Crowley, B. J. B.; Gregori, G.
2014-12-01
The general theory of the scattering of electromagnetic radiation in atomic plasmas and metals, in the non-relativistic regime, in which account is taken of the Kramers-Heisenberg polarization terms in the Hamiltonian, is described from a quantum mechanical viewpoint. As well as deriving the general formula for the double differential Thomson scattering cross section in an isotropic finite temperature multi-component system, this work also considers closely related phenomena such as absorption, refraction, Raman scattering, resonant (Rayleigh) scattering and Bragg scattering, and derives many essential relationships between these quantities. In particular, the work introduces the concept of scattering strength and the strength-density field which replaces the normal particle density field in the standard treatment of scattering by a collection of similar particles and it is the decomposition of the strength-density correlation function into more familiar-looking components that leads to the final result. Comparisons are made with previous work, in particular that of Chihara [1].
NASA Astrophysics Data System (ADS)
Zurek, Wojciech Hubert
2009-03-01
Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the quantum fragility of a state of a single quantum system can lead to the classical robustness of states in their correlated multitude; shows how effective `wave-packet collapse' arises as a result of the proliferation throughout the environment of imprints of the state of the system; and provides a framework for the derivation of Born's rule, which relates the probabilities of detecting states to their amplitudes. Taken together, these three advances mark considerable progress towards settling the quantum measurement problem.
NASA Astrophysics Data System (ADS)
Brown, Matthew J.
2014-02-01
The framework of quantum frames can help unravel some of the interpretive difficulties i the foundation of quantum mechanics. In this paper, I begin by tracing the origins of this concept in Bohr's discussion of quantum theory and his theory of complementarity. Engaging with various interpreters and followers of Bohr, I argue that the correct account of quantum frames must be extended beyond literal space-time reference frames to frames defined by relations between a quantum system and the exosystem or external physical frame, of which measurement contexts are a particularly important example. This approach provides superior solutions to key EPR-type measurement and locality paradoxes.
NASA Astrophysics Data System (ADS)
Moulick, Subhayan Roy; Panigrahi, Prasanta K.
2016-06-01
We propose the idea of a quantum cheque scheme, a cryptographic protocol in which any legitimate client of a trusted bank can issue a cheque, that cannot be counterfeited or altered in anyway, and can be verified by a bank or any of its branches. We formally define a quantum cheque and present the first unconditionally secure quantum cheque scheme and show it to be secure against any no-signalling adversary. The proposed quantum cheque scheme can been perceived as the quantum analog of Electronic Data Interchange, as an alternate for current e-Payment Gateways.
Nonparadoxical loss of information in black hole evaporation in a quantum collapse model
NASA Astrophysics Data System (ADS)
Modak, Sujoy K.; Ortíz, Leonardo; Peña, Igor; Sudarsky, Daniel
2015-06-01
We consider a novel approach to address the black hole information paradox. The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as "the measurement problem." The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as "continuous spontaneous localization" (CSL), which was originally developed in the context of many-particle nonrelativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two -dimensional Callan-Giddings-Harvey-Strominger model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.
Meson-exchange-current corrections to magnetic moments in quantum hadrodynamics
Morse, T.M.
1990-01-01
Corrections to the magnetic moments of the non-relativistic shell model (Schmidt lines) have a long history. In the early fifties calculations of pion exchange and core polarization contributions to nuclear magnetic moments were initiated. These calculations matured by the early eighties to include other mesons and the delta isobar. Relativistic nuclear shell model calculations are relatively recent. Meson exchange and the delta isobar current contributions to the magnetic moments of the relativistic shell model have remained largely unexplored. The disagreement between the valence values of spherical relativistic mean-field models and experiment was a major problem with early (1975-1985) quantum hydrodynamics (QHD) calculations of magnetic moments. Core polarization calculations (1986-1988) have been found to resolve the large discrepancy, predicting isoscalar magnetic moments to within typically five percent of experiment. The isovector magnetic moments, however, are about twice as far from experiment with an average discrepancy of about ten percent. The pion, being the lightest of the mesons, has historically been expected to dominate isovector corrections. Because this has been found to be true in non-relativistic calculations, the author calculated the pion corrections in the framework of QHD. The seagull and in-flight pion exchange current diagram corrections to the magnetic moments of eight finite nuclei (plus or minus one valence nucleon from the magic A = 16 and A = 40 doubly closed shell systems) are calculated in the framework of QHD, and compared with earlier non-relativistic calculations and experiment.
Spacetime Conformal Fluctuations and Quantum Dephasing
NASA Astrophysics Data System (ADS)
Bonifacio, Paolo M.
2009-06-01
Any quantum system interacting with a complex environment undergoes decoherence. Empty space is filled with vacuum energy due to matter fields in their ground state and represents an underlying environment that any quantum particle has to cope with. In particular quantum gravity vacuum fluctuations should represent a universal source of decoherence. To study this problem we employ a stochastic approach that models spacetime fluctuations close to the Planck scale by means of a classical, randomly fluctuating metric (random gravity framework). We enrich the classical scheme for metric perturbations over a curved background by also including matter fields and metric conformal fluctuations. We show in general that a conformally modulated metric induces dephasing as a result of an effective nonlinear newtonian potential obtained in the appropriate nonrelativistic limit of a minimally coupled Klein-Gordon field. The special case of vacuum fluctuations is considered and a quantitative estimate of the expected effect deduced. Secondly we address the question of how conformal fluctuations could physically arise. By applying the random gravity framework we first show that standard GR seems to forbid spontaneous conformal metric modulations. Finally we argue that a different result follows within scalar-tensor theories of gravity such as e.g. Brans-Dicke theory. In this case a conformal modulation of the metric arises naturally as a result of the fluctuations in the Brans-Dicke field and quantum dephasing of a test particle is expected to occur. For large negative values of the coupling parameter the conformal fluctuations may also contribute to alleviate the well known problem of the large zero point energy due to quantum matter fields.
Correlations in quantum plasmas. II. Algebraic tails
NASA Astrophysics Data System (ADS)
Cornu, F.
1996-05-01
For a system of point charges that interact through the three-dimensional electrostatic Coulomb potential (without any regularization) and obey the laws of nonrelativistic quantum mechanics with Bose or Fermi statistics, the static correlations between particles are shown to have a 1/r6 tail, at least at distances that are large with respect to the length of exponential screening. After a review of previous work, a term-by-term diagrammatic proof is given by using the formalism of paper I, where the quantum particle-particle correlations are expressed in terms of classical-loop distribution functions. The integrable graphs of the resummed Mayer-like diagrammatics for the loop distributions contain bonds between loops that decay either exponentially or algebraically, with a 1/r3 leading term analogous to a dipole-dipole interaction. This reflects the fact that the charge-charge or multipole-charge interactions between clusters of particles surrounded by their polarization clouds are exponentially screened, as at a classical level, whereas the multipole-multipole interactions are only partially screened. The correlation between loops decays as 1/r3, but the spherical symmetry of the quantum fluctuations makes this power law fall to 1/r5, and the harmonicity of the Coulomb potential eventually enforces the correlations between quantum particles to decay only as 1/r6. The coefficient of the 1/r6 tail at low density is planned to be given in a subsequent paper. Moreover, because of Coulomb screening, the induced charge density, which describes the response to an external infinitesimal charge, is shown to fall off as 1/r8, while the charge-charge correlation in the medium decreases as 1/r10. However, in spite of the departure of the quantum microscopic correlations from the classical exponential clustering, the total induced charge is still essentially determined by the exponentially screened charge-charge interactions, as in classical macroscopic electrostatics.
RADIO AND X-RAY OBSERVATIONS OF THE TYPE Ic SN 2007gr REVEAL AN ORDINARY, NON-RELATIVISTIC EXPLOSION
Soderberg, A. M.; Brunthaler, A.; Nakar, E.; Chevalier, R. A.; Bietenholz, M. F.
2010-12-10
We present extensive radio and X-ray observations of the nearby Type Ic SN 2007gr in NGC 1058 obtained with the Very Large Array (VLA) and the Chandra X-ray Observatory and spanning 5 to 150 days after explosion. Through our detailed modeling of these data, we estimate the properties of the blast wave and the circumstellar environment. We find evidence for a freely expanding and non-relativistic explosion with an average blast wave velocity, v-bar {approx}0.2c, and a total internal energy for the radio emitting material of E {approx} 2 x 10{sup 46} erg assuming equipartition of energy between electrons and magnetic fields ({epsilon}{sub e} = {epsilon}{sub B} = 0.1). The temporal and spectral evolution of the radio emission points to a stellar wind-blown environment shaped by a steady progenitor mass loss rate of M-dot {approx}6x10{sup -7} M{sub sun} yr{sup -1} (wind velocity, v{sub w} = 10{sup 3} km s{sup -1}). These parameters are fully consistent with those inferred for other SNe Ibc and are in line with the expectations for an ordinary, homologous SN explosion. Our results are at odds with those of Paragi et al. who recently reported evidence for a relativistic blast wave in SN 2007gr based on their claim that the radio emission was resolved away in a low signal-to-noise Very Long Baseline Interferometry (VLBI) observation. Here we show that the exotic physical scenarios required to explain the claimed relativistic velocity-extreme departures from equipartition and/or a highly collimated outflow-are excluded by our detailed VLA radio observations. Moreover, we present an independent analysis of the VLBI data and propose that a modest loss of phase coherence provides a more natural explanation for the apparent flux density loss which is evident on both short and long baselines. We conclude that SN 2007gr is an ordinary Type Ibc supernova.
Quantum coherence versus quantum uncertainty
NASA Astrophysics Data System (ADS)
Luo, Shunlong; Sun, Yuan
2017-08-01
The notion of measurement is of both foundational and instrumental significance in quantum mechanics, and coherence destroyed by measurements (decoherence) lies at the very heart of quantum to classical transition. Qualitative aspects of this spirit have been widely recognized and analyzed ever since the inception of quantum theory. However, axiomatic and quantitative investigations of coherence are attracting great interest only recently with several figures of merit for coherence introduced [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014), 10.1103/PhysRevLett.113.140401]. While these resource theoretic approaches have many appealing and intuitive features, they rely crucially on various notions of incoherent operations which are sophisticated, subtle, and not uniquely defined, as have been critically assessed [Chitambar and Gour, Phys. Rev. Lett. 117, 030401 (2016), 10.1103/PhysRevLett.117.030401]. In this paper, we elaborate on the idea that coherence and quantum uncertainty are dual viewpoints of the same quantum substrate, and address coherence quantification by identifying coherence of a state (with respect to a measurement) with quantum uncertainty of a measurement (with respect to a state). Consequently, coherence measures may be set into correspondence with measures of quantum uncertainty. In particular, we take average quantum Fisher information as a measure of quantum uncertainty, and introduce the corresponding measure of coherence, which is demonstrated to exhibit desirable properties. Implications for interpreting quantum purity as maximal coherence, and quantum discord as minimal coherence, are illustrated.
Quantum entanglement, quantum communication and the limits of quantum computing
NASA Astrophysics Data System (ADS)
Ambainis, Andris
Quantum entanglement is a term describing the quantum correlations between different parts of a quantum system. Quantum information theory has developed sophisticated techniques to quantify and study quantum entanglement. In this thesis, we show how to apply those techniques to problems in quantum algorithms, complexity theory, communication and cryptography. The main results are: (1) quantum communication protocols that are exponentially more efficient that conventional (classical) communication protocols, (2) unconditionally secure quantum protocols for cryptographic problems, (3) a new "quantum adversary" method for proving lower bounds on quantum algorithms, (4) a study of "one clean qubit computation", a model related to the experimental implementation of quantum computers using NMR (nucleo-magnetic resonance) technology.
NASA Astrophysics Data System (ADS)
Garcia, M. G.; de Castro, A. S.; Castro, L. B.; Alberto, P.
2017-03-01
New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approach.
NASA Astrophysics Data System (ADS)
Kullie, O.; Zhang, H.; Kolb, D.
2008-07-01
Using two spinor minimax method combined with finite element methods accompanied with extrapolation and counterpoise techniques enable us to obtain relativistic highly accurate results for two atomic molecules. Like in our previous work for the (Hartree-) Dirac-Fock-Slater (DFS) functional we investigate in this work the density functional approximations of the relativistic and non-relativistic local-density functional, presenting highly accurate benchmark results of chemical properties on the dimers of the group 11 (Ib) of the periodic table of elements. The comparison with experimental values and literature's results shows that DFS is better behaved than the other two local functionals.
Quantum Larmor radiation in a conformally flat universe
NASA Astrophysics Data System (ADS)
Kimura, Rampei; Nakamura, Gen; Yamamoto, Kazuhiro
2011-02-01
We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics. A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the scalar quantum electrodynamics. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e2ℏ is determined by a nonlocal integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. DPRVDAQ1550-7998 80, 105019 (2009)10.1103/PhysRevD.80.105019], which investigated the quantum correction to the Larmor radiation from a charged particle in a nonrelativistic motion in a homogeneous electric field.
Coupling between graphene and intersubband collective excitations in quantum wells
NASA Astrophysics Data System (ADS)
Gonzalez de la Cruz, G.
2017-08-01
Recently, strong light-matter coupling between the electromagnetic modes in plasmonic metasurfaces with quantum-engineering electronic intersubband transitions in quantum wells has been demonstrated experimentally (Benz et al., [14], Lee et al., [15]). These novel materials combining different two-dimensional electronic systems offer new opportunities for tunable optical devices and fundamental studies of collective excitations driven by interlayer Coulomb interactions. In this work, our aim is to study the plasmon spectra of a hybrid structure consisting of conventional two-dimensional electron gas (2DEG) in a semiconductor quantum well and a graphene sheet with an interlayer separation of a. This electronic bilayer structure is immersed in a nonhomgeneous dielectric background of the system. We use a simple model in which the graphene surface plasmons and both; the intrasubband and intersubband collective electron excitations in the quantum well are coupled via screened Coulomb interaction. Here we calculate the dispersion of these relativistic/nonrelativistic new plasmon modes taking into account the thickness of the quantum well providing analytical expressions in the long-wavelength limit.
Quantum Reference Frames in Flat Space-Time and Gravity
NASA Astrophysics Data System (ADS)
Mayburov, S.
2002-12-01
It was argued recently that in Quantum Mechanics (QM) the correct definition of physical reference frame (RF) must differ principally from universally accepted one. [1]. The reason is that in exact theory the quantum properties of any massive object M1 with which physical RF F1 associated must be taken into account, despite their possible smallness in laboratory conditions. Consequently F1 evolution must obey to Schrodinger equation, and its free state relative to external observer at rest F0 is the localizable wave packet Ψ(x1,t), not the classical trajectory. As the example F1 can be rocket in outer space and F0 earth, M0 → ∞. If F1 localized state Ψ(x,t0) ~ δ(x) prepared by F0 it will smear in space unrestrictedly with the time σx ~ t1/2. This smearing introduces additional uncertainty into the measurement of particles mi space coordinates by F1 xi1 = xi-x1 in F1, because x1 is also operator, mi states transformations between two such quantum RFs includes quantum corrections to Galilean transformations, which depends on RFs states vectors [1]. Consistent nonrelativistic quantization in such RFs of free particles mi and other quantum systems in two alternative formalisms was proposed [2]...
Quantum Larmor radiation in a conformally flat universe
Kimura, Rampei; Nakamura, Gen; Yamamoto, Kazuhiro
2011-02-15
We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics. A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the scalar quantum electrodynamics. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e{sup 2}({h_bar}/2{pi}) is determined by a nonlocal integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D 80, 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a nonrelativistic motion in a homogeneous electric field.
Infinite variance in fermion quantum Monte Carlo calculations
NASA Astrophysics Data System (ADS)
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
Modified stochastic variational approach to non-Hermitian quantum systems
NASA Astrophysics Data System (ADS)
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.
Topics in topological and holomorphic quantum field theory
NASA Astrophysics Data System (ADS)
Vyas, Ketan
We investigate topological quantum field theories (TQFTs) in two, three, and four dimensions, as well as holomorphic quantum field theories (HQFTs) in four dimensions. After a brief overview of the two-dimensional (gauged) A and B models and the corresponding the category of branes, we construct analogous three-dimensional (gauged) A and B models and discuss the two-category of boundary conditions. Compactification allows us to identify the category of line operators in the three-dimensional A and B models with the category of branes in the corresponding two-dimensional A and B models. Furthermore, we use compactification to identify the two-category of surface operators in the four-dimensional GL theory at t = 1 and t = i with the two-category of boundary conditions in the corresponding three-dimensional A and B model, respectively. We construct a four-dimensional HQFT related to N = 1 supersymmetric quantum chromodynamics (SQCD) with gauge group SU(2) and two flavors, as well as a four-dimensional HQFT related to the Seiberg dual chiral model. On closed K ̈ahler surfaces with h^(2,0) > 0, we show that the correlation functions of holomorphic SQCD formally compute certain Donaldson invariants. For simply-connected elliptic surfaces (and their blow-ups), we show that the corresponding correlation functions in the holomorphic chiral model explicitly compute these Donaldson invariants.
PT symmetry in classical and quantum statistical mechanics.
Meisinger, Peter N; Ogilvie, Michael C
2013-04-28
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with PT-symmetry include Z(N) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural PT-symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate PT-symmetric Hamiltonian.
Infinite variance in fermion quantum Monte Carlo calculations.
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
Quantum games as quantum types
NASA Astrophysics Data System (ADS)
Delbecque, Yannick
In this thesis, we present a new model for higher-order quantum programming languages. The proposed model is an adaptation of the probabilistic game semantics developed by Danos and Harmer [DH02]: we expand it with quantum strategies which enable one to represent quantum states and quantum operations. Some of the basic properties of these strategies are established and then used to construct denotational semantics for three quantum programming languages. The first of these languages is a formalisation of the measurement calculus proposed by Danos et al. [DKP07]. The other two are new: they are higher-order quantum programming languages. Previous attempts to define a denotational semantics for higher-order quantum programming languages have failed. We identify some of the key reasons for this and base the design of our higher-order languages on these observations. The game semantics proposed in this thesis is the first denotational semantics for a lambda-calculus equipped with quantum types and with extra operations which allow one to program quantum algorithms. The results presented validate the two different approaches used in the design of these two new higher-order languages: a first one where quantum states are used through references and a second one where they are introduced as constants in the language. The quantum strategies presented in this thesis allow one to understand the constraints that must be imposed on quantum type systems with higher-order types. The most significant constraint is the fact that abstraction over part of the tensor product of many unknown quantum states must not be allowed. Quantum strategies are a new mathematical model which describes the interaction between classical and quantum data using system-environment dialogues. The interactions between the different parts of a quantum system are described using the rich structure generated by composition of strategies. This approach has enough generality to be put in relation with other
NASA Astrophysics Data System (ADS)
Levy, Amikam; Diósi, Lajos; Kosloff, Ronnie
2016-05-01
In this work we present the concept of a quantum flywheel coupled to a quantum heat engine. The flywheel stores useful work in its energy levels, while additional power is extracted continuously from the device. Generally, the energy exchange between a quantum engine and a quantized work repository is accompanied by heat, which degrades the charging efficiency. Specifically when the quantum harmonic oscillator acts as a work repository, quantum and thermal fluctuations dominate the dynamics. Quantum monitoring and feedback control are applied to the flywheel in order to reach steady state and regulate its operation. To maximize the charging efficiency one needs a balance between the information gained by measuring the system and the information fed back to the system. The dynamics of the flywheel are described by a stochastic master equation that accounts for the engine, the external driving, the measurement, and the feedback operations.
NASA Astrophysics Data System (ADS)
Braun, Daniel; Giraud, Olivier; Braun, Peter A.
2010-03-01
We introduce and study a measure of ``quantumness'' of a quantum state based on its Hilbert-Schmidt distance from the set of classical states. ``Classical states'' were defined earlier as states for which a positive P-function exists, i.e. they are mixtures of coherent states [1]. We study invariance properties of the measure, upper bounds, and its relation to entanglement measures. We evaluate the quantumness of a number of physically interesting states and show that for any physical system in thermal equilibrium there is a finite critical temperature above which quantumness vanishes. We then use the measure for identifying the ``most quantum'' states. Such states are expected to be potentially most useful for quantum information theoretical applications. We find these states explicitly for low-dimensional spin-systems, and show that they possess beautiful, highly symmetric Majorana representations. [4pt] [1] Classicality of spin states, Olivier Giraud, Petr Braun, and Daniel Braun, Phys. Rev. A 78, 042112 (2008)
Topological quantum scattering under the influence of a nontrivial boundary condition
NASA Astrophysics Data System (ADS)
Mota, Herondy
2016-04-01
We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein-Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov-Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov-Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.
Generalized quantum similarity in atomic systems: A quantifier of relativistic effects
NASA Astrophysics Data System (ADS)
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.
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.
Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
Lamata, L.; Leon, J.; Schaetz, T.; Solano, E.
2007-06-22
We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters.
Weakly relativistic quantum kinetic theory for electrostatic wave modes in magnetized plasmas
Hussain, Azhar; Stefan, Martin; Brodin, Gert
2014-03-15
We have derived the electrostatic dispersion relation in a magnetized plasma using a recently developed quantum kinetic model based on the Dirac equation. The model contains weakly relativistic spin effects such as Thomas precession, the polarization currents associated with the spin and the spin-orbit coupling. It turns out that for strictly electrostatic perturbations the non-relativistic spin effects vanish, and the modification of the classical dispersion relation is solely associated with the relativistic terms. Several new wave modes appear due the electron spin effects, and an example for astrophysical plasmas are given.
Is there a "most perfect fluid" consistent with quantum field theory?
Cohen, Thomas D
2007-07-13
It was recently conjectured that the ratio of the shear viscosity to entropy density eta/s for any fluid always exceeds [formula: see text]. A theoretical counterexample to this bound can be constructed from a nonrelativistic gas by increasing the number of species in the fluid while keeping the dynamics essentially independent of the species type. The question of whether the underlying structure of relativistic quantum field theory generically inhibits the realization of such a system and thereby preserves the possibility of a universal bound is considered here. Using rather conservative assumptions, it is shown here that a metastable gas of heavy mesons in a particular controlled regime of QCD provides a realization of the counterexample and is consistent with a well-defined underlying relativistic quantum field theory. Thus, quantum field theory appears to impose no lower bound on eta/s, at least for metastable fluids.
Quantum mechanical E × B drift velocity in a weakly inhomogeneous electromagnetic field
NASA Astrophysics Data System (ADS)
Chan, Poh Kam; Oikawa, Shun-ichi; Kosaka, Wataru
2017-07-01
The analytical solution for the quantum mechanical drift velocity for a non-relativistic spinless charged particle of E × B drift in the presence of a weakly inhomogeneous electric and magnetic field for the magnetized plasma is presented. Using the Heisenberg equation of motion, the time evolution of the position and momentum operators for the charged particle is solved. From the time dependent operators, the analytical solution of the time dependent momenta operators and position operators is derived. The quantum mechanical expansion rates of variances are shown to agree with the numerical results. Most importantly, the quantum mechanical E × B drift velocity coincides perfectly with the classical drift velocity in the limit of Planck's constant being zero. With higher order electric field inhomogeneity, low energy particles would drift faster than what the classical drift theory predicts.
Real-time quantum dynamics of heavy-quark systems at high temperature
NASA Astrophysics Data System (ADS)
Akamatsu, Yukinao
2013-02-01
On the basis of the closed-time-path formalism of nonequilibrium quantum field theory, we derive the real-time quantum dynamics of heavy-quark systems. Even though our primary goal is the description of heavy quarkonia, our method allows a unified description of the propagation of single heavy quarks as well as their bound states. To make calculations tractable, we deploy leading-order perturbation theory and consider the nonrelativistic limit. Various dynamical equations, such as the master equation for quantum Brownian motion and the time-evolution equation for heavy-quark and quarkonium forward correlators, are obtained from a single operator: the renormalized effective Hamiltonian. We are thus able to reproduce previous results of perturbative calculations of the drag force and the complex potential simultaneously. In addition, we present stochastic time-evolution equations for the heavy-quark and quarkonium wave function, which are equivalent to the dynamical equations.
An efficient matrix product operator representation of the quantum chemical Hamiltonian
Keller, Sebastian Reiher, Markus; Dolfi, Michele Troyer, Matthias
2015-12-28
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.
An efficient matrix product operator representation of the quantum chemical Hamiltonian.
Keller, Sebastian; Dolfi, Michele; Troyer, Matthias; Reiher, Markus
2015-12-28
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries - abelian and non-abelian - and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.
NASA Astrophysics Data System (ADS)
Tartakovskii, Alexander
2012-07-01
Part I. Nanostructure Design and Structural Properties of Epitaxially Grown Quantum Dots and Nanowires: 1. Growth of III/V semiconductor quantum dots C. Schneider, S. Hofling and A. Forchel; 2. Single semiconductor quantum dots in nanowires: growth, optics, and devices M. E. Reimer, N. Akopian, M. Barkelid, G. Bulgarini, R. Heeres, M. Hocevar, B. J. Witek, E. Bakkers and V. Zwiller; 3. Atomic scale analysis of self-assembled quantum dots by cross-sectional scanning tunneling microscopy and atom probe tomography J. G. Keizer and P. M. Koenraad; Part II. Manipulation of Individual Quantum States in Quantum Dots Using Optical Techniques: 4. Studies of the hole spin in self-assembled quantum dots using optical techniques B. D. Gerardot and R. J. Warburton; 5. Resonance fluorescence from a single quantum dot A. N. Vamivakas, C. Matthiesen, Y. Zhao, C.-Y. Lu and M. Atature; 6. Coherent control of quantum dot excitons using ultra-fast optical techniques A. J. Ramsay and A. M. Fox; 7. Optical probing of holes in quantum dot molecules: structure, symmetry, and spin M. F. Doty and J. I. Climente; Part III. Optical Properties of Quantum Dots in Photonic Cavities and Plasmon-Coupled Dots: 8. Deterministic light-matter coupling using single quantum dots P. Senellart; 9. Quantum dots in photonic crystal cavities A. Faraon, D. Englund, I. Fushman, A. Majumdar and J. Vukovic; 10. Photon statistics in quantum dot micropillar emission M. Asmann and M. Bayer; 11. Nanoplasmonics with colloidal quantum dots V. Temnov and U. Woggon; Part IV. Quantum Dot Nano-Laboratory: Magnetic Ions and Nuclear Spins in a Dot: 12. Dynamics and optical control of an individual Mn spin in a quantum dot L. Besombes, C. Le Gall, H. Boukari and H. Mariette; 13. Optical spectroscopy of InAs/GaAs quantum dots doped with a single Mn atom O. Krebs and A. Lemaitre; 14. Nuclear spin effects in quantum dot optics B. Urbaszek, B. Eble, T. Amand and X. Marie; Part V. Electron Transport in Quantum Dots Fabricated by
Novel features of nuclear chromodynamics
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.
2017-03-01
I review a number of QCD topics where the nuclear environment provides new insights into fundamental aspects of the strong interactions. The topics include novel perspectives for nuclear physics, such as the hidden color of nuclear form factors, the relation of the nuclear force at short distances to quark interchange interactions, the effects of "color transparency" on the baryon-to-meson anomaly in hard heavy-ion colisions, flavor-dependent antishadowing, novel exotic multiquark states, the anomalous nuclear dependence of quarkonium hadroproduction, flavor-dependent antishadowing, and the breakdown of sum rules for nuclear structure functions. I also briefly discuss the insights into hadron physics and color confinement that one obtains from light-front holography, including supersymmetric features of the hadron spectrum. I also note that the virtual Compton amplitude on a proton (or nucleus) can be measured for two spacelike photons q21, q22 < 0 using positronium-proton scattering [e+e-]p→ e+e-p'.
Dissipative quantum computing with open quantum walks
Sinayskiy, Ilya; Petruccione, Francesco
2014-12-04
An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates.
Discovery of Novel Liver-Stage Antimalarials through Quantum Similarity
Sullivan, David J.; Liu, Yi; Mott, Bryan T.; Kaludov, Nikola; Martinov, Martin N.
2015-01-01
Without quantum theory any understanding of molecular interactions is incomplete. In principal, chemistry, and even biology, can be fully derived from non-relativistic quantum mechanics. In practice, conventional quantum chemical calculations are computationally too intensive and time consuming to be useful for drug discovery on more than a limited basis. A previously described, original, quantum-based computational process for drug discovery and design bridges this gap between theory and practice, and allows the application of quantum methods to large-scale in silico identification of active compounds. Here, we show the results of this quantum-similarity approach applied to the discovery of novel liver-stage antimalarials. Testing of only five of the model-predicted compounds in vitro and in vivo hepatic stage drug inhibition assays with P. berghei identified four novel chemical structures representing three separate quantum classes of liver-stage antimalarials. All four compounds inhibited liver-stage Plasmodium as a single oral dose in the quantitative PCR mouse liver-stage sporozoites-challenge model. One of the newly identified compounds, cethromycin [ABT-773], a macrolide-quinoline hybrid, is a drug with an extensive (over 5,000 people) safety profile warranting its exploitation as a new weapon for the current effort of malaria eradication. The results of our molecular modeling exceed current state-of-the-art computational methods. Drug discovery through quantum similarity is data-driven, agnostic to any particular target or disease process that can evaluate multiple phenotypic, target-specific, or co-crystal structural data. This allows the incorporation of additional pharmacological requirements, as well as rapid exploration of novel chemical spaces for therapeutic applications. PMID:25951139
NASA Astrophysics Data System (ADS)
Turkington, M. D.; Ballance, C. P.; Hibbert, A.; Ramsbottom, C. A.
2016-08-01
In this work we explore the validity of employing a modified version of the nonrelativistic structure code civ3 for heavy, highly charged systems, using Na-like tungsten as a simple benchmark. Consequently, we present radiative and subsequent collisional atomic data compared with corresponding results from a fully relativistic structure and collisional model. Our motivation for this line of study is to benchmark civ3 against the relativistic grasp0 structure code. This is an important study as civ3 wave functions in nonrelativistic R -matrix calculations are computationally less expensive than their Dirac counterparts. There are very few existing data for the W LXIV ion in the literature with which we can compare except for an incomplete set of energy levels available from the NIST database. The overall accuracy of the present results is thus determined by the comparison between the civ3 and grasp0 structure codes alongside collisional atomic data computed by the R -matrix Breit-Pauli and Dirac codes. It is found that the electron-impact collision strengths and effective collision strengths computed by these differing methods are in good general agreement for the majority of the transitions considered, across a broad range of electron temperatures.
NASA Astrophysics Data System (ADS)
Loheac, Andrew C.; Drut, Joaquín E.
2017-05-01
We analyze the pressure and density equations of state of unpolarized nonrelativistic fermions at finite temperature in one spatial dimension with contact interactions. For attractively interacting regimes, we perform a third-order lattice perturbation theory calculation, assess its convergence properties by comparing with hybrid Monte Carlo results (there is no sign problem in this regime), and demonstrate agreement with real Langevin calculations. For repulsive interactions, we present lattice perturbation theory results as well as complex Langevin calculations, with a modified action to prevent uncontrolled excursions in the complex plane. Although perturbation theory is a common tool, our implementation of it is unconventional; we use a Hubbard-Stratonovich transformation to decouple the system and automate the application of Wick's theorem, thus generating the diagrammatic expansion, including symmetry factors, at any desired order. We also present an efficient technique to tackle nested Matsubara frequency sums without relying on contour integration, which is independent of dimension and applies to both relativistic and nonrelativistic systems, as well as all energy-independent interactions. We find exceptional agreement between perturbative and nonperturbative results at weak couplings, and furnish predictions based on complex Langevin at strong couplings. We additionally present perturbative calculations of up to the fifth-order virial coefficient for repulsive and attractive couplings. Both the lattice perturbation theory and complex Langevin formalisms can easily be extended to a variety of situations including polarized systems, bosons, and higher dimension.
NASA Astrophysics Data System (ADS)
Reynolds, Helen
2000-03-01
ability keeping track of the equations and their meaning. However, the text continues to be accessible and moves swiftly from `quantum classics' such as the harmonic oscillator to electrical conductivity and the collapse of stars. Reassuringly, Treiman takes time out to ask `What's going on?' where he considers the question of how probabilities get converted into `facts' when things are measured. His own fascination with the subject comes through as he considers the different interpretations of quantum mechanics. The chapter on `building blocks' starts in 1932 when ` ... it could seem that all the basic building blocks of the whole world were at last in hand'. Swiftly and succinctly it moves through to the standard model, acknowledging that a closer look would ` ... quickly carry us far afield into highly technical thickets'. The final chapter tackles the more difficult subject of quantum field theory. This is a very swift journey through quantum electrodynamics and quantum chromodynamics. It is the final summary that stands out, however. The author reminds us what to marvel about: the miracles of quantum theory that are ` ... outrageous to common sense and intuition'. This is a useful book for any science department. It will be of particular use to those of us who studied the subject some time ago and who need to refresh their memories, for example teachers of A-level physics. The asides about `what is going on' and the history that is included make it a `book' rather than a `textbook'. First-year undergraduates, or just possibly motivated and mathematically able A-level students, would also benefit. Beware, however. The mathematics is not trivial and you would arguably need to have met it before in order to cope. Although the book occasionally relapses into textbook style you are left with a sense of the wonder of the subject and an appreciation of the beauty of the mathematics that underpins it.
Quantum computer games: quantum minesweeper
NASA Astrophysics Data System (ADS)
Gordon, Michal; Gordon, Goren
2010-07-01
The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical minesweeper the goal of the game is to discover all the mines laid out on a board without triggering them, in the quantum version there are several classical boards in superposition. The goal is to know the exact quantum state, i.e. the precise layout of all the mines in all the superposed classical boards. The player can perform three types of measurement: a classical measurement that probabilistically collapses the superposition; a quantum interaction-free measurement that can detect a mine without triggering it; and an entanglement measurement that provides non-local information. The application of the concepts taught by quantum minesweeper to one-way quantum computing are also presented.
The formal path integral and quantum mechanics
Johnson-Freyd, Theo
2010-11-15
Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
Trevors, J T; Masson, L
2011-01-01
During his famous 1943 lecture series at Trinity College Dublin, the reknown physicist Erwin Schrodinger discussed the failure and challenges of interpreting life by classical physics alone and that a new approach, rooted in Quantum principles, must be involved. Quantum events are simply a level of organization below the molecular level. This includes the atomic and subatomic makeup of matter in microbial metabolism and structures, as well as the organic, genetic information code of DNA and RNA. Quantum events at this time do not elucidate, for example, how specific genetic instructions were first encoded in an organic genetic code in microbial cells capable of growth and division, and its subsequent evolution over 3.6 to 4 billion years. However, due to recent technological advances, biologists and physicists are starting to demonstrate linkages between various quantum principles like quantum tunneling, entanglement and coherence in biological processes illustrating that nature has exerted some level quantum control to optimize various processes in living organisms. In this article we explore the role of quantum events in microbial processes and endeavor to show that after nearly 67 years, Schrödinger was prophetic and visionary in his view of quantum theory and its connection with some of the fundamental mechanisms of life.
NASA Astrophysics Data System (ADS)
Giesel, Kristina
The following sections are included: * Canonical Quantization of General Relativity * General Relativity in Connection Variables * Holonomy-Flux Algebra and its Representation(s) * The Ashtekar-Lewandowski Representation and the Kinematical Hilbert Space of LQG * The Quantum Einstein's Equations of Loop Quantum Gravity * Geometric Operators and Their Properties * Summary * References
NASA Technical Reports Server (NTRS)
Lee, H.; Kok, P.; Dowling, J. P.
2002-01-01
This paper addresses the formal equivalence between the Mach-Zehnder interferometer, the Ramsey spectroscope, and a specific quantum logical gate. Based on this equivalence we introduce the quantum Rosetta Stone, and we describe a projective measurement scheme for generating the desired correlations between the interferometric input states in order to achieve Heisenberg-limited sensitivity.
NASA Technical Reports Server (NTRS)
Abrams, D.; Williams, C.
1999-01-01
This thesis describes several new quantum algorithms. These include a polynomial time algorithm that uses a quantum fast Fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases for which all know classical algorithms require exponential time.
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2004-11-01
Financial mathematics is currently almost completely dominated by stochastic calculus. Presenting a completely independent approach, this book applies the mathematical and conceptual formalism of quantum mechanics and quantum field theory (with particular emphasis on the path integral) to the theory of options and to the modeling of interest rates. Many new results, accordingly, emerge from the author's perspective.
Quantum Computation Toward Quantum Gravity
NASA Astrophysics Data System (ADS)
Zizzi, P. A.
2001-08-01
The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin -1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.
Bubin, Sergiy; Komasa, Jacek; Stanke, Monika; Adamowicz, Ludwik
2010-03-21
We present very accurate quantum mechanical calculations of the three lowest S-states [1s(2)2s(2)((1)S(0)), 1s(2)2p(2)((1)S(0)), and 1s(2)2s3s((1)S(0))] of the two stable isotopes of the boron ion, (10)B(+) and (11)B(+). At the nonrelativistic level the calculations have been performed with the Hamiltonian that explicitly includes the finite mass of the nucleus as it was obtained by a rigorous separation of the center-of-mass motion from the laboratory frame Hamiltonian. The spatial part of the nonrelativistic wave function for each state was expanded in terms of 10,000 all-electron explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians were variationally optimized using a procedure involving the analytical energy gradient determined with respect to the nonlinear parameters. The nonrelativistic wave functions of the three states were subsequently used to calculate the leading alpha(2) relativistic corrections (alpha is the fine structure constant; alpha=1/c, where c is the speed of light) and the alpha(3) quantum electrodynamics (QED) correction. We also estimated the alpha(4) QED correction by calculating its dominant component. A comparison of the experimental transition frequencies with the frequencies obtained based on the energies calculated in this work shows an excellent agreement. The discrepancy is smaller than 0.4 cm(-1).
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
1995-04-01
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
2006-11-01
Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos
Entropic corrected Newton's law of gravitation and the loop quantum black hole gravitational atom
NASA Astrophysics Data System (ADS)
Aragão, R. G. L.; Silva, C. A. S.
2016-07-01
One proposal by Verlinde is that gravity is not a fundamental, but an entropic force (Verlinde in JHEP 1104:029, 2011. arXiv:hep-th/1001.0785). Based on this new interpretation of the gravity, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that such corrections could be inherited by Newton's law. In this sense, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravity in an observationally accessible regimes. On the other hand, loop quantum gravity is a theory that provide a scheme to approach the quantum properties of spacetime. From this theory, emerges a quantum corrected semiclassical black hole solution called loop quantum black hole or self-dual black hole. Among the interesting features of loop quantum black holes, is the fact that they give rise to a modified entropy-area relation where quantum gravity corrections are present. In this work, we obtain a quantum corrected Newton's law from the entropy-area relation given by loop quantum black holes by using the nonrelativistic Verlinde's approach. Moreover, in order to relate our results with the recent experimental activity, we consider the quantum mechanical properties of a huge gravitational atom consisting in a light neutral elementary particle in the presence of a loop quantum black hole.
A wave equation interpolating between classical and quantum mechanics
NASA Astrophysics Data System (ADS)
Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.
2015-10-01
We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.
Light generation via quantum interaction of electrons with periodic nanostructures
NASA Astrophysics Data System (ADS)
Tsesses, Shai; Bartal, Guy; Kaminer, Ido
2017-01-01
The Smith-Purcell effect is a hallmark of light-matter interactions in periodic structures, resulting in light emission with distinct spectral and angular distribution. We find yet undiscovered effects in Smith-Purcell radiation that arise due to the quantum nature of light and matter, through an approach based on exact energy and momentum conservation. The effects include emission cutoff, convergence of emission orders, and a possible second photoemission process, appearing predominantly in structures with nanoscale periodicities (a few tens of nanometers or less), accessible by recent nanofabrication advances. We further present ways to manipulate the effects by varying the geometry or by accounting for a refractive index. Our derivation emphasizes the fundamental relation between Smith-Purcell radiation and Čerenkov radiation, and paves the way to alternative kinds of light sources wherein nonrelativistic electrons create Smith-Purcell radiation in nanoscale, on-chip devices. Finally, the path towards experimental realizations of these effects is discussed.
Spectral geometry of power-law potentials in quantum mechanics
NASA Astrophysics Data System (ADS)
Hall, Richard L.
1989-06-01
It is supposed that a single particle moves in openR3 in an attractive central power-law potential V(q)(r)=sgn(q)rq, q>-2, and obeys nonrelativistic quantum mechanics. This paper is concerned with the question: How do the discrete eigenvalues Enl(q) of the Hamiltonian H=-Δ+V(q) depend on the power parameter q\\? Pure power-law potentials have the elementary property that, for p
Hidden symmetries of dynamics in classical and quantum physics
NASA Astrophysics Data System (ADS)
Cariglia, Marco
2014-10-01
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as nonrelativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of nontrivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher-dimensional black holes, the Dirac equation, and supergravity with and without fluxes, providing a tool to probe the dynamics of nonlinear systems.
Minimum energy surface required by quantum memory devices.
van Dam, Wim; Nguyen, Hieu D
2013-06-21
We address the question of what physical resources are required and sufficient to store classical information. While there is no lower bound on the required energy or space to store information, we find that there is a nonzero lower bound for the product P =
Dynamical gauge effects in an open quantum network
NASA Astrophysics Data System (ADS)
Zhao, Jianshi; Price, Craig; Liu, Qi; Gemelke, Nathan
2016-05-01
We describe new experimental techniques for simulation of high-energy field theories based on an analogy between open thermodynamic systems and effective dynamical gauge-fields following SU(2) × U(1) Yang-Mills models. By coupling near-resonant laser-modes to atoms moving in a disordered optical environment, we create an open system which exhibits a non-equilibrium phase transition between two steady-state behaviors, exhibiting scale-invariant behavior near the transition. By measuring transport of atoms through the disordered network, we observe two distinct scaling behaviors, corresponding to the classical and quantum limits for the dynamical gauge field. This behavior is loosely analogous to dynamical gauge effects in quantum chromodynamics, and can mapped onto generalized open problems in theoretical understanding of quantized non-Abelian gauge theories. Additional, the scaling behavior can be understood from the geometric structure of the gauge potential and linked to the measure of information in the local disordered potential, reflecting an underlying holographic principle. We acknowledge support from NSF Award No.1068570, and the Charles E. Kaufman Foundation.
ERIC Educational Resources Information Center
Peterson, Ivars
1989-01-01
An analogy from the game of baseball can be used to examine the philosophy involved in statistics surrounding quantum mechanical events. The "Strong Baseball Principle" is proposed and discussed. (CW)
Ladd, T D; Jelezko, F; Laflamme, R; Nakamura, Y; Monroe, C; O'Brien, J L
2010-03-04
Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.
Kaminker, A.D.; Levenfish, K.P.; Yakovlev, D.G. ); Amsterdamski, P.; Haensel, P. )
1992-10-15
A general formalism is developed for calculating the neutrino emissivities of synchrotron and {ital e}{sup {minus}}{ital e+} annihilation radiations in a plasma in the presence of a large magnetic field {ital B}{similar to}10{sup 12}--10{sup 14} G. As a first step, the formalism is used to calculate the synchrotron and annihilation radiations from a nonrelativistic electron plasma (density {rho}{approx lt}10{sup 6} g cm{sup {minus}3}, temperature {ital T}{approx lt}6{times}10{sup 9} K) including the cases of nondegenerate and degenerate electrons, and of quantizing and nonquantizing magnetic fields. We conclude that these processes can be important for neutrino production in a hot plasma of neutron star envelopes.
J/ψ(ψ') production at the Tevatron and LHC at O(α(s)4v4) in nonrelativistic QCD.
Ma, Yan-Qing; Wang, Kai; Chao, Kuang-Ta
2011-01-28
We present a complete evaluation for J/ψ(ψ') prompt production at the Tevatron and LHC at next-to-leading order in nonrelativistic QCD, including color-singlet, color-octet, and higher charmonia feeddown contributions. The short-distance coefficients of 3P(J)([8]) at next-to-leading order are found to be larger than leading order by more than an order of magnitude but with a minus sign at high transverse momentum p(T). Two new linear combinations of color-octet matrix elements are obtained from the CDF data, and used to predict J/ψ production at the LHC, which agrees with the CMS data. The possibility of (1)S(0)([8]) dominance and the J/ψ polarization puzzle are also discussed.
2016-03-24
oxide layer that is between the indium island and gold contacts. This forms a tunnel barrier for electrons. As the temperature is decreased... islands . Low densities of indium islands have been shown to increase the photoluminescence of an ensemble of InAs quantum dots. Indium islands have also...we investigated self-assembled MBE grown indium plasmonic nanostructures, or indium islands . While quantum dots degrade more significantly as they
NASA Astrophysics Data System (ADS)
Stapp, Henry P.
2012-05-01
Robert Griffiths has recently addressed, within the framework of a `consistent quantum theory' that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are not entailed by the precepts of quantum mechanics. Thus whatever is proved is not a feature of quantum mechanics, but is a property of a theory that tries to combine quantum theory with quasi-classical features that go beyond what is entailed by quantum theory itself. One cannot logically prove properties of a system by establishing, instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths' rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his `consistent quantum theory' shows that the cited proof is valid within that restrictive version of quantum theory. An added section responds to Griffiths' reply, which cites general possibilities of ambiguities that might make what is to be proved ill-defined, and hence render the pertinent `consistent framework' ill defined. But the vagaries that he cites do not upset the proof in question, which, both by its physical formulation and by explicit identification, specify the framework to be used. Griffiths confirms the validity of the proof insofar as that pertinent framework is used. The section also shows
Quantum correlations and distinguishability of quantum states
NASA Astrophysics Data System (ADS)
Spehner, Dominique
2014-07-01
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.
Quantum technology: the second quantum revolution.
Dowling, Jonathan P; Milburn, Gerard J
2003-08-15
We are currently in the midst of a second quantum revolution. The first quantum revolution gave us new rules that govern physical reality. The second quantum revolution will take these rules and use them to develop new technologies. In this review we discuss the principles upon which quantum technology is based and the tools required to develop it. We discuss a number of examples of research programs that could deliver quantum technologies in coming decades including: quantum information technology, quantum electromechanical systems, coherent quantum electronics, quantum optics and coherent matter technology.
Zhu, X. P.; Zhang, Z. C.; Lei, M. K.; Pushkarev, A. I.
2016-01-15
High-intensity pulsed ion beam (HIPIB) with ion current density above Child-Langmuir limit is achieved by extracting ion beam from anode plasma of ion diodes with suppressing electron flow under magnetic field insulation. It was theoretically estimated that with increasing the magnetic field, a maximal value of ion current density may reach nearly 3 times that of Child-Langmuir limit in a non-relativistic mode and close to 6 times in a highly relativistic mode. In this study, the behavior of ion beam enhancement by magnetic insulation is systematically investigated in three types of magnetically insulated ion diodes (MIDs) with passive anode, taking into account the anode plasma generation process on the anode surface. A maximal enhancement factor higher than 6 over the Child-Langmuir limit can be obtained in the non-relativistic mode with accelerating voltage of 200–300 kV. The MIDs differ in two anode plasma formation mechanisms, i.e., surface flashover of a dielectric coating on the anode and explosive emission of electrons from the anode, as well as in two insulation modes of external-magnetic field and self-magnetic field with either non-closed or closed drift of electrons in the anode-cathode (A-K) gap, respectively. Combined with ion current density measurement, energy density characterization is employed to resolve the spatial distribution of energy density before focusing for exploring the ion beam generation process. Consistent results are obtained on three types of MIDs concerning control of neutralizing electron flows for the space charge of ions where the high ion beam enhancement is determined by effective electron neutralization in the A-K gap, while the HIPIB composition of different ion species downstream from the diode may be considerably affected by the ion beam neutralization during propagation.
NASA Astrophysics Data System (ADS)
Zhu, X. P.; Zhang, Z. C.; Pushkarev, A. I.; Lei, M. K.
2016-01-01
High-intensity pulsed ion beam (HIPIB) with ion current density above Child-Langmuir limit is achieved by extracting ion beam from anode plasma of ion diodes with suppressing electron flow under magnetic field insulation. It was theoretically estimated that with increasing the magnetic field, a maximal value of ion current density may reach nearly 3 times that of Child-Langmuir limit in a non-relativistic mode and close to 6 times in a highly relativistic mode. In this study, the behavior of ion beam enhancement by magnetic insulation is systematically investigated in three types of magnetically insulated ion diodes (MIDs) with passive anode, taking into account the anode plasma generation process on the anode surface. A maximal enhancement factor higher than 6 over the Child-Langmuir limit can be obtained in the non-relativistic mode with accelerating voltage of 200-300 kV. The MIDs differ in two anode plasma formation mechanisms, i.e., surface flashover of a dielectric coating on the anode and explosive emission of electrons from the anode, as well as in two insulation modes of external-magnetic field and self-magnetic field with either non-closed or closed drift of electrons in the anode-cathode (A-K) gap, respectively. Combined with ion current density measurement, energy density characterization is employed to resolve the spatial distribution of energy density before focusing for exploring the ion beam generation process. Consistent results are obtained on three types of MIDs concerning control of neutralizing electron flows for the space charge of ions where the high ion beam enhancement is determined by effective electron neutralization in the A-K gap, while the HIPIB composition of different ion species downstream from the diode may be considerably affected by the ion beam neutralization during propagation.
Kinetic potentials in quantum mechanics
NASA Astrophysics Data System (ADS)
Hall, Richard L.
1984-09-01
Suppose that the Hamiltonian H=-Δ+vf(r) represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics. The discrete eigenvalues Enl=Fnl(v) of H may be expressed as a Legendre transformation Fnl(v)=mins≳0(s+vf¯nl(s)), n=1,2,3,..., l=0,1,2,..., where the ``kinetic potentials'' f¯nl(s) associated with f(r) are defined by f¯nl(s) =infDnl supψ∈Dnl, ∥ψ∥=1 ∫ ψ(r) f ([ψ,-Δψ)/s]1/2r)ψ(r)d3r, and Dnl is an n-dimensional subspace of L2(R3) labeled by Ylm(θ,φ), m=0, and contained in the domain D(H) of H. If the potential has the form f(r)=∑Ni=1 g(i)( f(i)(r)) then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ∑Ni=1 g(i)( f¯nl(i)(s)). This nice behavior of the kinetic potentials leads to a constructive global approximation theory for Schrödinger eigenvalues. As an illustration, detailed recipes are provided for arbitrary linear combinations of power-law potentials and the log potential. For the linear plus Coulomb potential and the quartic anharmonic oscillator the approximate eigenvalues are compared to accurate values found by numerical integration.
Quantum electrodynamics and fundamental constants
NASA Astrophysics Data System (ADS)
Wundt, Benedikt Johannes Wilhelm
The unprecedented precision achieved both in the experimental measurements as well as in the theoretical description of atomic bound states make them an ideal study object for fundamental physics and the determination of fundamental constants. This requires a careful study of the effects from quantum electrodynamics (QED) on the interaction between the electron and the nucleus. The two theoretical approaches for the evaluation of QED corrections are presented and discussed. Due to the presence of two energy scales from the binding potential and the radiation field, an overlapping parameter has to be used in both approaches in order to separate the energy scales. The different choices for the overlapping parameter in the two methods are further illustrated in a model example. With the nonrelativistic theory, relativistic corrections in order ( Zalpha)2 to the two-photon decay rate of ionic states are calculated, as well as the leading radiative corrections of alpha( Zalpha)2ln[(Zalpha)-2 ]. It is shown that the corrections is gauge-invariant under a "hybrid" gauge transformation between Coulomb and Yennie gauge. Furthermore, QED corrections for Rydberg states in one-electron ions are investigated. The smallness of the corrections and the absence of nuclear size corrections enable very accurate theoretical predictions. Measuring transition frequencies and comparing them to the theoretical predictions, QED theory can be tested more precisely. In turn, this could yield a more accurate value for the Rydberg constant. Using a transition in a nucleus with a well determined mass, acting as a reference, a comparison to transition in other nuclei can even allow to determined nuclear masses. Finally, in order to avoid an additional uncertainty in nuclei with non zero nuclear spin, QED self-energy corrections to the hyperfine structure up to order alpha(Zalpha)2Delta EHFS are determined for highly excited Rydberg states.