Bonitz, Michael
2016-01-01
This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.
Hydrodynamic transport functions from quantum kinetic theory
Calzetta, E A; Ramsey, S
2000-01-01
Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with $\\lambda \\Phi ^{4}$ self-interaction we need to include 4 loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success...
Kinetic Quantum Theory of Gravity
DeAquino, F
2002-01-01
Starting from the action function we have derived a theoretical background that leads to quantization of gravity and the deduction of a correlation between the gravitational and inertial masses, which depends on the kinetic momentum of the particle. We show that there is a reaffirmation of the strong equivalence principle and consequently the Einstein's equations are preserved. In fact such equations are deduced here directly from this kinetic approach to Gravity. Moreover, we have obtained a generalized equation for inertial forces, which incorporates the Mach's principle into Gravitation. Also, we have deduced the equation of Entropy; the Hamiltonian for a particle in an electromagnetic field and the reciprocal fine structure constant. It is possible to deduce the expression of the Casimir force and also to explain the Inflation Period and the Missing Matter without assuming the existence of vacuum fluctuations. This new approach for Gravity will allow us to understand some crucial matters in Cosmology.
Kinetic Quantum Theory of Gravity
DeAquino, F
2002-01-01
Gravity is here quantized starting from the generalization of the action function. This leads to an equation of correlation between gravitational and inertial masses, which depends on the particle's kinetic energy. We show that there is a reaffirmation of the strong equivalence principle and consequently the Einstein's equations are preserved. In fact such equations are deduced here directly from this kinetic approach to Gravity. Moreover, we have obtained a generalized equation for inertial forces, which incorporates the Mach's principle into Gravitation. Also, we have deduced the equation of Entropy; the Hamiltonian for a particle in an electromagnetic field and the reciprocal fine structure constant. It is possible to deduce the expression of the Casimir force and also to explain the Inflation Period and the Missing Matter without assuming the existence of vacuum fluctuations. This new approach for Gravity will allow us to understand some crucial matters in Cosmology.
Quantum kinetic theories in degenerate plasmas
Brodin, Gert; Ekman, Robin; Zamanian, Jens
2017-01-01
In this review we give an overview of the recent work on quantum kinetic theories of plasmas. We focus, in particular, on the case where the electrons are fully degenerate. For such systems, perturbation methods using the distribution function can be problematic. Instead we present a model that considers the dynamics of the Fermi surface. The advantage of this model is that, even though the value of the distribution function can be greatly perturbed outside the equilibrium Fermi surface, deformation of the Fermi surface is small up to very large amplitudes. Next, we investigate the short-scale dynamics for which the Wigner-Moyal equation replaces the Vlasov equation. In particular, we study wave-particle interaction, and deduce that new types of wave damping can occur due to the simultaneous absorption (or emission) of multiple wave quanta. Finally, we consider exchange effects within a quantum kinetic formalism to find a model that is more accurate than those using exchange potentials from density functional theory. We deduce the exchange corrections to the dispersion relations for Langmuir and ion-acoustic waves. In comparison to results based on exchange potentials deduced from density functional theory we find that the latter models are reasonably accurate for Langmuir waves, but rather inaccurate for ion acoustic waves.
Quantum Kinetic Theory and Applications Electrons, Photons, Phonons
Vasko, Fedir T
2006-01-01
This lecture-style monograph is addressed to several categories of readers. First, it will be useful for graduate students studying theory. Second, the topics covered should be interesting for postgraduate students of various specializations. Third, the researchers who want to understand the background of modern theoretical issues in more detail can find a number of useful results here. The phenomena covered involve kinetics of electron, phonon, and photon systems in solids. The dynamical properties and interactions of electrons, phonons, and photons are briefly described in Chapter 1. Further, in Chapters 2-8, the authors present the main theoretical methods: linear response theory, various kinetic equations for the quasiparticles under consideration, and diagram technique. The presentation of the key approaches is always accompanied by solutions of concrete problems to illustrate ways to apply the theory. The remaining chapters are devoted to various manifestations of quantum transport in solids. The choice...
Radiative Transfer Reconsidered as a Quantum Kinetic Theory Problem
Indian Academy of Sciences (India)
J. Rosato
2015-12-01
We revisit the radiative transfer theory from first principles approach, inspired from quantum kinetic theory. The radiation field is described within the second quantization formalism. A master equation for the radiation density operator is derived and transformed into a balance relation in the phase space, which involves nonlocal terms owing to radiation coherence. In a perturbative framework, we focus on the lowest order term in $\\hbar$-expansion and show that the radiation coherence results in an alteration of the photon group velocity. An application to the formation of hydrogen lines in stellar atmospheres is performed as an illustration.
Kinetic Theory of the Quantum Field Systems With Unstable Vacuum
Smolyansky, S A; Prozorkevich, A V
2003-01-01
The description of quantum field systems with meta-stable vacuum is motivated by studies of many physical problems (the decay of disoriented chiral condensate, the resonant decay of CP-odd meta-stable states, self-consistent model of QGP pre-equilibrium evolution, the phase transition problem in the systems with broken symmetry etc). A non-perturbative approach based on the kinetic description within the framework of the quasi-particle representation was proposed here. We restrict ourselves to scalar field theory with potentials of polynomial type. The back reaction mechanism, i.e. the particle production influence on background field is also discussed. Using the oscillator representation, we derive the generalized kinetic equation with non-pertrubative source term for description of particle-antiparticle creation under action of background field and equation of motion for it. As an illustrative example we consider one-component scalar theory with double-well potential. On this example, we study some features...
Spectral methods in chemistry and physics applications to kinetic theory and quantum mechanics
Shizgal, Bernard
2015-01-01
This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficient...
Manning, Phillip
2011-01-01
The study of quantum theory allowed twentieth-century scientists to examine the world in a new way, one that was filled with uncertainties and probabilities. Further study also led to the development of lasers, the atomic bomb, and the computer. This exciting new book clearly explains quantum theory and its everyday uses in our world.
Generalized quantum kinetic expansion: Higher-order corrections to multichromophoric Förster theory.
Wu, Jianlan; Gong, Zhihao; Tang, Zhoufei
2015-08-21
For a general two-cluster energy transfer network, a new methodology of the generalized quantum kinetic expansion (GQKE) method is developed, which predicts an exact time-convolution equation for the cluster population evolution under the initial condition of the local cluster equilibrium state. The cluster-to-cluster rate kernel is expanded over the inter-cluster couplings. The lowest second-order GQKE rate recovers the multichromophoric Förster theory (MCFT) rate. The higher-order corrections to the MCFT rate are systematically included using the continued fraction resummation form, resulting in the resummed GQKE method. The reliability of the GQKE methodology is verified in two model systems, revealing the relevance of higher-order corrections.
Quantum kinetics of spinning neutral particles: General theory and Spin wave dispersion
Andreev, P A
2013-01-01
Plasma physics give an example of physical system of particles with the long range interaction. At small velocity of particles we can consider the plasma approximately as a system of particles with the Coulomb interaction. The Coulomb interaction is isotropic. Systems of spinning neutral particles have long-range anisotropic interparticle interaction. So, they can reveal more reach properties than plasma. Furthermore for studying of systems of spinning particles we can develop kinetic and hydrodynamic methods analogous to used for the plasma. We derive kinetic equations by a new method, which is the generalization of the many-particle quantum hydrodynamics. Obtained set of kinetic equations is truncated, so we have closed set of two equations. One of them is the kinetic equation for quantum distribution function. The second equation is the equation for the spin-distribution. Which describes the spin kinetic evolution and gives contribution in time evolution of the distribution function. Our method allows to o...
Somers, Kieran P; Simmie, John M; Metcalfe, Wayne K; Curran, Henry J
2014-03-21
Due to the rapidly growing interest in the use of biomass derived furanic compounds as potential platform chemicals and fossil fuel replacements, there is a simultaneous need to understand the pyrolysis and combustion properties of such molecules. To this end, the potential energy surfaces for the pyrolysis relevant reactions of the biofuel candidate 2-methylfuran have been characterized using quantum chemical methods (CBS-QB3, CBS-APNO and G3). Canonical transition state theory is employed to determine the high-pressure limiting kinetics, k(T), of elementary reactions. Rice-Ramsperger-Kassel-Marcus theory with an energy grained master equation is used to compute pressure-dependent rate constants, k(T,p), and product branching fractions for the multiple-well, multiple-channel reaction pathways which typify the pyrolysis reactions of the title species. The unimolecular decomposition of 2-methylfuran is shown to proceed via hydrogen atom transfer reactions through singlet carbene intermediates which readily undergo ring opening to form collisionally stabilised acyclic C5H6O isomers before further decomposition to C1-C4 species. Rate constants for abstraction by the hydrogen atom and methyl radical are reported, with abstraction from the alkyl side chain calculated to dominate. The fate of the primary abstraction product, 2-furanylmethyl radical, is shown to be thermal decomposition to the n-butadienyl radical and carbon monoxide through a series of ring opening and hydrogen atom transfer reactions. The dominant bimolecular products of hydrogen atom addition reactions are found to be furan and methyl radical, 1-butene-1-yl radical and carbon monoxide and vinyl ketene and methyl radical. A kinetic mechanism is assembled with computer simulations in good agreement with shock tube speciation profiles taken from the literature. The kinetic mechanism developed herein can be used in future chemical kinetic modelling studies on the pyrolysis and oxidation of 2-methylfuran
Quantum field kinetics of QCD quark-gluon transport theory for light-cone dominated processes
Kinder-Geiger, Klaus
1996-01-01
A quantum kinetic formalism is developed to study the dynamical interplay of quantum and statistical-kinetic properties of non-equilibrium multi-parton systems produced in high-energy QCD processes. The approach provides the means to follow the quantum dynamics in both space-time and energy-momentum, starting from an arbitrary initial configuration of high-momentum quarks and gluons. Using a generalized functional integral representation and adopting the `closed-time-path' Green function techniques, a self-consistent set of equations of motions is obtained: a Ginzburg-Landau equation for a possible color background field, and Dyson-Schwinger equations for the 2-point functions of the gluon and quark fields. By exploiting the `two-scale nature' of light-cone dominated QCD processes, i.e. the separation between the quantum scale that specifies the range of short-distance quantum fluctuations, and the kinetic scale that characterizes the range of statistical binary inter- actions, the quantum-field equations of ...
Quantum-kinetic equations for time correlation functions in higher-order perturbation theory
Leermakers, M.C.J.; Suttorp, L.G.
1981-01-01
The memory kernel of the kinetic equation for the time correlation function of a quantum fluid is determined both in third order of the interaction strength and in the low-density approximation. The results are obtained with the help of a diagram representation for the kernel. The connection with
Quantum algorithmic information theory
Svozil, Karl
1995-01-01
The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capa...
Kinetic theory and transport phenomena
Soto, Rodrigo
2016-01-01
This textbook presents kinetic theory, which is a systematic approach to describing nonequilibrium systems. The text is balanced between the fundamental concepts of kinetic theory (irreversibility, transport processes, separation of time scales, conservations, coarse graining, distribution functions, etc.) and the results and predictions of the theory, where the relevant properties of different systems are computed. The book is organised in thematic chapters where different paradigmatic systems are studied. The specific features of these systems are described, building and analysing the appropriate kinetic equations. Specifically, the book considers the classical transport of charges, the dynamics of classical gases, Brownian motion, plasmas, and self-gravitating systems, quantum gases, the electronic transport in solids and, finally, semiconductors. Besides these systems that are studied in detail, concepts are applied to some modern examples including the quark–gluon plasma, the motion of bacterial suspen...
Irreversible processes kinetic theory
Brush, Stephen G
2013-01-01
Kinetic Theory, Volume 2: Irreversible Processes deals with the kinetic theory of gases and the irreversible processes they undergo. It includes the two papers by James Clerk Maxwell and Ludwig Boltzmann in which the basic equations for transport processes in gases are formulated, together with the first derivation of Boltzmann's ""H-theorem"" and a discussion of this theorem, along with the problem of irreversibility.Comprised of 10 chapters, this volume begins with an introduction to the fundamental nature of heat and of gases, along with Boltzmann's work on the kinetic theory of gases and s
Quantum biological information theory
Djordjevic, Ivan B
2016-01-01
This book is a self-contained, tutorial-based introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors as well as their effects. Integrates quantum information and quantum biology concepts; Assumes only knowledge of basic concepts of vector algebra at undergraduate level; Provides a thorough introduction to basic concepts of quantum information processing, quantum information theory, and quantum biology; Includes in-depth discussion of the quantum biological channel modelling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models o...
Raedt, Hans De; Binder, K; Ciccotti, G
1996-01-01
The purpose of this set of lectures is to introduce the general concepts that are at the basis of the computer simulation algorithms that are used to study the behavior of condensed matter quantum systems. The emphasis is on the underlying concepts rather than on specific applications. Topics treate
Nielsen, M. A.
2000-01-01
Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent quantum information, and entanglement. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory, and of this Dissertation. In particular, I demonstrate several novel limits to the informa...
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Nielsen, M A
1998-01-01
Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent quantum information, and entanglement. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory, and of this Dissertation. In particular, I demonstrate several novel limits to the information processing ability of quantum mechanics. Results of especial interest include: the demonstration of limitations to the class of measurements which may be performed in quantum mechanics; a capacity theorem giving achievable limits to the transmission of classical information through a two-way noiseless quantum channel; resource bounds on distributed quantum computation; a new proof of the quantum noiseless channel coding theorem; an information-theoretic characterization of the conditions under which quantum error-cor...
Kinetics of the benzyl + O(3P) reaction: a quantum chemical/statistical reaction rate theory study.
da Silva, Gabriel; Bozzelli, Joseph W
2012-12-14
The resonance stabilized benzyl radical is an important intermediate in the combustion of aromatic hydrocarbons and in polycyclic aromatic hydrocarbon (PAH) formation in flames. Despite being a free radical, benzyl is relatively stable in thermal, oxidizing environments, and is predominantly removed through bimolecular reactions with open-shell species other than O(2). In this study the reaction of benzyl with ground-state atomic oxygen, O((3)P), is examined using quantum chemistry and statistical reaction rate theory. C(7)H(7)O energy surfaces are generated at the G3SX level, and include several novel pathways. Transition state theory is used to describe elementary reaction kinetics, with canonical variational transition state theory applied for barrierless O atom association with benzyl. Apparent rate constants and branching ratios to different product sets are obtained as a function of temperature and pressure from solving the time-dependent master equation, with RRKM theory for microcanonical k(E). These simulations indicate that the benzyl + O reaction predominantly forms the phenyl radical (C(6)H(5)) plus formaldehyde (HCHO), with lesser quantities of the C(7)H(6)O products benzaldehyde, ortho-quinone methide, and para-quinone methide (+H), along with minor amounts of the formyl radical (HCO) + benzene. Addition of O((3)P) to the methylene site in benzyl produces a highly vibrationally excited C(7)H(7)O* adduct, the benzoxyl radical, which can β-scission to benzaldehyde + H and phenyl + HCHO. In order to account for the experimental observation of benzene as the major reaction product, a roaming radical mechanism is proposed that converts the nascent products phenyl and HCHO to benzene + HCO. Oxygen atom addition at the ortho and para ring sites in benzyl, which has not been previously considered, is shown to lead to the quinone methides + H; these species are less-stable isomers of benzaldehyde that are proposed as important combustion intermediates, but
Bates, David Robert
1962-01-01
Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postula
Quantum electronics basic theory
Fain, V M; Sanders, J H
1969-01-01
Quantum Electronics, Volume 1: Basic Theory is a condensed and generalized description of the many research and rapid progress done on the subject. It is translated from the Russian language. The volume describes the basic theory of quantum electronics, and shows how the concepts and equations followed in quantum electronics arise from the basic principles of theoretical physics. The book then briefly discusses the interaction of an electromagnetic field with matter. The text also covers the quantum theory of relaxation process when a quantum system approaches an equilibrium state, and explai
Kinetic mean field theories: Results of energy constraint in maximizing entropy
Stell, G.; Karkheck, J.; Beijeren, H. van
1983-01-01
Structure of liquids and solids; crystallography Classical, semiclassical, and quantum theories of liquid structure Statistical theories of liquid structure - Kinetic and transport theory of fluids; physical properties of gases Kinetic and transport theory
Kinetic theory of nonideal gases and nonideal plasmas
Klimontovich, Yu L
2013-01-01
Kinetic Theory of Nonideal Gases and Nonideal Plasmas presents the fundamental aspects of the kinetic theory of gases and plasmas. The book consists of three parts, which attempts to present some of the ideas, methods and applications in the study of the kinetic processes in nonideal gases and plasmas. The first part focuses on the classical kinetic theory of nonideal gases. The second part discusses the classical kinetic theory of fully ionized plasmas. The last part is devoted to the quantum kinetic theory of nonideal gases and plasmas. A concluding chapter is included, which presents a shor
Bastin, Ted
2009-07-01
List of participants; Preface; Part I. Introduction: 1. The function of the colloquium - editorial; 2. The conceptual problem of quantum theory from the experimentalist's point of view O. R. Frisch; Part II. Niels Bohr and Complementarity: The Place of the Classical Language: 3. The Copenhagen interpretation C. F. von Weizsäcker; 4. On Bohr's views concerning the quantum theory D. Bohm; Part III. The Measurement Problem: 5. Quantal observation in statistical interpretation H. J. Groenewold; 6. Macroscopic physics, quantum mechanics and quantum theory of measurement G. M. Prosperi; 7. Comment on the Daneri-Loinger-Prosperi quantum theory of measurement Jeffrey Bub; 8. The phenomenology of observation and explanation in quantum theory J. H. M. Whiteman; 9. Measurement theory and complex systems M. A. Garstens; Part IV. New Directions within Quantum Theory: What does the Quantum Theoretical Formalism Really Tell Us?: 10. On the role of hidden variables in the fundamental structure of physics D. Bohm; 11. Beyond what? Discussion: space-time order within existing quantum theory C. W. Kilmister; 12. Definability and measurability in quantum theory Yakir Aharonov and Aage Petersen; 13. The bootstrap idea and the foundations of quantum theory Geoffrey F. Chew; Part V. A Fresh Start?: 14. Angular momentum: an approach to combinatorial space-time Roger Penrose; 15. A note on discreteness, phase space and cohomology theory B. J. Hiley; 16. Cohomology of observations R. H. Atkin; 17. The origin of half-integral spin in a discrete physical space Ted Bastin; Part VI. Philosophical Papers: 18. The unity of physics C. F. von Weizsäcker; 19. A philosophical obstacle to the rise of new theories in microphysics Mario Bunge; 20. The incompleteness of quantum mechanics or the emperor's missing clothes H. R. Post; 21. How does a particle get from A to B?; Ted Bastin; 22. Informational generalization of entropy in physics Jerome Rothstein; 23. Can life explain quantum mechanics? H. H
Bao, Junwei Lucas; Zheng, Jingjing; Truhlar, Donald G
2016-03-02
Pressure-dependent reactions are ubiquitous in combustion and atmospheric chemistry. We employ a new calibration procedure for quantum Rice-Ramsperger-Kassel (QRRK) unimolecular rate theory within a chemical activation mechanism to calculate the pressure-falloff effect of a radical association with an aromatic ring. The new theoretical framework is applied to the reaction of H with toluene, which is a prototypical reaction in the combustion chemistry of aromatic hydrocarbons present in most fuels. Both the hydrogen abstraction reactions and the hydrogen addition reactions are calculated. Our system-specific (SS) QRRK approach is adjusted with SS parameters to agree with multistructural canonical variational transition state theory with multidimensional tunneling (MS-CVT/SCT) at the high-pressure limit. The new method avoids the need for the usual empirical estimations of the QRRK parameters, and it eliminates the need for variational transition state theory calculations as a function of energy, although in this first application we do validate the falloff curves by comparing SS-QRRK results without tunneling to multistructural microcanonical variational transition state theory (MS-μVT) rate constants without tunneling. At low temperatures, the two approaches agree well with each other, but at high temperatures, SS-QRRK tends to overestimate falloff slightly. We also show that the variational effect is important in computing the energy-resolved rate constants. Multiple-structure anharmonicity, torsional-potential anharmonicity, and high-frequency-mode vibrational anharmonicity are all included in the rate computations, and torsional anharmonicity effects on the density of states are investigated. Branching fractions, which are both temperature- and pressure-dependent (and for which only limited data is available from experiment), are predicted as a function of pressure.
Wilde, Mark M
2017-01-01
Developing many of the major, exciting, pre- and post-millennium developments from the ground up, this book is an ideal entry point for graduate students into quantum information theory. Significant attention is given to quantum mechanics for quantum information theory, and careful studies of the important protocols of teleportation, superdense coding, and entanglement distribution are presented. In this new edition, readers can expect to find over 100 pages of new material, including detailed discussions of Bell's theorem, the CHSH game, Tsirelson's theorem, the axiomatic approach to quantum channels, the definition of the diamond norm and its interpretation, and a proof of the Choi–Kraus theorem. Discussion of the importance of the quantum dynamic capacity formula has been completely revised, and many new exercises and references have been added. This new edition will be welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theo...
Zeh, H D
1999-01-01
This is a brief reply to Goldstein's article on ``Quantum Theory Without Observers'' in Physics Today. It is pointed out that Bohm's quantum mechanics is successful only because it keeps Schrödinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.
Mandl, Franz
2010-01-01
Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic
Wentzel, Gregor
2003-01-01
A prominent figure in twentieth-century physics, Gregor Wentzel made major contributions to the development of quantum field theory, first in Europe and later at the University of Chicago. His Quantum Theory of Fields offers a knowledgeable view of the original literature of elementary quantum mechanics and helps make these works accessible to interested readers.An introductory volume rather than an all-inclusive account, the text opens with an examination of general principles, without specification of the field equations of the Lagrange function. The following chapters deal with particular
Quantum Cosmology: Effective Theory
Bojowald, Martin
2012-01-01
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge of specific properties of quantum states, it remained difficult to make testable predictions. For quantum cosmology to be part of empirical science, it must allow for a systematic framework in which corrections to well-tested classical equations can be derived, with any ambiguities and ignorance sufficiently parameterized. As in particle and condensed-matter physics, a successful viewpoint is one of effective theories, adapted to specific issues one encounters in quantum cosmology. This review presents such an effective framework of quantum cosmology, taking into account, among other things, space-time structures, covariance, the problem of time and the anomaly issue.
Energy Technology Data Exchange (ETDEWEB)
Sadovskii, Michael V.
2013-06-01
This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The work illustrates the unity of modern theoretical physics by combining approaches and concepts of the quantum field theory and modern condensed matter theory. The inductive approach allows a deep understanding of ideas and methods used for solving problems in this field.
Zeh, H. D.
1998-01-01
This is a brief reply to Goldstein's article on ``Quantum Theory Without Observers'' in Physics Today. It is pointed out that Bohm's pilot wave theory is successful only because it keeps Schr\\"odinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.
Zeh, H. D.
1999-04-01
This is a brief reply to S. Goldstein's article "Quantum theory without observers" in Physics Today. It is pointed out that Bohm's pilot wave theory is successful only because it keeps Schrödinger's (exact) wave mechanics unchanged, while the rest of it is observationally meaningless and solely based on classical prejudice.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Friedberg, R; Hohenberg, P C
2014-09-01
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'compatible quantum theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory
Friedberg, R.; Hohenberg, P. C.
2014-09-01
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call ‘compatible quantum theory (CQT)’, consists of a ‘microscopic’ part (MIQM), which applies to a closed quantum system of any size, and a ‘macroscopic’ part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths (‘c-truths’), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
Energy Technology Data Exchange (ETDEWEB)
Aastrup, Johannes; Moeller Grimstrup, Jesper
2016-10-15
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeo-morphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi-classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost-commutative algebra emerges from the holonomy-diffeomorphism algebra in the same limit. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Experimental quantum field theory
Bell, J S
1977-01-01
Presented here, is, in the opinion of the author, the essential minimum of quantum field theory that should be known to cultivated experimental particle physicists. The word experimental describes not only the audience aimed at but also the level of mathematical rigour aspired to. (0 refs).
Zeidler, Eberhard
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction). From the reviews: "… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from othe...
Von Weizsäcker, Carl Friedrich
1988-01-01
1- presentation of quantum theory in present-day physics. 2- a flash-back on the history : from Planck to Copenhagen. 3- the Copenhagen interpretation. 4- reconstrucction of Abstract Quantum Theory. 5- recent interpretations. 6- the philosophy of the mind. 7- concrete quantum theory. 8- the non-locality. This second tape contains the debate following the talk of the professor.
Hoehn, Philipp A
2016-01-01
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S's state as O's `catalogue of knowledge' about S; no ontic assumptions are necessary. From the rules we derive the state spaces for N qubits and show that (a) they coincide with the set of density matrices over N qubit Hilbert spaces; (b) states evolve unitarily under the group $\\rm{PSU}(2^N)$ according to the von Neumann evolution equation; and (c) the binary questions by means of which O interrogates the systems corresponds to projective measurements on Pauli operators with outcome probabilities given by the Born rule. Besides offering a novel conceptual perspective on qubit quantum theory, the reconstruction also unravels new structural insights. Namely, we show that, in a quadratic information measure, (d) qubits satisfy informational complementarity inequalities...
Aastrup, Johannes
2015-01-01
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi-classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi-classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the...
Quantum information theory mathematical foundation
Hayashi, Masahito
2017-01-01
This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an impro...
Quantum kinetics derivation as generalization of the quantum hydrodynamics method
Andreev, Pavel A
2012-01-01
We present a new way of quantum kinetic equation derivation. This method appears as a natural generalization of the many-particle quantum hydrodynamic method. Kinetic equations are derived for different system of particles. First of all we consider quantum plasma and pay special attention to the spin evolution. We show that we need a set of two kinetic equations for description of spinning particles. One of these equations is the equation for distribution function, however this equation contains new function, even in the self-consistent field approximation. This is a spin-distribution function introduced in the paper. Therefore we have to derive kinetic equation for spin distribution function evolution, which is presented here and used to construct a closed set of kinetic equations. We also present kinetic equation for system of neutral particles with a short-range interaction in the first order by the interaction radius approximation. We derive a set of kinetic equations for particles having electric dipole ...
Gurau, R; Rivasseau, V
2008-01-01
We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define non-perturbatively {\\it differential} renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the Grosse-Wulkenhaar model. Perhaps most importantly it removes the space-time background from its central place in QFT, paving the way for a nonperturbative definition of field theory in noninteger dimension.
Quantum mechanics theory and experiment
Beck, Mark
2012-01-01
This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...
Gripaios, Ben
2014-01-01
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is `freer', in the sense that the non-interacting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree- and loop-level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behaviour is radically different to both classical fluids and quantum fields, with interesting physical consequences for fluids in the low temperature regime.
Quantum Information Theory - an Invitation
Werner, R. F.
2001-01-01
We give a non-technical introduction of the basic concepts of Quantum Information Theory along the distinction between possible and impossible machines. We then proceed to describe the mathematical framework of Quantum Information Theory. The capacities of a quantum channel for classical and for quantum information are defined in a unified scheme, and a mathematical characterization of all teleportation and dense coding schemes is given.
Disco Dancing and Kinetic Theory
Karakas, Mehmet
2010-01-01
This paper provides an example of an innovative science activity used in a science methods course for future elementary teachers at a small university in northeastern Turkey. The activity aims to help prospective elementary teachers understand kinetic-molecular theory in a simple way and to expose these preservice teachers to an innovative…
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Quantum Lévy Processes and Fractional Kinetics
Kusnezov, D; Dang, G D; Kusnezov, Dimitri; Bulgac, Aurel; Dang, Giu Do
1999-01-01
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We find that the reduced density matrix can display dynamics given by fractional kinetic equations. In particular we derive a fractional extension of Kramers equation.
Quantum mechanics of 4-derivative theories
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Salvio, Alberto [Universidad Autonoma de Madrid and Instituto de Fisica Teorica IFT-UAM/CSIC, Departamento de Fisica Teorica, Madrid (Spain); Strumia, Alessandro [Dipartimento di Fisica, Universita di Pisa (Italy); CERN, Theory Division, Geneva (Switzerland); INFN, Pisa (Italy)
2016-04-15
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm. (orig.)
Quantum mechanics of 4-derivative theories.
Salvio, Alberto; Strumia, Alessandro
2016-01-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
Theory of interacting quantum fields
Rebenko, Alexei L
2012-01-01
This monograph is devoted to the systematic and encyclopedic presentation of the foundations of quantum field theory. It represents mathematical problems of the quantum field theory with regardto the new methods of the constructive and Euclidean field theory formed for the last thirty years of the 20th century on the basis of rigorous mathematical tools of the functional analysis, the theory of operators, and the theory of generalized functions. The book is useful for young scientists who desire to understand not only the formal structure of the quantum field theory but also its basic concepts and connection with classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of functional integration.
Quantum paradoxes quantum theory for the perplexed
Aharonov, Yakir
2005-01-01
A Guide through the Mysteries of Quantum Physics!Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect. Together with Daniel Rohrlich of the Weizmann Institute, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language
Bayesian Intersubjectivity and Quantum Theory
Pérez-Suárez, Marcos; Santos, David J.
2005-02-01
Two of the major approaches to probability, namely, frequentism and (subjectivistic) Bayesian theory, are discussed, together with the replacement of frequentist objectivity for Bayesian intersubjectivity. This discussion is then expanded to Quantum Theory, as quantum states and operations can be seen as structural elements of a subjective nature.
Quantum Mechanics and Quantum Field Theory
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Quantum information theory and quantum statistics
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Petz, D. [Alfred Renyi Institute of Mathematics, Budapest (Hungary)
2008-07-01
Based on lectures given by the author, this book focuses on providing reliable introductory explanations of key concepts of quantum information theory and quantum statistics - rather than on results. The mathematically rigorous presentation is supported by numerous examples and exercises and by an appendix summarizing the relevant aspects of linear analysis. Assuming that the reader is familiar with the content of standard undergraduate courses in quantum mechanics, probability theory, linear algebra and functional analysis, the book addresses graduate students of mathematics and physics as well as theoretical and mathematical physicists. Conceived as a primer to bridge the gap between statistical physics and quantum information, a field to which the author has contributed significantly himself, it emphasizes concepts and thorough discussions of the fundamental notions to prepare the reader for deeper studies, not least through the selection of well chosen exercises. (orig.)
Quantum Transition-State Theory
Hele, Timothy J H
2014-01-01
This dissertation unifies one of the central methods of classical rate calculation, `Transition-State Theory' (TST), with quantum mechanics, thereby deriving a rigorous `Quantum Transition-State Theory' (QTST). The resulting QTST is identical to ring polymer molecular dynamics transition-state theory (RPMD-TST), which was previously considered a heuristic method, and whose results we thereby validate. The key step in deriving a QTST is alignment of the flux and side dividing surfaces in path-integral space to obtain a quantum flux-side time-correlation function with a non-zero $t\\to 0_+$ limit. We then prove that this produces the exact quantum rate in the absence of recrossing by the exact quantum dynamics, fulfilling the requirements of a QTST. Furthermore, strong evidence is presented that this is the only QTST with positive-definite Boltzmann statistics and therefore the pre-eminent method for computation of thermal quantum rates in direct reactions.
The quantum theory of measurement
Busch, Paul; Mittelstaedt, Peter
1996-01-01
The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables and unsharp pointers.
Recoverability in quantum information theory
Wilde, Mark M
2015-01-01
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information...
Studies in quantum information theory
Menicucci, Nicolas C.
Quantum information theory started as the backdrop for quantum computing and is often considered only in relation to this technology, which is still in its infancy. But quantum information theory is only partly about quantum computing. While much of the interest in this field is spurred by the possible use of quantum computers for code breaking using fast factoring algorithms, to a physicist interested in deeper issues, it presents an entirely new set of questions based on an entirely different way of looking at the quantum world. This thesis is an exploration of several topics in quantum information theory. But it is also more than this. This thesis explores the new paradigm brought about by quantum information theory---that of physics as the flow of information. The thesis consists of three main parts. The first part describes my work on continuous-variable cluster states, a new platform for quantum computation. This begins with background material discussing classical and quantum computation and emphasizing the physical underpinnings of each, followed by a discussion of two recent unorthodox models of quantum computation. These models are combined into an original proposal for quantum computation using continuous-variable cluster states, including a proposed optical implementation. These are followed by a mathematical result radically simplifying the optical construction. Subsequent work simplifies this connection even further and provides a constructive proposal for scalable generation of large-scale cluster states---necessary if there is to be any hope of using this method in practical quantum computation. Experimental implementation is currently underway by my collaborators at The University of Virginia. The second part describes my work related to the physics of trapped ions, starting with an overview of the basic theory of linear ion traps. Although ion traps are often discussed in terms of their potential use for quantum computation, my work looks at their
Karkheck, John; Stell, George
1981-08-01
A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several
Collisions in Chiral Kinetic Theory
Chen, Jing-Yuan; Stephanov, Mikhail A
2015-01-01
Using a covariant formalism, we construct a chiral kinetic theory Lorentz invariant to order $\\mathcal O(\\hbar)$ which includes collisions. We find a new contribution to the particle number current due to the side jumps required by the conservation of angular momentum during collisions. We also find a conserved symmetric stress-energy tensor as well as the $H$-function obeying Boltzmann's $H$-theorem. We demonstrate their use by finding a general equilibrium solution and the values of the anomalous transport coefficients characterizing chiral vortical effect.
Comments on quantum probability theory.
Sloman, Steven
2014-01-01
Quantum probability theory (QP) is the best formal representation available of the most common form of judgment involving attribute comparison (inside judgment). People are capable, however, of judgments that involve proportions over sets of instances (outside judgment). Here, the theory does not do so well. I discuss the theory both in terms of descriptive adequacy and normative appropriateness.
Time, chance and quantum theory
Sudbery, Anthony
2016-01-01
I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future statements, and a contextual theory of truth which gives objective and subjective perspectives equal validity.
Energy Technology Data Exchange (ETDEWEB)
Green, H.S. [Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, SA (Australia)
1998-12-31
It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein`s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein`s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation. Copyright (1998) CSIRO Australia 33 refs.
Quantum Field Theory in (0 + 1) Dimensions
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
On the theory of time dilation in chemical kinetics
Baig, Mirza Wasif
2012-01-01
The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying theories of chemical kinetics, which are transition state theory, collision theory and Marcus theory, with the special theory of relativity. Lorentz transformations of Boltzmann constant and energy spacing between permitted quantum levels of molecules are quantum mechanically proved to be Lorentz variant. The relativistic statistical thermodynamics has been developed to explain quasiequilibrium existing between reactants and activated complex. The newly formulated Lorentz transformation of the rate constant from Arrhenius Equation, of the collision frequency and of the Eyring and Marcus equations renders the rate law also Lorentz variant. For a moving observer moving at fractions of the speed of light along the reaction coordinate the transition state possess less kinetic energy to sweep translation over it. This results in the slower transformation of...
Relativistic Kinetic Theory: An Introduction
Sarbach, Olivier
2013-01-01
We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincare one-form on this bundle, from which the symplectic form and a volume form are constructed. Then, we define an appropriate Hamiltonian on the bundle which, together with the symplectic form yields the Liouville vector field. The corresponding flow, when projected onto the base manifold, generates geodesic motion. Whenever the flow is restricted to energy surfaces corresponding to a negative value of the Hamiltonian, its projection describes a family of future-directed timelike geodesics. A collisionless gas is described by a distribution function on such an energy surface, satisfying the Liouville equation. Fibre integrals of the distribution function determine the particle current density and the stress-energy ten...
Elementary Concepts of Quantum Theory
Warren, J. W.
1974-01-01
Discusses the importance and difficulties of teaching basic quantum theory. Presents a discussion of wave-particle duality, indeterminacy, the nature of a quantized state of a system, and the exclusion principle. (MLH)
Quantum theory a wide spectrum
Manoukian, E B
2006-01-01
Suitable for instructors and graduate students in Physics, and researchers and professional scientists in Theoretical Physics, this textbook focuses on Quantum Theory. It includes traditional topics and contains numerous problems some of which are challenging enough for research
Introduction to quantum information theory
Nielsen, M. A.
2000-01-01
This is an expanded and revised text for a fifteen minute talk given at the University of Queensland Physics Camp, September 2000. The focus is on the goals and motivations for studying quantum information theory, rather than on technical results.
Quantum Theory is an Information Theory
D'Ariano, Giacomo M.; Perinotti, Paolo
2016-03-01
In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.
Lectures on quantum field theory
Das, Ashok
2008-01-01
This book consists of the lectures for a two-semester course on quantum field theory, and as such is presented in a quite informal and personal manner. The course starts with relativistic one-particle systems, and develops the basics of quantum field theory with an analysis of the representations of the Poincaré group. Canonical quantization is carried out for scalar, fermion, Abelian and non-Abelian gauge theories. Covariant quantization of gauge theories is also carried out with a detailed description of the BRST symmetry. The Higgs phenomenon and the standard model of electroweak interactio
Fractional statistics and quantum theory
Khare, Avinash
1997-01-01
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f
Energy Technology Data Exchange (ETDEWEB)
Vukmirovic, Nenad; Wang, Lin-Wang
2009-11-10
This review covers the description of the methodologies typically used for the calculation of the electronic structure of self-assembled and colloidal quantum dots. These are illustrated by the results of their application to a selected set of physical effects in quantum dots.
Quantum field theory competitive models
Tolksdorf, Jürgen; Zeidler, Eberhard
2009-01-01
For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: 'To bring together outstanding experts working in...
Razavy, Mohsen
2014-01-01
In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined. In addition by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and ...
Introduction to quantum Thurston theory
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L O [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation); Penner, R C [University of Southern California, Los Angeles (United States)
2003-12-31
This is a survey of the theory of quantum Teichmueller and Thurston spaces. The Thurston (or train track) theory is described and quantized using the quantization of coordinates for Teichmueller spaces of Riemann surfaces with holes. These surfaces admit a description by means of the fat graph construction proposed by Penner and Fock. In both theories the transformations in the quantum mapping class group that satisfy the pentagon relation play an important role. The space of canonical measured train tracks is interpreted as the completion of the space of observables in 3D gravity, which are the lengths of closed geodesics on a Riemann surface with holes. The existence of such a completion is proved in both the classical and the quantum cases, and a number of algebraic structures arising in the corresponding theories are discussed.
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
Recoverability in quantum information theory
Wilde, Mark
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This is based on arXiv:1505.04661, now accepted for publication in Proceedings of the Royal Society A. I acknowledge support from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Propensity, Probability, and Quantum Theory
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals
Hamilton, I. P.; Mosna, Ricardo A.; Site, L. Delle
2006-01-01
We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quant...
A Naturally Renormalized Quantum Field Theory
2006-01-01
It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space togeth...
WKB approximation and tunneling in theories with noncanonical kinetic terms
González, Mariana Carrillo; Masoumi, Ali; Solomon, Adam R.; Trodden, Mark
2017-09-01
Tunneling is a fascinating aspect of quantum mechanics that renders the local minima of a potential meta-stable, with important consequences for particle physics, for the early hot stage of the universe, and more speculatively, for the behavior of the putative multiverse. While this phenomenon has been studied extensively for systems which have canonical kinetic terms, many theories of fundamental physics contain fields with noncanonical kinetic structures. It is therefore desirable to have a detailed framework for calculating tunneling rates and initial states after tunneling for these theories. In this work we present such a rigorous formulation and illustrate its use by applying it to a number of examples.
Reformulating and Reconstructing Quantum Theory
Hardy, Lucien
2011-01-01
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following: [Axiom 1] Operations correspond to operators. [Axiom 2] Every complete set of positive operators corresponds to a complete set of operations. The following operational postulates are shown to be equivalent to these mathematical axioms: [P1] Definiteness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state. [P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. [P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components. [P4] Compound permutatability. There exis...
Division Algebras and Quantum Theory
Baez, John C
2011-01-01
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way". It is perhaps easiest to see it in the study of irreducible unitary representations of groups on complex Hilbert spaces. These representations come in three kinds: those that are not isomorphic to their own dual (the truly "complex" representations), those that are self-dual thanks to a symmetric bilinear pairing (which are "real", in that they are the complexifications of representations on real Hilbert spaces), and those that are self-dual thanks to an antisymmetric bilinear pairing (which are...
The quantum field theory interpretation of quantum mechanics
de la Torre, Alberto C.
2015-01-01
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Arfi, Badredine
2007-02-01
Most game-theoretic studies of strategic interaction assume independent individual strategies as the basic unit of analysis. This paper explores the effects of non-independence on strategic interaction. Two types of non-independence effects are considered. First, the paper considers subjective non-independence at the level of the individual actor by looking at how choice ambivalence shapes the decision-making process. Specifically, how do alternative individual choices superpose with one another to “constructively/destructively” shape each other's role within an actor's decision-making process? This process is termed as quantum superposition of alternative choices. Second, the paper considers how inter-subjective non-independence across actors engenders collective strategies among two or more interacting actors. This is termed as quantum entanglement of strategies. Taking into account both types of non-independence effect makes possible the emergence of a new collective equilibrium, without assuming signaling, prior “contract” agreement or third-party moderation, or even “cheap talk”. I apply these ideas to analyze the equilibrium possibilities of a situation wherein N actors play a quantum social game of cooperation. I consider different configurations of large- N quantum entanglement using the approach of density operator. I specifically consider the following configurations: star-shaped, nearest-neighbors, and full entanglement.
Quantum Field Theory, Revised Edition
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
Introduction to quantum field theory
Chang, Shau-Jin
1990-01-01
This book presents in a short volume the basics of quantum field theory and many body physics. The first part introduces the perturbative techniques without sophisticated apparatus and applies them to numerous problems including quantum electrodynamics (renormalization), Fermi and Bose gases, the Brueckner theory of nuclear system, liquid Helium and classical systems with noise. The material is clear, illustrative and the important points are stressed to help the reader get the understanding of what is crucial without overwhelming him with unnecessary detours or comments. The material in the s
Holography, Quantum Geometry, and Quantum Information Theory
Directory of Open Access Journals (Sweden)
P. A. Zizzi
2000-03-01
Full Text Available Abstract: We interpret the Holographic Conjecture in terms of quantum bits (qubits. N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labelled by the spin-Ã‚Â½ representation of SU(2, which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, and leads to a picture of the early inflationary universe in terms of quantum computation. A discrete micro-causality emerges, where the time parameter is being defined by the discrete increase of entropy. Then, the model is analysed in the framework of the theory of presheaves (varying sets on a causal set and we get a quantum history. A (bosonic Fock space of the whole history is considered. The Fock space wavefunction, which resembles a Bose-Einstein condensate, undergoes decoherence at the end of inflation. This fact seems to be responsible for the rather low entropy of our universe.
de Wit, Bernard
1990-01-01
After a brief and practical introduction to field theory and the use of Feynman diagram, we discuss the main concept in gauge theories and their application in elementary particle physics. We present all the ingredients necessary for the construction of the standard model.
2013-02-15
Matthew James, Andre Carvalho and Michael Hush completed some work analyzing cross-phase modulation using single photon quantum filtering techniques...ANU Michael Hush January – June, 2012, Postdoc, ANU Matthew R. James Professor, Australian National University Ian R. Petersen Professor...appear, IEEE Trans. Aut. Control., 2013. A. R. R. Carvalho, M. R. Hush , and M. R. James, “Cavity driven by a single photon: Conditional dynamics and
Are Quantum Theory Questions Epistemic?
Directory of Open Access Journals (Sweden)
Viviana Yaccuzzi Polisena
2013-12-01
Full Text Available How to displace-move quantum theory [Ǭ] questions-problems to philosophy? Seeing the collapse of our society’s cultural-intellectual-morals, the philosophy of the 21st century has to contribute to the formation of new principles-formalisms: the big task of the contemporary philosophy ©] is to innovate, to transform the building of the knowledge! Which is the role of the contemporary philosopher? (Noam Chomsky. Building science so that it is more human, out of the scientific mercantilism so that it does not continue transgressing that which is most precious: the thought-life. The ideas that I propose demand a deep cultural-epistemiologicscientific-philosophical-ethical rethinking that goes from quantum entities up to life in society. The starting idea is «the quantum [Ǭ], the paradigm of the contemporary science ©]» (Bernard D’Espagnat. I propose to displace-move questions of the quantum theory [Ǭ]: spin, measure, layering to the field of philosophy (φ to build generic symbols. Can the contemporary episteme model the collapse of the ? For a philosopher, can understanding the importance and the behaviour of the spin bring something new to philosophy ? Can information of the states of the spin be used to observe in a holographic way the pattern energy-information contained in the quantum entities? Is quantum [Ǭ] physics mechanical?
Semiclassical and quantum Liouville theory
Menotti, P
2006-01-01
We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincare' accessory parameters. This provides the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the case of n finite charges and m infinitesimal. With the same technique we compute the exact Green function on the sphere on the background of three finite singularities. Turning to the full quantum problem we address the calculation of the quantum determinant on the background of three finite charges and of the further perturbative corrections. The zeta function regularization provides a theory which is not invariant under local conformal transformations. Instead by employing a regularization suggested in the case of the pseu...
Interpreting quantum theory a therapeutic approach
Friederich, Simon
2014-01-01
Is it possible to approach quantum theory in a 'therapeutic' vein that sees its foundational problems as arising from mistaken conceptual presuppositions? The book explores the prospects for this project and, in doing so, discusses such fascinating issues as the nature of quantum states, explanation in quantum theory, and 'quantum non-locality'.
Interpreting quantum theory a therapeutic approach
Friederich, S
2014-01-01
Is it possible to approach quantum theory in a 'therapeutic' vein that sees its foundational problems as arising from mistaken conceptual presuppositions? The book explores the prospects for this project and, in doing so, discusses such fascinating issues as the nature of quantum states, explanation in quantum theory, and 'quantum non-locality'.
Interference and inequality in quantum decision theory
Energy Technology Data Exchange (ETDEWEB)
Cheon, Taksu, E-mail: taksu.cheon@kochi-tech.ac.j [Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782-8502 (Japan); Takahashi, Taiki, E-mail: ttakahashi@lynx.let.hokudai.ac.j [Laboratory of Social Psychology, Department of Behavioral Science, Faculty of Letters, Hokkaido University, N.10, W.7, Kita-ku, Sapporo 060-0810 (Japan)
2010-12-01
The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data indicating the breakdown of classical explanations are critically examined with quantum theory using the full set of quantum phases.
Interpreting Quantum Theory : A Therapeutic Approach
Friederich, Simon
2014-01-01
Debates about the foundations of quantum theory usually circle around two main challenges: the so-called 'measurement problem' and a claimed tension between quantum theory and relativity theory that arises from the phenomena labelled 'quantum non-locality'. This work explores the possibility of a 't
Interpreting Quantum Theory : A Therapeutic Approach
Friederich, Simon
2014-01-01
Debates about the foundations of quantum theory usually circle around two main challenges: the so-called 'measurement problem' and a claimed tension between quantum theory and relativity theory that arises from the phenomena labelled 'quantum non-locality'. This work explores the possibility of a 't
Quantum theory of acoustoelectric interaction
DEFF Research Database (Denmark)
Mosekilde, Erik
1974-01-01
term, significant in the classical-collision-dominated regime only, the dielectric response function and the acoustic gain factor for a piezoelectrically active sound wave are obtained for the quantum and semiclassical-microscopic regimes. The manner in which the theory can be extended to the collision......Within the self-consistent-field approximation, a quantum-mechanical derivation is given for the dielectric response function of an arbitrarily degenerate free-electron gas which is subjected to a drift field. Neglecting in the equation of motion for the one-electron density operator a convection...
Zitterbewegung in quantum field theory
Institute of Scientific and Technical Information of China (English)
Wang Zhi-Yong; Xiong Cai-Dong
2008-01-01
Traditionally,the zitterbewegung (ZB) of the Dirac electron has just been studied at the level of quantum mechanics.Seeing the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic,graphene,and superconducting systems,etc.,this paper presents a quantum-field-theory investigation on ZB and obtains the con clusion that,the ZB of an electron arises from the influence of virtual electron-positron pairs (or vacuum fluctuations)on the electron.
Preskill, John
2016-01-01
This is the 10th and final chapter of my book on Quantum Information, based on the course I have been teaching at Caltech since 1997. An early version of this chapter (originally Chapter 5) has been available on the course website since 1998, but this version is substantially revised and expanded. The level of detail is uneven, as I've aimed to provide a gentle introduction, but I've also tried to avoid statements that are incorrect or obscure. Generally speaking, I chose to include topics that are both useful to know and relatively easy to explain; I had to leave out a lot of good stuff, but on the other hand the chapter is already quite long. This is a working draft of Chapter 10, which I will continue to update. See the URL on the title page for further updates and drafts of other chapters, and please send me an email if you notice errors. Eventually, the complete book will be published by Cambridge University Press.
The Early Development of Kinetic Theory.
Whitaker, Robert D.
1979-01-01
A review of the work of Bernoulli and other early contributors to kinetic theory. One significant point is that the most outstanding work in this early period was done by a little-known Scotsman, John J. Waterston. (BB)
Quantum Field Theory A Modern Perspective
Parameswaran Nair, V
2005-01-01
Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it gr...
Probability representation of kinetic equation for open quantum system
Man'ko, V I; Shchukin, E V
2003-01-01
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
Thermal physics kinetic theory and thermodynamics
Singh, Devraj; Yadav, Raja Ram
2016-01-01
THERMAL PHYSICS: Kinetic Theory and Thermodynamics is designed for undergraduate course in Thermal Physics and Thermodynamics. The book provides thorough understanding of the fundamental principles of the concepts in Thermal Physics. The book begins with kinetic theory, then moves on liquefaction, transport phenomena, the zeroth, first, second and third laws, thermodynamics relations and thermal conduction. The book concluded with radiation phenomenon. KEY FEATURES: * Include exercises * Short Answer Type Questions * Long Answer Type Questions * Numerical Problems * Multiple Choice Questions
Noncommutative quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Grosse, H. [Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Wien (Austria); Wulkenhaar, R. [Mathematisches Institut der Westfaelischen Wilhelms-Universitaet, Einsteinstrasse 62, 48149 Muenster (Germany)
2014-09-11
We summarize our recent construction of the φ{sup 4}-model on four-dimensional Moyal space. This is achieved by solving the quartic matrix model for a general external matrix in terms of the solution of a non-linear equation for the 2-point function and the eigenvalues of that matrix. The β-function vanishes identically. For the Moyal model, the theory of Carleman type singular integral equations reduces the construction to a fixed point problem. The resulting Schwinger functions in position space are symmetric and invariant under the full Euclidean group. The Schwinger 2-point function is reflection positive iff the diagonal matrix 2-point function is a Stieltjes function. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Entropy, Topological Theories and Emergent Quantum Mechanics
Directory of Open Access Journals (Sweden)
D. Cabrera
2017-02-01
Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a ﬁnite dimensional Hilbert space of quantum states. Speciﬁcally, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological ﬁeld theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.
Lagrangian-Only Quantum Theory
Wharton, K B
2013-01-01
Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path integral or quantum field theory, a promising alternative is to only consider field histories for which the Lagrangian density is always zero. With this change, it appears possible to replace amplitudes with equally-weighted probabilities. This paper demonstrates a proof-of-principle for this approach, using a toy Lagrangian that corresponds to an arbitrary spin state. In this restricted framework one can derive both the Born rule and its limits of applicability. The fact that the Lagrangian obeys future boundary constraints also results in the first continuous, spacetime-based, hidden-variable description of a Bell-inequality-violating system.
Foundations of quantum theory and quantum information applications
Galvão, E F
2002-01-01
This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement characterisation, and of a few quantum information protocols. Quantum non-locality and contextuality are shown to be essential for different implementations of quantum information protocols known as quantum random access codes and quantum communication complexity protocols. I derive sufficient experimental conditions for tests of these quantum properties. I also discuss how the distribution of quantum information through quantum cloning processes can be useful in quantum computing. Regarding entanglement characterisation, some results are obtained relating two problems, that of additivity of the relative entropy of entanglement, and that of identifying different types of tripartite entanglement in the asymptotic regime of manipulations of many copies of a given state. The thesis end...
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Quantum theory of human communication
Slowikowski, Wojtek; Nielsen, Erik B.
2004-01-01
We use notions and techniques of Quantum Field Theory to formulate and investigate basic concepts and mechanisms of human communication. We start with attitudes which correspond to photons frequencies, then we introduce states-of-mind which correspond to wave functions. Finally, by way of the second quantization, we come to states-of-opinions which correspond to states of quantized radiation fields. In the present paper we shall only investigate superpositions of pairs of coherent states (e.g...
Semiclassical and quantum Liouville theory
Menotti, Pietro
2005-01-01
We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincare' accessory parameters. This provides the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the cas...
Parallelization of Kinetic Theory Simulations
Howell, Jim; Colbry, Dirk; Pickett, Rodney; Staber, Alec; Sagert, Irina; Strother, Terrance
2013-01-01
Numerical studies of shock waves in large scale systems via kinetic simulations with millions of particles are too computationally demanding to be processed in serial. In this work we focus on optimizing the parallel performance of a kinetic Monte Carlo code for astrophysical simulations such as core-collapse supernovae. Our goal is to attain a flexible program that scales well with the architecture of modern supercomputers. This approach requires a hybrid model of programming that combines a message passing interface (MPI) with a multithreading model (OpenMP) in C++. We report on our approach to implement the hybrid design into the kinetic code and show first results which demonstrate a significant gain in performance when many processors are applied.
Relativistic quantum information theory and quantum reference frames
Palmer, Matthew C
2013-01-01
This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of localised qubits in curved spacetimes. For example, this concerns quantum experiments on free-space photons and electrons in the vicinity of the Earth. From field theory a description of localised qubits that traverse classical trajectories in curved spacetimes is obtained, for photons and massive spin-1/2 fermions. The equations governing the evolution of the two-dimensional quantum state and its absolute phase are determined. Quantum information theory of these qubits is then developed. The Stern-Gerlach measurement formalism for massive spin-1/2 fermions is also derived from field theory. In the latter category of research, the process of changing reference frames is considered for the case where the reference frames are quantum systems. As part of this process, it is shown that...
Kinetic Theory of the Inner Magnetospheric Plasma
Khazanov, George V
2011-01-01
This book provides a broad introduction to the kinetic theory of space plasma physics with the major focus on the inner magnetospheric plasma. It is designed to provide a comprehensive description of the different kinds of transport equations for both plasma particles and waves with an emphasis on the applicability and limitations of each set of equations. The major topics are: Kinetic Theory of Superthermal Electrons, Kinetic Foundation of the Hydrodynamic Description of Space Plasmas (including wave-particle interaction processes), and Kinetic Theory of the Terrestrial Ring Current. Distinguishable features of this book are the analytical solutions of simplified transport equations. Approximate analytic solutions of transport phenomena are very useful because they help us gain physical insight into how the system responds to varying sources of mass, momentum and energy and also to various external boundary conditions. They also provide us a convenient method to test the validity of complicated numerical mod...
The development of elementary quantum theory
Capellmann, Herbert
2017-01-01
This book traces the evolution of the ideas that eventually resulted in the elementary quantum theory in 1925/26. Further, it discusses the essential differences between the fundamental equations of Quantum Theory derived by Born and Jordan, logically comprising Quantum Mechanics and Quantum Optics, and the traditional view of the development of Quantum Mechanics. Drawing on original publications and letters written by the main protagonists of that time, it shows that Einstein’s contributions from 1905 to 1924 laid the essential foundations for the development of Quantum Theory. Einstein introduced quantization of the radiation field; Born added quantized mechanical behavior. In addition, Born recognized that Quantum Mechanics necessarily required Quantum Optics; his radical concept of truly discontinuous and statistical quantum transitions (“quantum leaps”) was directly based on Einstein’s physical concepts.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
Kinetic theory of hard spheres
Beijeren, H. van; Ernst, M.H.
1979-01-01
Kinetic equations for the hard-sphere system are derived by diagrammatic techniques. A linear equation is obtained for the one-particle-one particle equilibrium time correlation function and a nonlinear equation for the one-particle distribution function in nonequilibrium. Both equations are nonloca
Quantum principal bundles and corresponding gauge theories
Durdevic, M
1995-01-01
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge transformations, are introduced and investigated. A natural differential calculus on quantum gauge bundles is constructed and analyzed. Kinematical and dynamical properties of corresponding gauge theories are discussed.
Random Matrix theory approach to Quantum mechanics
Chaitanya, K. V. S. Shiv
2015-01-01
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of random matrix theory. This study helps in identify the potential appear in the joint probability distribution function in the random matrix theory as a super potential. This approach allows to extend the random matrix theory to the newly discovered exceptional ...
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr
2015-01-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2016-11-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Quantum theory allows for absolute maximal contextuality
Amaral, Barbara; Cunha, Marcelo Terra; Cabello, Adán
2015-12-01
Contextuality is a fundamental feature of quantum theory and a necessary resource for quantum computation and communication. It is therefore important to investigate how large contextuality can be in quantum theory. Linear contextuality witnesses can be expressed as a sum S of n probabilities, and the independence number α and the Tsirelson-like number ϑ of the corresponding exclusivity graph are, respectively, the maximum of S for noncontextual theories and for the theory under consideration. A theory allows for absolute maximal contextuality if it has scenarios in which ϑ /α approaches n . Here we show that quantum theory allows for absolute maximal contextuality despite what is suggested by the examination of the quantum violations of Bell and noncontextuality inequalities considered in the past. Our proof is not constructive and does not single out explicit scenarios. Nevertheless, we identify scenarios in which quantum theory allows for almost-absolute-maximal contextuality.
The decoupling approach to quantum information theory
Dupuis, Frédéric
2010-01-01
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and ha...
Psychophysical Interpretation of Quantum theory
Pradhan, Rajat K
2013-01-01
It is shown that the formalism of quantum theory naturally incorporates the psychophysical parallelism and thereby interprets itself, if the subjective aspects are taken as equal partners alongside the objective aspects as determinants of Reality as a Whole. The inevitable interplay of the subject (observer) and the object (observed) in making up Reality is brought out succinctly through a comprehensive psychophysical interpretation which includes in its bosom the truths of many of the major interpretations proposed so far as essential ingredients. At the heart of this novel approach lies the interpretation of the complex conjugate quantities such as the conjugate wave function {\\Psi}*(r, t), the bra vector , and the observable A etc. respectively. This brings out the psycho-physical parallelism lying hidden in the quantum mechanical formalism in a quite straightforward manner. The measurement process is shown to be a two-step process comprising objective interaction through the retarded waves and subjective ...
Goyal, Philip; Skilling, John
2009-01-01
Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that it is possible to derive the complex nature of the quantum formalism directly from the assumption that a pair of real numbers is associated to each sequence of measurement outcomes, and that the probability of this sequence is a real-valued function of this number pair. By making use of elementary symmetry and consistency conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes.
An Introduction to Quantum Field Theory
Peskin, Michael E
1995-01-01
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the sta
Finite-dimensional collisionless kinetic theory
Burby, J W
2016-01-01
A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.
A first course in topos quantum theory
Energy Technology Data Exchange (ETDEWEB)
Flori, Cecilia [Perimeter Institute for Theoretical Studies, Waterloo, ON (Canada)
2013-06-01
Written by a leading researcher in the field. Concise course-tested textbook. Includes worked-out problems In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory's unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics - such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer - is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory. This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a ''neo-realist'' classical physics theory again.
Linear response theory for quantum open systems
Wei, J. H.; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
Neutrino quantum kinetic equations: The collision term
Blaschke, Daniel N.; Cirigliano, Vincenzo
2016-08-01
We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.
Neutrino Quantum Kinetic Equations: The Collision Term
Blaschke, Daniel N
2016-01-01
We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.
Quantum Theory of Continuum Optomechanics
Rakich, Peter
2016-01-01
We present the basic ingredients of continuum optomechanics, i.e. the suitable extension of cavity-optomechanical concepts to the interaction of photons and phonons in an extended waveguide. We introduce a real-space picture and argue which coupling terms may arise in leading order in the spatial derivatives. This picture allows us to discuss quantum noise, dissipation, and the correct boundary conditions at the waveguide entrance. The connections both to optomechanical arrays as well as to the theory of Brillouin scattering in waveguides are highlighted. We identify the 'strong coupling regime' of continuum optomechanics that may be accessible in future experiments.
Introduction to the quantum theory
Park, David
2005-01-01
More than a chance to gain new insights into physics, this book offers students the opportunity to look at what they already know about the subject in an improved way. Geared toward upper-level undergraduates and graduate students, this self-contained first course in quantum mechanics consists of two parts: the first covers basic theory, and the second part presents selected applications. Numerous problems of varying difficulty examine not only the steps of the proofs but also related ideas.Starting with an introduction that ventures beyond classical physics, the first part examines the physic
A first course in topos quantum theory
Flori, Cecilia
2013-01-01
In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility o...
Quantum cellular automata and free quantum field theory
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-02-01
In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.
Neutrix Calculus and Finite Quantum Field Theory
Ng, Y J
2004-01-01
In general, quantum field theories require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series in their interaction couplings. We propose to apply neutrix calculus, developed by van der Corput and Hadamard in connection with asymptotic series, to tackle divergent integrals, yielding finite renormalizations for the parameters in quantum field theories. We observe that quantum gravity theories are rendered more manageable, and that both renormalizable field theories and effective field theories can be accommodated in the framework of neutrix calculus.
The role of quantum discord in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Streltsov, Alexander [ICFO - The Institute of Photonic Sciences, Castelldefels (Spain)
2014-07-01
Quantum correlations beyond entanglement - in particular represented by quantum discord - have become a major research field in the last few years. In this talk we report on the role of quantum discord in several fundamental tasks in quantum information theory. Starting with the role of quantum discord in the quantum measurement process, we also discuss its role in the tasks of information sharing and entanglement distribution. Finally, we also show the limits of these results and present possible ways to go beyond these limits.
Localisation in Quantum Field Theory
Balachandran, A P
2016-01-01
In nonrelativistic quantum mechanics , Born's principle of localisation is as follows: For a single particle, if a wave function $\\psi_K$ vanishes outside a spatial region $K$, it is said to be localised in $K$. In particular if a spatial region $K'$ is disjoint from $K$, a wave function $\\psi_{K'}$ localised in $K'$ is orthogonal to $\\psi_K$. Such a principle of localisation does not exist compatibly with relativity and causality in quantum field theory (Newton and Wigner) or interacting point particles (Currie,Jordan and Sudarshan).It is replaced by symplectic localisation of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localisation gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with `continuous' spin. This review outlines the basic principles underlying symplectic localisation and shows or mentions its deep implications. In particular, it has the potential to affect...
Thermodynamics and the structure of quantum theory
Krumm, Marius; Barrett, Jonathan; Mueller, Markus P
2016-01-01
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Results in quantum gravity and general ideas of what a fundamental theory should look like suggest that thermodynamics plays a major role in the foundations of physics. In this paper, we address the question of which parts of quantum theory are already determined by compatibility with thermodynamics, and which aspects may still admit modification. We employ two postulates that any probabilistic theory with reasonable thermodynamic behavior should arguably satisfy. In the framework of generalized probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechan...
Unusual signs in quantum field theory
O'Connell, Donal
Quantum field theory is by now a mature field. Nevertheless, certain physical phenomena remain difficult to understand. This occurs in some cases because well-established quantum field theories are strongly coupled and therefore difficult to solve; in other cases, our current understanding of quantum field theory seems to be inadequate. In this thesis, we will discuss various modifications of quantum field theory which can help to alleviate certain of these problems, either in their own right or as a component of a greater computational scheme. The modified theories we will consider all include unusual signs in some aspect of the theory. We will also discuss limitations on what we might expect to see in experiments, imposed by sign constraints in the customary formulation of quantum field theory.
Quartic quantum theory: an extension of the standard quantum mechanics
Zyczkowski, Karol
2008-01-01
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher dimensional convex body of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system ...
Directory of Open Access Journals (Sweden)
Gift S.
2009-01-01
Full Text Available In this paper, a new Quantum Theory of Magnetic Interaction is proposed. This is done under a relaxation of the requirement of covariance for Lorentz Boost Transformations. A modified form of local gauge invariance in which fermion field phase is allowed to vary with each space point but not each time point, leads to the introduction of a new compensatory field different from the electromagnetic field associated with the photon. This new field is coupled to the magnetic flux of the fermions and has quanta called magnatons, which are massless spin 1 particles. The associated equation of motion yields the Poisson equation for magnetostatic potentials. The magnatons mediate the magnetic interaction between magnetic dipoles including magnets and provide plausi- ble explanations for the Pauli exclusion principle, Chemical Reactivity and Chemical Bonds. This new interaction has been confirmed by numerical experiments. It estab- lishes magnetism as a force entirely separate from the electromagnetic interaction and converts all of classical magnetism into a quantum theory.
Quantum chemistry simulation on quantum computers: theories and experiments.
Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng
2012-07-14
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.
Introductory Lectures on Quantum Field Theory
Alvarez-Gaumé, Luís
2014-01-01
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String Theory.
Einstein's strugges with quantum theory a reappraisal
Home, Dipankar
2007-01-01
Einstein’s Struggles with Quantum Theory: A Reappraisal by Dipankar Home and Andrew Whitaker provides a detailed account of Albert Einstein’s thinking in regard to quantum physics. Until recently, most of Einstein’s views on quantum physics were dismissed and even ridiculed; some critics even suggested that Einstein was not able to grasp the complexities of the formalism of quantum theory and subtleties of the standard interpretation of this theory known as the Copenhagen interpretation put forward by Niels Bohr and his colleagues. But was that true? Modern scholarship argues otherwise, insist Drs. Home and Whitaker, who painstakingly explain the questions Einstein raised as well as offer a detailed discussion of Einstein’s position and major contributions to quantum theory, connecting them with contemporary studies on fundamental aspects of this theory. This unique book presents a mathematical as well as a non-mathematical route through the theories, controversies, and investigations, making the disc...
Quantum Transition State Theory for proton transfer reactions in enzymes
Bothma, Jacques P; McKenzie, Ross H
2009-01-01
We consider the role of quantum effects in the transfer of hyrogen-like species in enzyme-catalysed reactions. This study is stimulated by claims that the observed magnitude and temperature dependence of kinetic isotope effects imply that quantum tunneling below the energy barrier associated with the transition state significantly enhances the reaction rate in many enzymes. We use a path integral approach which provides a general framework to understand tunneling in a quantum system which interacts with an environment at non-zero temperature. Here the quantum system is the active site of the enzyme and the environment is the surrounding protein and water. Tunneling well below the barrier only occurs for temperatures less than a temperature $T_0$ which is determined by the curvature of potential energy surface near the top of the barrier. We argue that for most enzymes this temperature is less than room temperature. For physically reasonable parameters quantum transition state theory gives a quantitative descr...
Some Issues in Quantum Information Theory
Institute of Scientific and Technical Information of China (English)
Run-Yao Duan; Zheng-Feng Ji; Yuan Feng; Ming-Sheng Ying
2006-01-01
Quantum information theory is a new interdisciplinary research field related to quantum mechanics, computer science, information theory, and applied mathematics. It provides completely new paradigms to do information processing tasks by employing the principles of quantum mechanics. In this review, we first survey some of the significant advances in quantum information theory in the last twenty years. We then focus mainly on two special subjects: discrimination of quantum objects and transformations between entanglements. More specifically, we first discuss discrimination of quantum states and quantum apparatus in both global and local settings. Secondly, we present systematical characterizations and equivalence relations of several interesting entanglement transformation phenomena, namely entanglement catalysis,multiple-copy entanglement transformation, and partial entanglement recovery.
Quantum entanglement: theory and applications
Energy Technology Data Exchange (ETDEWEB)
Schuch, N.
2007-10-10
This thesis deals with various questions concerning the quantification, the creation, and the application of quantum entanglement. Entanglement arises due to the restriction to local operations and classical communication. We investigate how the notion of entanglement changes if additional restrictions in form of a superselection rule are imposed and show that they give rise to a new resource. We characterize this resource and demonstrate that it can be used to overcome the restrictions, very much as entanglement can overcome the restriction to local operations by teleportation. We next turn towards the optimal generation of resources. We show how squeezing can be generated as efficiently as possible from noisy squeezing operations supplemented by noiseless passive operations, and discuss the implications of this result to the optimal generation of entanglement. The difficulty in describing the behaviour of correlated quantum many-body systems is ultimately due to the complicated entanglement structure of multipartite states. Using quantum information techniques, we investigate the ground state properties of lattices of harmonic oscillators. We derive an exponential decay of correlations for gapped systems, compute the dependence of correlation length and gap, and investigate the notion of criticality by relating a vanishing energy gap to an algebraic decay of correlations. Recently, ideas from entanglement theory have been applied to the description of many-body systems. Matrix Product States (MPS), which have a particularly simple interpretation from the point of quantum information, perform extremely well in approximating the ground states of local Hamiltonians. It is generally believed that this is due to the fact that both ground states and MPS obey an entropic area law. We clarify the relation between entropy scaling laws and approximability by MPS, and in particular find that an area law does not necessarily imply approximability. Using the quantum
Quantum mechanics II a second course in quantum theory
Landau, Rubin H
2004-01-01
Here is a readable and intuitive quantum mechanics text that covers scattering theory, relativistic quantum mechanics, and field theory. This expanded and updated Second Edition - with five new chapters - emphasizes the concrete and calculable over the abstract and pure, and helps turn students into researchers without diminishing their sense of wonder at physics and nature.As a one-year graduate-level course, Quantum Mechanics II: A Second Course in Quantum Theory leads from quantum basics to basic field theory, and lays the foundation for research-oriented specialty courses. Used selectively, the material can be tailored to create a one-semester course in advanced topics. In either case, it addresses a broad audience of students in the physical sciences, as well as independent readers - whether advanced undergraduates or practicing scientists
Free Quantum Field Theory from Quantum Cellular Automata
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Kinetic theory of free electron lasers
Energy Technology Data Exchange (ETDEWEB)
Hafizi, B. [Naval Research Lab., Washington, DC (United States); Roberson, C.W. [Office of Naval Research, Arlington, VA (United States)
1995-12-31
We have developed a relativistic kinetic theory of free electron lasers (FELs). The growth rate, efficiency, filling factor and radius of curvature of the radiation wave fronts are determined. We have used the theory to examine the effects of beam compression on growth rate. The theory has been extended to include self field effects on FEL operation. These effects are particularly important in compact, low voltage FELs. The surprising result is that the self field contribution to the beam quality is opposite to the emittance contribution. Hence self fields can improve beam quality, particularly in compact, low voltage FELs.
Remark on non-Abelian classical kinetic theory
Laine, Mikko; Laine, Mikko; Manuel, Cristina
2002-01-01
It is known that non-Abelian classical kinetic theory reproduces the Hard Thermal/Dense Loop (HTL/HDL) effective action of QCD, obtained after integrating out the hardest momentum scales from the system, as well as the first higher dimensional operator beyond the HTL/HDL level. We discuss here its applicability at still higher orders, by comparing the exact classical effective action obtained in the static limit, with the 1-loop quantum effective potential. We remark that while correct types of operators arise, the classical colour algebra reproduces correctly the prefactor of the 4-point function $tr A_0^4$ only for matter in asymptotically high dimensional colour representations.
Quantum Mechanics as a Principle Theory
Bub, J
1999-01-01
I show how quantum mechanics, like the theory of relativity, can be understood as a 'principle theory' in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999).
De Sitter Symmetry and Quantum Theory
Lev, Felix M
2011-01-01
De Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de Sitter algebra. This approach gives a new perspective on fundamental notions of quantum theory. We discuss applications of the approach to the cosmological constant problem, gravity and particle theory.
The conceptual basis of Quantum Field Theory
Hooft, G. 't
2007-01-01
Relativistic Quantum Field Theory is a mathematical scheme to describe the sub-atomic particles and forces. The basic starting point is that the axioms of Special Relativity on the one hand and those of Quantum Mechanics on the other, should be combined into one theory. The fundamental ingredients f
A nilpotent symmetry of quantum gauge theories
Lahiri, Amitabha
2001-09-01
For the Becchi-Rouet-Stora-Tyutin invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher-order ghost terms are also possible.
Quantum tunneling and field electron emission theories
Liang, Shi-Dong
2013-01-01
Quantum tunneling is an essential issue in quantum physics. Especially, the rapid development of nanotechnology in recent years promises a lot of applications in condensed matter physics, surface science and nanodevices, which are growing interests in fundamental issues, computational techniques and potential applications of quantum tunneling. The book involves two relevant topics. One is quantum tunneling theory in condensed matter physics, including the basic concepts and methods, especially for recent developments in mesoscopic physics and computational formulation. The second part is the f
Haag's theorem in renormalised quantum field theories
Klaczynski, Lutz
2016-01-01
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.
Reconstruction and Reinvention in Quantum Theory
Dickson, Michael
2015-10-01
I consider the fact that there are a number of interesting ways to `reconstruct' quantum theory, and suggest that, very broadly speaking, a form of `instrumentalism' makes good sense of the situation. This view runs against some common wisdom, which dismisses instrumentalism as `cheap'. In contrast, I consider how an instrumentalist might think about the reconstruction theorems, and, having made a distinction between `reconstructing' quantum theory and `reinventing' quantum theory, I suggest that there is an adequate (not `cheap') instrumentalist approach to the theory (and to these theorems) that invokes both.
Quantum field theory for the gifted amateur
Lancaster, Tom
2014-01-01
Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in ...
Kinetic theory molecular dynamics and hot dense matter: theoretical foundations.
Graziani, F R; Bauer, J D; Murillo, M S
2014-09-01
Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as "kinetic theory molecular dynamics," or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the N-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD
Quantum theory informational foundations and foils
Spekkens, Robert
2016-01-01
This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information. Topics include: operational alternatives to quantum theory, information-theoretic reconstructions of the quantum formalism, mathematical frameworks for operational theories, and device-independent features of the set of quantum correlations. Powered by the injection of fresh ideas from the field of Quantum Information and Computation, the foundations of Quantum Mechanics are in the midst of a renaissance. The last two decades have seen an explosion of new results and research directions, attracting broad interest in the scientific community. The variety and number of different approaches, however, makes it challenging for a newcomer to obtain a big picture of the field and of its high-level goals. Here, fourteen original contributions from leading experts in the field cover some of the most promising research directions that have emerged in the new wave of quant...
A simple theory of protein folding kinetics
Pande, Vijay S
2010-01-01
We present a simple model of protein folding dynamics that captures key qualitative elements recently seen in all-atom simulations. The goals of this theory are to serve as a simple formalism for gaining deeper insight into the physical properties seen in detailed simulations as well as to serve as a model to easily compare why these simulations suggest a different kinetic mechanism than previous simple models. Specifically, we find that non-native contacts play a key role in determining the mechanism, which can shift dramatically as the energetic strength of non-native interactions is changed. For protein-like non-native interactions, our model finds that the native state is a kinetic hub, connecting the strength of relevant interactions directly to the nature of folding kinetics.
DEFF Research Database (Denmark)
Yan, Wei
2015-01-01
We investigate the hydrodynamic theory of metals, offering systematic studies of the linear-response dynamics for an inhomogeneous electron gas. We include the quantum functional terms of the Thomas-Fermi kinetic energy, the von Weizsa¨cker kinetic energy, and the exchange-correlation Coulomb...... response of complex metallic nanostructures, including quantum effects, by adjusting theory parameters appropriately....... energies under the local density approximation. The advantages, limitations, and possible improvements of the hydrodynamic theory are transparently demonstrated. The roles of various parameters in the theory are identified. We anticipate that the hydrodynamic theory can be applied to investigate the linear...
Dynamical symmetry breaking in quantum field theories
Miransky, Vladimir A
1993-01-01
The phenomenon of dynamical symmetry breaking (DSB) in quantum field theory is discussed in a detailed and comprehensive way. The deep connection between this phenomenon in condensed matter physics and particle physics is emphasized. The realizations of DSB in such realistic theories as quantum chromodynamics and electroweak theory are considered. Issues intimately connected with DSB such as critical phenomenona and effective lagrangian approach are also discussed.
Renormalizable Quantum Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning
2002-01-01
The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.
Quantum gravity from theory to experimental search
Kiefer, Claus; Lämmerzahl, Claus
2003-01-01
The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spacetime cannot be fundamentally correct. Hence there should exist a broader theory comprising both in appropriate limits, i.e., quantum gravity. This book gives readers a comprehensive introduction accessible to interested non-experts to the main issues surrounding the search for quantum gravity. These issues relate to fundamental questions concerning the various formalisms of quantization; specific questions concerning concrete processes, like gravitational collapse or black-hole evaporation; and the all important question concerning the possibility of experimental tests of quantum-gravity effects.
Theory and simulation of strong correlations in quantum Coulomb systems
Bonitz, M; Filinov, A V; Golubnychiy, V O; Kremp, D; Gericke, D O; Murillo, M S; Filinov, V S; Fortov, V; Hoyer, W; Koch, S W
2003-01-01
Strong correlations in quantum Coulomb systems (QCS) are attracting increasing interest in many fields ranging from dense plasmas and semiconductors to metal clusters and ultracold trapped ions. Examples are bound states in dense plasmas (atoms, molecules, clusters) and semiconductors (excitons, trions, biexcitons) or Coulomb crystals. We present first-principle simulation results of these systems including path integral Monte Carlo simulations of the equilibrium behaviour of dense hydrogen and electron-hole plasmas and molecular dynamics and quantum kinetic theory simulations of the nonequilibrium properties of QCS. Finally, we critically assess potential and limitations of the various methods in their application to Coulomb systems.
The conceptual framework of quantum field theory
Duncan, Anthony
2012-01-01
The book attempts to provide an introduction to quantum field theory emphasizing conceptual issues frequently neglected in more "utilitarian" treatments of the subject. The book is divided into four parts, entitled respectively "Origins", "Dynamics", "Symmetries", and "Scales". The emphasis is conceptual - the aim is to build the theory up systematically from some clearly stated foundational concepts - and therefore to a large extent anti-historical, but two historical Chapters ("Origins") are included to situate quantum field theory in the larger context of modern physical theories. The three remaining sections of the book follow a step by step reconstruction of this framework beginning with just a few basic assumptions: relativistic invariance, the basic principles of quantum mechanics, and the prohibition of physical action at a distance embodied in the clustering principle. The "Dynamics" section of the book lays out the basic structure of quantum field theory arising from the sequential insertion of quan...
Quantum Field Theory in a Semiotic Perspective
Günter Dosch, Hans; Sieroka, Norman
2005-01-01
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincaré, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly ac...
Supergeometry in locally covariant quantum field theory
Hack, Thomas-Paul; Schenkel, Alexander
2015-01-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc --> S*Alg to the category of super-*-algebras which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc --> eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the en...
Quartic quantum theory: an extension of the standard quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Zyczkowski, Karol [Institute of Physics, Jagiellonian University, Krakow (Poland); Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland)], E-mail: karol@tatry.if.uj.edu.pl
2008-09-05
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability distributions can be embedded inside a higher-dimensional convex body M{sub N}{sup Q} of mixed quantum states, one can further increase the dimensionality constructing the set of extended quantum states. The embedding proposed corresponds to an assumption that the physical system described in the N-dimensional Hilbert space is coupled with an auxiliary subsystem of the same dimensionality. The extended theory works for simple quantum systems and is shown to be a non-trivial generalization of the standard quantum theory for which K = N{sup 2}. Imposing certain restrictions on initial conditions and dynamics allowed in the quartic theory one obtains quadratic theory as a special case. By imposing even stronger constraints one arrives at the classical theory, for which K = N.
Emergent "Quantum" Theory in Complex Adaptive Systems.
Minic, Djordje; Pajevic, Sinisa
2016-04-30
Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.
Multichannel Quantum Defect Theory a Quantum Poincaré Map
Leyvraz, F; Lombardi, M; Seligman, T H
1999-01-01
The multichannel quantum defect theory (MQDT) can be reinterpreted as a quantum Poincare map in representation of angular momentum. We chose a simplified model for Rydberg molecules where the limit classical map is known and MQDT delivers the exact quantization of this map, which is a finite unitary matrix by construction. The result has two important implications: On one hand we have a paradigm of a true quantum Poincare map without semi-classical input and on the other hand we get an entirely new insight into the significance of MQDT. We obtain a new signature of quantum chaos and a more reliable method to calculate eigenfunctions in MQDT.
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Representation Theory of Algebraic Groups and Quantum Groups
Gyoja, A; Shinoda, K-I; Shoji, T; Tanisaki, Toshiyuki
2010-01-01
Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics
Quantum theory of Thomson scattering
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].
IS PT -SYMMETRIC QUANTUM THEORY FALSE AS A FUNDAMENTAL THEORY?
Directory of Open Access Journals (Sweden)
Miloslav Znojil
2016-06-01
Full Text Available Yi-Chan Lee et al. claim (cf. Phys. Rev. Lett. 112, 130404 (2014 that the “recent extension of quantum theory to non-Hermitian Hamiltonians” (which is widely known under the nickname of “PT-symmetric quantum theory” is “likely false as a fundamental theory”. By their opinion their results “essentially kill any hope of PT-symmetric quantum theory as a fundamental theory of nature”. In our present text we explain that their toy-model-based considerations are misleading and that they do not imply any similar conclusions.
Is quantum theory compatible with special relativity?
Indian Academy of Sciences (India)
M Bahrami; A Shafiee; M Saravani; M Golshani
2013-03-01
How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity.
Pilot-wave theory and quantum fields
Struyve, Ward
2010-10-01
Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schrödinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.
Holism, Physical Theories and Quantum Mechanics
Seevinck, M P
2004-01-01
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. I propose an operational criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if some determination (measurement) of the global properties in the theory which can be determined by global measurements, can not be implemented by local operations and classical communication. This approach is contrasted with the well known approaches to holism in terms of supervenience. I will argue that the latter have a limited scope and need to be extended using the criterion for holism proposed here in order to satisfactory address the issue for physical theories. I formalize this criterion for classical particle physics and Bohmian mechanics as represented on a Cartesian phase and configuration space, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum ope...
"Scars" connect classical and quantum theory
Monteiro, T
1990-01-01
Chaotic systems are unstable and extremely sensitive to initial condititions. So far, scientists have been unable to demonstrate that the same kind of behaviour exists in quantum or microscopic systems. New connections have been discovered though between classical and quantum theory. One is the phenomena of 'scars' which cut through the wave function of a particle (1 page).
Random subspaces in quantum information theory
Hayden, Patrick
2005-03-01
The selection of random unitary transformations plays a role in quantum information theory analogous to the role of random hash functions in classical information theory. Recent applications have included protocols achieving the quantum channel capacity and methods for extending superdense coding from bits to qubits. In addition, the corresponding random subspaces have proved useful for studying the structure of bipartite and multipartite entanglement. In quantum information theory, we're fond of saying that Hilbert space is a big place, the implication being that there's room for the unexpected to occur. The goal of this talk is to further bolster this homespun wisdowm. I'm going to present a number of results in quantum information theory that stem from the initially counterintuitive geometry of high-dimensional vector spaces, where subspaces with highly extremal properties are the norm rather than the exception. Peter Shor has shown, for example, that randomly selected subspaces can be used to send quantum information through a noisy quantum channel at the highest possible rate, that is, the quantum channel capacity. More recently, Debbie Leung, Andreas Winter and I demonstrated that a randomly chosen subspace of a bipartite quantum system will likely contain nothing but nearly maximally entangled states, even if the subspace is nearly as large as the original system in qubit terms. This observation has implications for communication, especially superdense coding.
Teaching Quantum Theory in the Introductory Course.
Hobson, Art
1996-01-01
Describes an approach to teaching quantum theory without math with emphasis on some innovative approaches and topics such as nonlocality and Bell's theorem. Written in the form of suggestions to prospective instructors. (JRH)
Parameterized quantum field theory without Haag's theorem
Seidewitz, Ed
2015-01-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that quantum field theory can be formulated, using an invariant, fifth path parameter in addition to the usual four position parameters, in such a way that Haag's theorem no longer applies, but such that the Dyson perturbation expansion for the sc...
Molecular quantum dynamics from theory to applications
Gatti, Fabien
2014-01-01
Emphasizing fundamental educational concepts, this book offers an accessible introduction that covers eigenstates, wave packets, quantum mechanical resonances and more. Examples show that high-level experiments and theory must work closely together.
Density functional theory in quantum chemistry
Tsuneda, Takao
2014-01-01
This book examines density functional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.
Field redefinition invariance in quantum field theory
Apfeldorf, K M; Apfeldorf, Karyn M; Ordonez, Carlos
1994-01-01
We investigate the consequences of field redefinition invariance in quantum field theory by carefully performing nonlinear transformations in the path integral. We first present a ``paradox'' whereby a 1+1 freemassless scalar theory on a Minkowskian cylinder is reduced to an effectively quantum mechanical theory. We perform field redefinitions both before and after reduction to suggest that one should not ignore operator ordering issues in quantum field theory. We next employ a discretized version of the path integral for a free massless scalar quantum field in d dimensions to show that beyond the usual jacobian term, an infinite series of divergent ``extra'' terms arises in the action whenever a nonlinear field redefinition is made. The explicit forms for the first couple of these terms are derived. We evaluate Feynman diagrams to illustrate the importance of retaining the extra terms, and conjecture that these extra terms are the exact counterterms necessary to render physical quantities invariant under fie...
Quantum theory - essential from cosmos to consciousness
Energy Technology Data Exchange (ETDEWEB)
Goernitz, T, E-mail: goernitz@em.uni-frankfurt.d [Institut fuer Didaktik der Physik, FB Physik J. W. Goethe-Universitaet Frankfurt/Main Mail: Karl-Mangold-Str. 13, D-81245 Muenchen (Germany)
2010-06-01
Quantum theory is the most successful physical theory. About one third of the gross national product in the developed countries results from its applications. But very often quantum theory is still declared as 'crazy' or 'not understandable'. However, quantum theory has a clear mathematical structure that expresses well-known experiences from every day life: A whole is often more than the sum of its parts, and not only the facts also the possibilities can act. If such structures become important then the consequences differ from the models of classical physics which rests on the fundamental differences between matter and motion, material and force, localization and extension, fullness and emptiness. From quantum theory one can learn that all these differences are useful in many cases but are not fundamental. There are equivalences between them, and these can be extended even to the equivalence between matter, energy and abstract quantum information. It is cosmological funded and is denominated as 'Protyposis' to avoid the connotation of information and meaning. Protyposis enables a fundamentally new understanding of matter which can be seen as 'formed', 'condensed' or 'designed' abstract quantum information. One result of the Protyposis is a derivation of Einstein's equations from the abstract quantum information. Another consequence is the ontological reality of the mind and its connection to a brain which can be explained without any dualistic model.
Quantum field theory II introductions to quantum gravity, supersymmetry and string theory
Manoukian, Edouard B
2016-01-01
This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics. The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The quantum aspect of gravitation, as described by the graviton, is introduced and perturbative quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute the one-loop contribution to the theory and renormalizability aspects of the perturbative theory are also discussed. This follows by introducing only the very basics of a non-perturbative, background-independent, formulation of quantum gravity, referred to as “loop quantum gravity”, which gives rise to a quantization of space. In the second part the author in...
Millicharged dark matter in quantum gravity and string theory.
Shiu, Gary; Soler, Pablo; Ye, Fang
2013-06-14
We examine the millicharged dark matter scenario from a string theory perspective. In this scenario, kinetic and mass mixings of the photon with extra U(1) bosons are claimed to give rise to small electric charges, carried by dark matter particles, whose values are determined by continuous parameters of the theory. This seems to contradict folk theorems of quantum gravity that forbid the existence of irrational charges in theories with a single massless gauge field. By considering the underlying structure of the U(1) mass matrix that appears in type II string compactifications, we show that millicharges arise exclusively through kinetic mixing, and require the existence of at least two exactly massless gauge bosons.
The decoupling approach to quantum information theory
Dupuis, Frédéric
2010-04-01
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently small.
Cosmological perturbation theory and quantum gravity
Brunetti, Romeo; Hack, Thomas-Paul; Pinamonti, Nicola; Rejzner, Katarzyna
2016-01-01
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Random matrix techniques in quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Collins, Benoît, E-mail: collins@math.kyoto-u.ac.jp [Department of Mathematics, Kyoto University, Kyoto 606-8502 (Japan); Département de Mathématique et Statistique, Université d’Ottawa, 585 King Edward, Ottawa, Ontario K1N6N5 (Canada); CNRS, Lyon (France); Nechita, Ion, E-mail: nechita@irsamc.ups-tlse.fr [Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching (Germany); Laboratoire de Physique Théorique, CNRS, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France)
2016-01-15
The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.
Quantum coding theory with realistic physical constraints
Yoshida, Beni
2010-01-01
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum error-correcting codes with geometrically local generators, (b) the feasibility of a self-correcting quantum memory. To investigate these problems, we study stabilizer codes supported by local interaction terms with translation and scale symmetries on a $D$-dimensional lattice. Our analysis uses the notion of topology emerging in geometric shapes of logical operators, which sheds a surprising new light on theory of quantum codes with physical constraints.
Quantum information theory with Gaussian systems
Energy Technology Data Exchange (ETDEWEB)
Krueger, O.
2006-04-06
This thesis applies ideas and concepts from quantum information theory to systems of continuous-variables such as the quantum harmonic oscillator. The focus is on three topics: the cloning of coherent states, Gaussian quantum cellular automata and Gaussian private channels. Cloning was investigated both for finite-dimensional and for continuous-variable systems. We construct a private quantum channel for the sequential encryption of coherent states with a classical key, where the key elements have finite precision. For the case of independent one-mode input states, we explicitly estimate this precision, i.e. the number of key bits needed per input state, in terms of these parameters. (orig.)
Quantum theory of electroabsorption in semiconductor nanocrystals.
Tepliakov, Nikita V; Leonov, Mikhail Yu; Baranov, Alexander V; Fedorov, Anatoly V; Rukhlenko, Ivan D
2016-01-25
We develop a simple quantum-mechanical theory of interband absorption by semiconductor nanocrystals exposed to a dc electric field. The theory is based on the model of noninteracting electrons and holes in an infinitely deep quantum well and describes all the major features of electroabsorption, including the Stark effect, the Franz-Keldysh effect, and the field-induced spectral broadening. It is applicable to nanocrystals of different shapes and dimensions (quantum dots, nanorods, and nanoplatelets), and will prove useful in modeling and design of electrooptical devices based on ensembles of semiconductor nanocrystals.
Toward a physical theory of quantum cognition.
Takahashi, Taiki
2014-01-01
Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani's three-stage theory of the development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed.
Quantum Stability of Chameleon Field Theories
Upadhye, Amol; Khoury, Justin
2012-01-01
Chameleon scalar fields are dark energy candidates which suppress fifth forces in high density regions of the universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound $m 0.0042$\\,eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well-controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential.
Generalizing Prototype Theory: A Formal Quantum Framework
Directory of Open Access Journals (Sweden)
Diederik eAerts
2016-03-01
Full Text Available Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
Generalizing Prototype Theory: A Formal Quantum Framework.
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
Relativistic quantum transport theory for electrodynamics
Zhuang, P; Zhuang, P; Heinz, U
1995-01-01
We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant formulation. We illustrate this statement in scalar and spinor QED. For scalar QED we derive Lorentz covariant transport and constraint equations directly from the Klein-Gordon equation rather than through the previously used Feshbach-Villars representation. We then consider pair production in a spatially homogeneous but time-dependent electric field and show that the pair density is derived much more easily via the energy averaging method than in the equal-time representation. Proceeding to spinor QED, we derive the covariant version of the equal-time equation derived by Bialynicki-Birula et al. We show that it must be supplemented by another self-adjoint equation to obtain a complete description of the covariant spinor Wigner operator. After spinor decomposition and energy averag...
Quantum gravity, effective fields and string theory
Bjerrum-Bohr, N E J
2004-01-01
We look at the various aspects of treating general relativity as a quantum theory. It is briefly studied how to consistently quantize general relativity as an effective field theory. A key achievement here is the long-range low-energy leading quantum corrections to both the Schwarzschild and Kerr metrics. The leading quantum corrections to the pure gravitational potential between two sources are also calculated, both in the mixed theory of scalar QED and quantum gravity and in the pure gravitational theory. The (Kawai-Lewellen-Tye) string theory gauge/gravity relations is next dealt with. We investigate if the KLT-operator mapping extends to the case of higher derivative effective operators. The KLT-relations are generalized, taking the effective field theory viewpoint, and remarkable tree-level amplitude relations between the field theory operators are derived. Quantum gravity is finally looked at from the the perspective of taking the limit of infinitely many spatial dimensions. It is verified that only a c...
Superconducting quantum circuits theory and application
Deng, Xiuhao
Superconducting quantum circuit models are widely used to understand superconducting devices. This thesis consists of four studies wherein the superconducting quantum circuit is used to illustrate challenges related to quantum information encoding and processing, quantum simulation, quantum signal detection and amplification. The existence of scalar Aharanov-Bohm phase has been a controversial topic for decades. Scalar AB phase, defined as time integral of electric potential, gives rises to an extra phase factor in wavefunction. We proposed a superconducting quantum Faraday cage to detect temporal interference effect as a consequence of scalar AB phase. Using the superconducting quantum circuit model, the physical system is solved and resulting AB effect is predicted. Further discussion in this chapter shows that treating the experimental apparatus quantum mechanically, spatial scalar AB effect, proposed by Aharanov-Bohm, can't be observed. Either a decoherent interference apparatus is used to observe spatial scalar AB effect, or a quantum Faraday cage is used to observe temporal scalar AB effect. The second study involves protecting a quantum system from losing coherence, which is crucial to any practical quantum computation scheme. We present a theory to encode any qubit, especially superconducting qubits, into a universal quantum degeneracy point (UQDP) where low frequency noise is suppressed significantly. Numerical simulations for superconducting charge qubit using experimental parameters show that its coherence time is prolong by two orders of magnitude using our universal degeneracy point approach. With this improvement, a set of universal quantum gates can be performed at high fidelity without losing too much quantum coherence. Starting in 2004, the use of circuit QED has enabled the manipulation of superconducting qubits with photons. We applied quantum optical approach to model coupled resonators and obtained a four-wave mixing toolbox to operate photons
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Super-relativity in the quantum theory
Leifer, P
2007-01-01
The relativity to the measuring device in quantum theory, i.e. the covariance of local dynamical variables relative transformations to moving quantum reference frame in Hilbert space, may be achieved only by the rejection of super-selection rule. In order to avoid the subjective nuance, I emphasis that the notion of "measurement" here, is nothing but the covariant differentiation procedure in the functional quantum phase space $CP(N-1)$, having pure objective sense of evolution. Transition to the local moving quantum reference frame leads to some particle-like solutions of quasi-linear field PDE in the dynamical space-time. Thereby, the functionally covariant quantum dynamics gives the perspective to unify the Einstein relativity and quantum principles which are obviously contradictable under the standard approaches.
Distinguishability and accessible information in quantum theory
Fuchs, C
1996-01-01
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states. These measures should have important appli- cations in quantum cryptography and quantum computation theory. The results reported include the following. An exact expression for the quantum fidelity between two mixed states is derived. The optimal measurement that gives rise to it is studied in detail. Several upper and lower bounds on the quantum mutual information are derived via similar techniques and compared to each other. Of note is a simple derivation of the important upper bound first proved by Holevo and an explicit expression for another (tighter) upper bound that appears implicitly in the same derivation. Several upper and lower bounds to the quan- tum Kullback relative information are derived. The measures developed are also applied to ferreting out the extent to which quantum systems must be disturbed by information...
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
2015-12-01
The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle "imitate any quantum system, including the physical world." With that in mind, we present an algorithm for a continuous-variable quantum computing architecture which gives an exponential speedup over the best-known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuous-variable states that is feasible with today's technology.
Classical Kinetic Theory of Landau Damping for Self-interacting Scalar Fields in the Broken Phase
1998-01-01
The classical kinetic theory of one-component self-interacting scalar fields is formulated in the broken symmetry phase and applied to the phenomenon of Landau damping. The domain of validity of the classical approach is found by comparing with the result of a 1-loop quantum calculation.
Quantum theory of laser-stimulated desorption
Slutsky, M. S.; George, T. F.
1978-01-01
A quantum theory of laser-stimulated desorption (LSDE) is presented and critically analyzed. It is shown how LSDE depends on laser-pulse characteristics and surface-lattice dynamics. Predictions of the theory for a Debye model of the lattice dynamics are compared to recent experimental results.
Book Review Bohmian Mechanics and Quantum Theory
Jäger, G
1999-01-01
A review of "Bohmian Mechanics and Quantum Theory: An Appraisal" (James Cushing, Arthur Fine and Sheldon Goldstein, Eds.), an extensive collection of articles on Bohmian mechanics. In addition to broad, critical overviews of Bohmian mechanics, the reviewed collection contains extensions and hybrid versions of the theory, as are several detailed applications to practical situtations.
Quantum Field Theory in de Sitter spacetime
So, Ashaq Hussain; Sibuea, Marlina Rosalinda; Akhoon, Shabir Ahmad; Khanday, Bilal Nisar; Majeed, Sajad Ul; Rather, Asloob Ahmad; Nahvi, Ishaq
2013-01-01
In this paper we will analyse quantum ?eld theory on de Sitter space- time. We will ?rst analyse a general scalar and vector ?eld theory on de Sitter spacetime. This is done by ?rst calculating these propagators on four-Sphere and then analytically continuing it to de Sitter spacetime.
Computer animations of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Cohen, E. (Centre d' Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique)
1992-07-01
A visualization mehtod for quantum field theories based on the transfer matrix formalism is presented. It generates computer animations simulating the time evolution of complex physical systems subject to local Hamiltonians. The method may be used as a means of gaining insight to theories such as QCD, and as an educational tool in explaining high-energy physics. (orig.).
Quantum field theory in a semiotic perspective
Energy Technology Data Exchange (ETDEWEB)
Dosch, H.G. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Mueller, V.F. [Technische Univ. Kaiserslautern (Germany). Fachbereich Physik; Sieroka, N. [Zurich Univ. (Switzerland)
2005-07-01
Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincare, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)
Theory and application of quantum molecular dynamics
Zeng Hui Zhang, John
1999-01-01
This book provides a detailed presentation of modern quantum theories for treating the reaction dynamics of small molecular systems. Its main focus is on the recent development of successful quantum dynamics theories and computational methods for studying the molecular reactive scattering process, with specific applications given in detail for a number of benchmark chemical reaction systems in the gas phase and the gas surface. In contrast to traditional books on collision in physics focusing on abstract theory for nonreactive scattering, this book deals with both the development and the appli
Group field cosmology: a cosmological field theory of quantum geometry
Calcagni, Gianluca; Oriti, Daniele
2012-01-01
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted to a field, the coordinates are minisuperspace variables, the kinetic operator is the Hamiltonian constraint operator, and the action features a nonlinear and possibly nonlocal interaction term. We discuss free-field classical solutions, the quantum propagator, and a mean-field approximation linearizing the equation of motion and augmenting the Hamiltonian constraint by an effective term mixing gravitational and matter variables. Depending on the choice of interaction, this can reproduce, for example, a cosmological constant, a scalar-field potential, or a curvature contribution.
Relativity, symmetry and the structure of quantum theory I Galilean quantum theory
Klink, William H
2015-01-01
Quantum theory is one of the most successful of all physical theories. Our everyday world is dominated by devices that function because of knowledge of the quantum world. Yet many, physicists and non-physicists alike, find the theory which explains the behavior of the quantum world baffling and strange. This book is the first in a series of three that argues that relativity and symmetry determine the structure of quantum theory. That is to say, the structure of quantum theory is what it is because of relativity and symmetry. There are different types of relativity, each leading to a particular type of quantum theory. This book deals specifically with what we call Newton relativity, the form of relativity built into Newtonian mechanics, and the quantum theory to which it gives rise, which we call Galilean (often misleadingly called non-relativistic) quantum theory. Key Features: • Meaning and significance of the term of relativity; discussion of the principle of relativity. • Relation of symmetry to relati...
Quantum field theory in a nutshell
Zee, A
2010-01-01
Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading
Ehrenfest's adiabatic hypothesis in Bohr's quantum theory
Pérez, Enric
2015-01-01
It is widely known that Paul Ehrenfest formulated and applied his adiabatic hypothesis in the early 1910s. Niels Bohr, in his first attempt to construct a quantum theory in 1916, used it for fundamental purposes in a paper which eventually did not reach the press. He decided not to publish it after having received the new results by Sommerfeld in Munich. Two years later, Bohr published "On the quantum theory of line-spectra." There, the adiabatic hypothesis played an important role, although it appeared with another name: the principle of mechanical transformability. In the subsequent variations of his theory, Bohr never suppressed this principle completely. We discuss the role of Ehrenfest's principle in the works of Bohr, paying special attention to its relation to the correspondence principle. We will also consider how Ehrenfest faced Bohr's uses of his more celebrated contribution to quantum theory, as well as his own participation in the spreading of Bohr's ideas.
Entanglement in non-Hermitian quantum theory
Indian Academy of Sciences (India)
Arun K Pati
2009-09-01
Entanglement is one of the key features of quantum world that has no classical counterpart. This arises due to the linear superposition principle and the tensor product structure of the Hilbert space when we deal with multiparticle systems. In this paper, we will introduce the notion of entanglement for quantum systems that are governed by non-Hermitian yet $\\mathcal{PT}$ -symmetric Hamiltonians. We will show that maximally entangled states in usual quantum theory behave like non-maximally entangled states in $\\mathcal{PT}$ -symmetric quantum theory. Furthermore, we will show how to create entanglement between two $\\mathcal{PT}$ qubits using non-Hermitian Hamiltonians and discuss the entangling capability of such interaction Hamiltonians that are non-Hermitian in nature.
Quantum Field Theory on Noncommutative Spaces
Szabó, R J
2003-01-01
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
Information and Entropy in Quantum Theory
Maroney, O J E
2004-01-01
We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then show how the notion of 'active information' in the Bohm interpretation provides a coherent explanation of the phenomena shown in these experiments. We then examine the relationship between information and entropy. The thought experiment connecting these two quantities is the Szilard Engine version of Maxwell's Demon, and it has been suggested that quantum measurement plays a key role in this. We provide the first complete ...
Numerical approach of the quantum circuit theory
Silva, J. J. B.; Duarte-Filho, G. C.; Almeida, F. A. G.
2017-03-01
In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.
Numerical approach of the quantum circuit theory
Energy Technology Data Exchange (ETDEWEB)
Silva, J.J.B., E-mail: jaedsonfisica@hotmail.com; Duarte-Filho, G.C.; Almeida, F.A.G.
2017-03-15
In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.
Quantum reality theory and philosophy
Allday, Jonathan
2009-01-01
PrefaceIntroductionAuthorPart I Our First Quantum Object: Light Some Opening Thoughts A Little Light Reading Lasers and Video Cameras Photons An Interference Experiment with Photons Interference as a Wave Effect Mach-Zehnder with Photons Delayed Choice Summary Endnotes Interlude 1: Another Interference Experiment Particles Electrons The Electron Gun The Stern-Gerlach Experiment Turning Things Round Things Get More Puzzling So, Where Did It Go? What Does It All Mean? Some Indications with Other Particles The Long and the Short of It Summary Endnotes Quantum States Where Are We Now? Describing C
Quantum Field Theory from First Principles
Esposito, Giampiero
2000-01-01
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential operators of Laplace type. There are however deep reasons to modify such a scheme and allow for pseudo-differential boundary-value problems. When the boundary operator is allowed to be pseudo-differential while remaining a projector, the conditions on its kernel...
Mossbauer neutrinos in quantum mechanics and quantum field theory
Kopp, Joachim
2009-01-01
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detecti...
Kinetic theory of diffusion-limited nucleation
Philippe, T.; Bonvalet, M.; Blavette, D.
2016-05-01
We examine binary nucleation in the size and composition space {R,c} using the formalism of the multivariable theory [N. V. Alekseechkin, J. Chem. Phys. 124, 124512 (2006)]. We show that the variable c drops out of consideration for very large curvature of the new phase Gibbs energy with composition. Consequently nuclei around the critical size have the critical composition, which is derived from the condition of criticality for the canonical variables and is found not to depend on surface tension. In this case, nucleation kinetics can be investigated in the size space only. Using macroscopic kinetics, we determine the general expression for the condensation rate when growth is limited by bulk diffusion, which accounts for both diffusion and capillarity and exhibits a different dependence with the critical size, as compared with the interface-limited regime. This new expression of the condensation rate for bulk diffusion-limited nucleation is the counterpart of the classical interface-limited result. We then extend our analysis to multicomponent solutions.
Casimir Effects in Renormalizable Quantum Field Theories
Graham, N; Weigel, H; Graham, Noah; Jaffe, Robert L.; Weigel, Herbert
2002-01-01
We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.
Casimir Effects in Renormalizable Quantum Field Theories
Graham, Noah; Jaffe, Robert L.; Weigel, Herbert
We present a framework for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.
Loop quantum gravity as an effective theory
Bojowald, Martin
2012-01-01
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable ambiguities at the dynamical level, allows for a meaningful phenomenology to be developed, by which it becomes falsifiable. The tradiational problems plaguing canonical quantum-gravity theories, such as the anomaly issue or the problem of time, can be overcome or are irrelevant at the effective level, resulting in consistent means of physical evaluations. This contribution presents aspects of canonical equations and related notions of (deformed) space-time structures and discusses implications in loop quantum gravity, such as signature change at high density from holonomy corrections, and falsifiability thanks to inverse-triad corrections.
Nonlinear theory of kinetic instabilities near threshold
Energy Technology Data Exchange (ETDEWEB)
Berk, H.L.; Pekker, M.S. [Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies; Breizman, B.N. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies]|[Budker Inst. of Nuclear Physics, Novosibirsk (Russian Federation)
1997-05-01
A new nonlinear equation has been derived and solved for the evolution of an unstable collective mode in a kinetic system close to the threshold of linear instability. The resonant particle response produces the dominant nonlinearity, which can be calculated iteratively in the near-threshold regime as long as the mode doe snot trap resonant particles. With sources and classical relaxation processes included, the theory describes both soft nonlinear regimes, where the mode saturation level is proportional to an increment above threshold, and explosive nonlinear regimes, where the mode grows to a level that is independent of the closeness to threshold. The explosive solutions exhibit mode frequency shifting. For modes that exist in the absence of energetic particles, the frequency shift is both upward and downward. For modes that require energetic particles for their existence, there is a preferred direction of the frequency shift. The frequency shift continues even after the mode traps resonant particles.
String Theory, Unification and Quantum Gravity
Stelle, K S
2012-01-01
An overview is given of the way in which the unification program of particle physics has evolved into the proposal of superstring theory as a prime candidate for unifying quantum gravity with the other forces and particles of nature. A key concern with quantum gravity has been the problem of ultraviolet divergences, which is naturally solved in string theory by replacing particles with spatially extended states as the fundamental excitations. String theory turns out, however, to contain many more extended-object states than just strings. Combining all this into an integrated picture, called M-theory, requires recognition of the r\\^ole played by a web of nonperturbative duality symmetries suggested by the nonlinear structures of the field-theoretic supergravity limits of string theory.
Basic Concepts of a Quantum Event Theory
Bostroem, K J
2004-01-01
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. Time and space are treated on exactly the same footing, namely as quantum mechanical observables on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics and cannot be formulated within the framework of unitary dynamics. As a most important aspect, the theory breaks with the concept of a continuously flowing time in favour of a discrete jump process in spacetime. All physical statements are formulated in terms of detector events rather than particle states. The physical object under consideration is a spinless particle in empty space. Yet the theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the strict sense. The Maxwell equations are derived as a straightforward consequence of some fundamental commutation relations. In the non-relativistic limit, and in the limit of infinitely small time uncertain...
Factorization algebras in quantum field theory
Costello, Kevin
2017-01-01
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
Undergraduate Lecture Notes in Topological Quantum Field Theory
2008-01-01
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
Quantum Holonomy Theory and Hilbert Space Representations
Aastrup, Johannes
2016-01-01
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state exist is left for later publications.
The physical principles of the quantum theory
Heisenberg, Werner
1949-01-01
The contributions of few contemporary scientists have been as far reaching in their effects as those of Nobel Laureate Werner Heisenberg. His matrix theory is one of the bases of modern quantum mechanics, while his ""uncertainty principle"" has altered our whole philosophy of science.In this classic, based on lectures delivered at the University of Chicago, Heisenberg presents a complete physical picture of quantum theory. He covers not only his own contributions, but also those of Bohr, Dirac, Bose, de Broglie, Fermi, Einstein, Pauli, Schrodinger, Somerfield, Rupp, ·Wilson, Germer, and others
On deformation theory of quantum vertex algebras
Grosse, H; Grosse, Harald; Schlesinger, Karl-Georg
2005-01-01
We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual Hochschild complex of an assocative algebra. We show that this system of equations results from an action principle. This might be the starting point for a perturbative treatment of the deformation problem of quantum vertex algebras. Our action generalizes the action of the Kodaira-Spencer theory of gravity and might therefore also be of relevance for applications in string theory.
Holism, physical theories and quantum mechanics
Seevinck, M. P.
Motivated by the question what it is that makes quantum mechanics a holistic theory (if so), I try to define for general physical theories what we mean by `holism'. For this purpose I propose an epistemological criterion to decide whether or not a physical theory is holistic, namely: a physical theory is holistic if and only if it is impossible in principle to infer the global properties, as assigned in the theory, by local resources available to an agent. I propose that these resources include at least all local operations and classical communication. This approach is contrasted with the well-known approaches to holism in terms of supervenience. The criterion for holism proposed here involves a shift in emphasis from ontology to epistemology. I apply this epistemological criterion to classical physics and Bohmian mechanics as represented on a phase and configuration space respectively, and for quantum mechanics (in the orthodox interpretation) using the formalism of general quantum operations as completely positive trace non-increasing maps. Furthermore, I provide an interesting example from which one can conclude that quantum mechanics is holistic in the above mentioned sense, although, perhaps surprisingly, no entanglement is needed.
Wilson lines in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Cherednikov, Igor Olegovich [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.; Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Mertens, Tom; Veken, Frederik F. van der [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.
2014-07-01
Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.
Theory of Quantum Loschmidt Echoes
Prosen, T.; Seligman, T. H.; Žnidarič, M.
In this paper we review our recent work on the theoretical approach to quantum Loschmidt echoes, i.e., various properties of the so-called echo dynamics -- the composition of forward and backward time evolutions generated by two slightly different Hamiltonians, such as the state autocorrelation function (fidelity) and the purity of a reduced density matrix traced over a subsystem (purity fidelity). Our main theoretical result is a linear response formalism, expressing the fidelity and purity fidelity in terms of integrated time autocorrelation function of the generator of the perturbation. Surprisingly, this relation predicts that the decay of fidelity is the slower the faster the decay of correlations. In particular for a static (time-independent) perturbation, and for non-ergodic and non-mixing dynamics where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a time scale ∝ 1/δ as opposed to mixing dynamics where the fidelity is found to decay exponentially on a time-scale ∝ 1/δ2, where δ is a strength of perturbation. A detailed discussion of a semi-classical regime of small effective values of Planck constant hbar is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behavior is recovered in the classical limit hbarto 0, as the two limits δto 0 and hbarto 0 do not commute. The theoretical results are demonstrated numerically for two models, the quantized kicked top and the multi-level Jaynes Cummings model. Our method can for example be applied to the stability analysis of quantum computation and quantum information processing.
Quantum bouncer: theory and experiment
Vankov, Anatoli Andrei
2009-01-01
The quantum bouncer (QB) concept is a known QM textbook example of confined particle, namely, a solution to the 1D Schroedinger equation for a linear potential (the so-called Airy equation). It would be a great methodological challenge to create such a QM object in laboratory. An attempt of observation of the QB ``running'' in the horizontal direction was recently made by the international team at the Laue-Langevin Institute, Grenoble. The experiment was performed with ultra-cold neutrons. In this paper, the experiment is analyzed in view of the authors' claim that ``neutron quantum states in Earth gravitational field'' are observed. The experimental apparatus is designed for measurements of horizontal flux of neutrons passing through an absorbing wave guide with a variable height of absorber. From our analysis, it follows, however, that in such a layout measured data are not sensitive to quantum probability density in the vertical direction. The overall conclusion is made that the experimental data do not co...
Introduction to the theory of quantum information processing
Bergou, János A
2013-01-01
Introduction to the Theory of Quantum Information Processing provides the material for a one-semester graduate level course on quantum information theory and quantum computing for students who have had a one-year graduate course in quantum mechanics. Many standard subjects are treated, such as density matrices, entanglement, quantum maps, quantum cryptography, and quantum codes. Also included are discussions of quantum machines and quantum walks. In addition, the book provides detailed treatments of several underlying fundamental principles of quantum theory, such as quantum measurements, the no-cloning and no-signaling theorems, and their consequences. Problems of various levels of difficulty supplement the text, with the most challenging problems bringing the reader to the forefront of active research. This book provides a compact introduction to the fascinating and rapidly evolving interdisciplinary field of quantum information theory, and it prepares the reader for doing active research in this area.
Wavelet-Based Quantum Field Theory
Directory of Open Access Journals (Sweden)
Mikhail V. Altaisky
2007-11-01
Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
Scattering theory the quantum theory of nonrelativistic collisions
Taylor, John R
2006-01-01
This graduate-level text is intended for any student of physics who requires a thorough grounding in the quantum theory of nonrelativistic scattering. It is designed for readers who are already familiar with the general principles of quantum mechanics and who have some small acquaintance with scattering theory. Study of this text will allow students of atomic or nuclear physics to begin reading the literature and tackling real problems, with a complete grasp of the underlying principles. For students of high-energy physics, it provides the necessary background for later study of relativistic p
Quantum Holonomy Theory, Lattice-Independent Formulation
Aastrup, Johannes
2016-01-01
Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD-algebra, which essentially encodes how local degrees of freedom are moved on a three-dimensional manifold. In this paper we continue the development of the theory by providing a lattice-independent formulation. We first define a Dirac type operator over a configuration space of Ashtekar connections and use it to formulate a graded version of the QHD-algebra. Next we formulate necessary conditions for a state to exist on this algebra and use the GNS construction to build a kinematical Hilbert space. Finally we find that operators, that correspond to the Dirac and gravitational Hamiltonians in a semi-classical limit, are background independent.
Towards the mathematics of quantum field theory
Paugam, Frédéric
2014-01-01
The aim of this book is to introduce mathematicians (and, in particular, graduate students) to the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in play. This should in turn promote interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, even if the mathematical one is the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second...
Boolean approach to dichotomic quantum measurement theories
Nagata, K.; Nakamura, T.; Batle, J.; Abdalla, S.; Farouk, A.
2017-02-01
Recently, a new measurement theory based on truth values was proposed by Nagata and Nakamura [Int. J. Theor. Phys. 55, 3616 (2016)], that is, a theory where the results of measurements are either 0 or 1. The standard measurement theory accepts a hidden variable model for a single Pauli observable. Hence, we can introduce a classical probability space for the measurement theory in this particular case. Additionally, we discuss in the present contribution the fact that projective measurement theories (the results of which are either +1 or -1) imply the Bell, Kochen, and Specker (BKS) paradox for a single Pauli observable. To justify our assertion, we present the BKS theorem in almost all the two-dimensional states by using a projective measurement theory. As an example, we present the BKS theorem in two-dimensions with white noise. Our discussion provides new insight into the quantum measurement problem by using this measurement theory based on the truth values.
Hierarchical theory of quantum adiabatic evolution
Zhang, Qi; Gong, Jiangbin; Wu, Biao
2014-12-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau-Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory.
Dual Field Theories of Quantum Computation
Vanchurin, Vitaly
2016-01-01
Given two quantum states of $N$ q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large $N$ limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an $N+1$ dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an $N$ dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli $Z$ matrices. Since such situation is not generic we call it the $Z$-problem. On the dual field the...
Quantum Lie theory a multilinear approach
Kharchenko, Vladislav
2015-01-01
This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
Quantum theory with bold operator tensors.
Hardy, Lucien
2015-08-06
In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory.
Quantum Transport Theory for Photonic Networks
Lei, Chan U
2010-01-01
In this paper, we develop a quantum transport theory to describe photonic transport in photonic networks. The photonic networks concerned in the paper consist of all-optical circuits incorporating photonic bandgap waveguides and driven resonators. The photoncurrents flowing through waveguides are entirely determined from the exact master equation of the driven resonators. The master equation of the driven resonators is obtained by explicitly eliminating all the waveguide degrees of freedom while the back-reactions between resonators and waveguides are fully taken into account. The relations between the driven photonic dynamics and photoncurrents are obtained. The quantum dissipation and quantum noise effects in photonic transport are also fully addressed. As an illustration, the theory is applied to the transport phenomena of a driven nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the driven resonator is demonstrated.
Quantum theory of elementary processes
Galiautdinov, Andrei
2002-01-01
In modern physics, one of the greatest divides is that between space-time and quantum fields, as the fiber bundle of the Standard Model indicates. However on the operational grounds the fields and spacetime are not very different. To describe a field in an experimental region we have to assign coordinates to the points of that region in order to speak of the "when" and "where" of the field itself. But to operationally study the topology and to coordinatize the region of spacetime, the use of ...
Theory of controlled quantum dynamics
Energy Technology Data Exchange (ETDEWEB)
De Martino, Salvatore; De Siena, Silvio; Illuminati, Fabrizio [Dipartimento di Fisica, Universita di Salerno, and INFN, Sezione di Napoli, Gruppo collegato di Salerno, Baronissi (Italy)
1997-06-07
We introduce a general formalism to obtain localized quantum wavepackets as dynamically controlled systems, in the framework of Nelson stochastic quantization. We show that in general the control is linear, and it amounts to introducing additional time-dependent terms in the potential. In this way one can construct for general systems either coherent packets following classical motion with constant dispersion, or coherent packets following classical motion whose time-dependent dispersion remains bounded for all times. We show that in the operatorial language our scheme amounts to introducing a suitable generalization to arbitrary potentials of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator. (author)
Theory of controlled quantum dynamics
De Martino, S; Illuminati, F; Martino, Salvatore De; Siena, Silvio De; Illuminati, Fabrizio
1997-01-01
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose spreading remains bounded for all times. In the standard operatorial framework our scheme corresponds to a suitable generalization of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator.
Quantum theory, deformation and integrability
Carroll, R
2000-01-01
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between qua
The Quantum Theory of Magnetism
Majlis, Norberto
2000-01-01
This book is intended as a basic text for a two-term graduate course for physicists, engineers and chemists with a background in quantum and statistical mechanics. What sets it apart from other publications on the subject is its extensive use of Greenâ€™s function techniques and its detailed discussion of the application of the mean-field approximation and dipoleâ€"dipole interactions in one, two and three dimensions. A chapter each has been devoted to low-dimensional systems, surface magnetism and layered systems. A total of 60 exercises have also been included.
Kinetic energy decomposition scheme based on information theory.
Imamura, Yutaka; Suzuki, Jun; Nakai, Hiromi
2013-12-15
We proposed a novel kinetic energy decomposition analysis based on information theory. Since the Hirshfeld partitioning for electron densities can be formulated in terms of Kullback-Leibler information deficiency in information theory, a similar partitioning for kinetic energy densities was newly proposed. The numerical assessments confirm that the current kinetic energy decomposition scheme provides reasonable chemical pictures for ionic and covalent molecules, and can also estimate atomic energies using a correction with viral ratios.
Stochastic chemical kinetics theory and (mostly) systems biological applications
Érdi, Péter; Lente, Gabor
2014-01-01
This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.
A Structurally Relativistic Quantum Theory. Part 1: Foundations
Grgin, Emile
2012-01-01
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A new number system with the properties needed to support an inherently relativistic quantum theory is brought to light and investigated to a point sufficient for applications.
Wilson lines in quantum field theory
Cherednikov, Igor O; Veken, Frederik F van der
2014-01-01
The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. It teaches how to perform independently with some elementary calculations on Wilson lines, and shows the recent development of the subject in different important areas of research.
Connecting and unmasking relativity and quantum theory
Koning, de W.L.; Willigenburg, van L.G.
2015-01-01
The answer lies right in front of us, but we refuse to see it. Both relativity and quantum theory, the two pillars of fundamental physics, are modified in this paper to make them also explain the physical phenomena they describe. With this explanation, all current inconsistencies between the two van
Formalism and Interpretation in Quantum Theory
Wilce, Alexander
2010-04-01
Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.
CDT: an entropic theory of quantum gravity
Ambjorn, J.; Goerlich, A.; Jurkiewicz, J.; Loll, R.
2010-01-01
In these lectures we describe how a theory of quantum gravity may be constructed in terms of a lattice formulation based on so-called causal dynamical triangulations (CDT). We discuss how the continuum limit can be obtained and how to define and measure diffeomorphism-invariant correlators. In four
Generalized theory of diffusion based on kinetic theory
Schäfer, T.
2016-10-01
We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite limit spin hydrodynamics is equivalent to a collisionless Boltzmann treatment of spin propagation. Spin hydrodynamics avoids unphysical effects that arise when the diffusion equation is used to describe to a strongly interacting gas with a dilute corona. We apply spin hydrodynamics to the problem of spin diffusion in a trapped atomic gas. We find that the observed spin relaxation rate in the high-temperature limit [Sommer et al., Nature (London) 472, 201 (2011), 10.1038/nature09989] is consistent with the diffusion constant predicted by kinetic theory.
A generalized Theory of Diffusion based on Kinetic Theory
Schaefer, Thomas
2016-01-01
We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite limit spin hydrodynamics is equivalent to a collisionless Boltzmann treatment of spin propagation. Spin hydrodynamics avoids unphysical effects that arise when the diffusion equation is used to describe to a strongly interacting gas with a dilute corona. We apply spin hydrodynamics to the problem of spin diffusion in a trapped atomic gas. We find that the observed spin relaxation rate in the high temperature limit [Sommer et al., Nature 472, 201 (2011)] is consistent with the diffusion constant predicted by kinetic theory.
Quantum Theory without Planck's Constant
Ralston, John P
2012-01-01
Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention. Despite long reference to experiment, review shows that Planck's constant cannot be obtained from the data of Ryberg, Davisson and Germer, Compton, or that used by Planck himself. In the new approach Planck's constant is tied to macroscopic conventions of Newtonian origin, which are dispensable. The precision of other fundamental constants is substantially improved by eliminating Planck's constant. The electron mass is determined about 67 times more precisely, and the unit of electric charge determined 139 times more precisely. Improvement in the experimental value of the fine structure constant allows new types of experiment to be compared towards finding "new physics." The long-standing goal of eliminating reliance on the artifact known as the International Prototype Kilogram can be accompl...
Discrete Scalar Quantum Field Theory
Gudder, Stan
2016-01-01
We begin with a description of spacetime by a 4-dimensional cubic lattice $\\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\\sscripthat$ corresponds to a cubic lattice of energy-momentum. This description implies that there is a discrete set of possible particle masses. We then define discrete scalar quantum fields on $\\sscript$. These fields are employed to define interaction Hamiltonians and scattering operators. Although the scattering operator $S$ cannot be computed exactly, approximations are possible. Whether $S$ is unitary is an unsolved problem. Besides the definitions of these operators, our main assumption is conservation of energy-momentum for a scattering process. This article concludes with various examples of perturbation approximations. These include simplified versions of electron-electron and electron-proton scattering as well as simple decay processes. We also define scattering cross-sections, decay ...
Theory of quantum Loschmidt echoes
Prosen, T; Znidaric, M; Prosen, Tomaz; Seligman, Thomas H.; Znidaric, Marko
2003-01-01
In this paper we review our recent work on the theoretical approach to quantum Loschmidt echoes, i.e. various properties of the so called echo dynamics -- the composition of forward and backward time evolutions generated by two slightly different Hamiltonians, such as the state autocorrelation function (fidelity) and the purity of a reduced density matrix traced over a subsystem (purity fidelity). Our main theoretical result is a linear response formalism, expressing the fidelity and purity fidelity in terms of integrated time autocorrelation function of the generator of the perturbation. Surprisingly, this relation predicts that the decay of fidelity is the slower the faster the decay of correlations. In particular for a static (time-independent) perturbation, and for non-ergodic and non-mixing dynamics where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a time scale 1/delta as opposed to mixing dynamics where the fidelity is found to decay...
Spinning Particles in Quantum Mechanics and Quantum Field Theory
Corradini, Olindo
2015-01-01
The first part of the lectures, given by O. Corradini, covers introductory material on quantum-mechanical Feynman path integrals, which are here derived and applied to several particle models. We start considering the nonrelativistic bosonic particle, for which we compute the exact path integrals for the case of the free particle and for the harmonic oscillator, and then describe perturbation theory for an arbitrary potential. We then move to relativistic particles, both bosonic and fermionic (spinning) particles. We first investigate them from the classical view-point, studying the symmetries of their actions, then consider their canonical quantization and path integrals, and underline the role these models have in the study of space-time quantum field theories (QFT), by introducing the "worldline" path integral representation of propagators and effective actions. We also describe a special class of spinning particles that constitute a first-quantized approach to higher-spin fields. Since the fifties the qua...
Problem Book in Quantum Field Theory
Radovanovič, Voja
2008-01-01
The Problem Book in Quantum Field Theory contains about 200 problems with solutions or hints that help students to improve their understanding and develop skills necessary for pursuing the subject. It deals with the Klein-Gordon and Dirac equations, classical field theory, canonical quantization of scalar, Dirac and electromagnetic fields, the processes in the lowest order of perturbation theory, renormalization and regularization. The solutions are presented in a systematic and complete manner. The material covered and the level of exposition make the book appropriate for graduate and undergraduate students in physics, as well as for teachers and researchers. The new edition is a corrected paperback edition for students.
Noncommutative Time in Quantum Field Theory
Salminen, Tapio
2011-01-01
We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-K\\"all\\'{e}n equation) and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of light-like noncommutativity.
Completely local interpretation of quantum field theory
Sverdlov, Roman
2010-01-01
The purpose of this paper is to come up with a framework that "converts" existing concepts from configuration space to ordinary one. This is done by modeling our universe as a big "computer" that simulates configuration space. If that "computer" exists in ordinary space and is ran by "classical" laws, our theory becomes "classical" by default. We have first applied this concept to a version of quantum field theory in which elementary particles have size (that is, a theory that does not yet exists). After that, we have also done the same with Pilot Wave model of discrete jumps, due to D\\"urr et el.
Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Solvay 1927: Quantum Theory at the Crossroads
Valentini, Antony
2011-04-01
We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. The proceedings of the conference contain much unexpected material, and are remarkable for their clear identification of key issues that remain controversial to this day. After providing a general overview, we focus on the extensive discussions of de Broglie's pilot-wave theory, which de Broglie presented for a many-body system, including the much misunderstood critique by Pauli.
Kinetic theory of fermions in curved spacetime
Fidler, Christian; Pitrou, Cyril
2017-06-01
We build a statistical description of fermions, taking into account the spin degree of freedom in addition to the momentum of particles, and we detail its use in the context of the kinetic theory of gases of fermions particles. We show that the one-particle distribution function needed to write a Liouville equation is a spinor valued operator. The degrees of freedom of this function are covariantly described by an intensity function and by a polarisation vector which are parallel transported by free streaming. Collisions are described on the microscopic level and lead to a Boltzmann equation for this operator. We apply our formalism to the case of weak interactions, which at low energies can be considered as a contact interaction between fermions, allowing us to discuss the structure of the collision term for a few typical weak-interaction mediated reactions. In particular we find for massive particles that a dipolar distribution of velocities in the interacting species is necessary to generate linear polarisation, as opposed to the case of photons for which linear polarisation is generated from the quadrupolar distribution of velocities.
Student friendly quantum field theory basic principles & quantum electrodynamics
Klauber, Robert D
2013-01-01
By incorporating extensive student input and innovative teaching methodologies, this book aims to make the process of learning quantum field theory easier, and thus more rapid, profound, and efficient, for both students and instructors. Comprehensive explanations are favored over conciseness, every step in derivations is included, and ‘big picture’ overviews are provided throughout. Typical student responses indicate how well the text achieves its aim.
Quantum cellular automaton theory of light
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-01
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space-time and mechanics (D'Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Quantum cellular automaton theory of light
Energy Technology Data Exchange (ETDEWEB)
Bisio, Alessandro, E-mail: alessandro.bisio@unipv.it; D’Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-15
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space–time and mechanics (D’Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
Complex numbers in quantum theory
Maynard, Glenn
In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: "What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function." This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. (Abstract shortened by ProQuest.).
Conformal invariance in quantum field theory
Todorov, Ivan T; Petkova, Valentina B
1978-01-01
The present volume is an extended and up-to-date version of two sets of lectures by the first author and it reviews more recent work. The notes aim to present a self-contained exposition of a constructive approach to conformal invariant quantum field theory. Other parts in application of the conformal group to quantum physics are only briefly mentioned. The relevant mathematical material (harmonic analysis on Euclidean conformal groups) is briefly summarized. A new exposition of physical applications is given, which includes an explicit construction of the vacuum operator product expansion for the free zero mass fields.
The Einstein-Vlasov System/Kinetic Theory
Directory of Open Access Journals (Sweden)
Håkan Andréasson
2011-05-01
Full Text Available The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.
Deriving quantum theory from its local structure and reversibility.
de la Torre, Gonzalo; Masanes, Lluís; Short, Anthony J; Müller, Markus P
2012-08-31
We investigate the class of physical theories with the same local structure as quantum theory but potentially different global structure. It has previously been shown that any bipartite correlations generated by such a theory can be simulated in quantum theory but that this does not hold for tripartite correlations. Here we explore whether imposing an additional constraint on this space of theories-that of dynamical reversibility-will allow us to recover the global quantum structure. In the particular case in which the local systems are identical qubits, we show that any theory admitting at least one continuous reversible interaction must be identical to quantum theory.
The universality question for noncommutative quantum field theory
Schlesinger, K G
2006-01-01
Present day physics rests on two main pillars: General relativity and quantum field theory. We discuss the deep and at the same time problematic interplay between these two theories. Based on an argument by Doplicher, Fredenhagen, and Roberts, we propose a possible universality property for noncommutative quantum field theory in the sense that any theory of quantum gravity should involve quantum field theories on noncommutative space-times as a special limit. We propose a mathematical framework to investigate such a universality property and start the discussion of its mathematical properties. The question of its connection to string theory could be a starting point for a new perspective on string theory.
Quantum theory of plasmons in nanostructures
DEFF Research Database (Denmark)
Winther, Kirsten Trøstrup
. For a theoretical description of plasmon in such materials, where the electrons are heavily confined in one or more directions, a quantum mechanical description of the electrons in the material is necessary. In this thesis, the ab initio methods Density functional theory (DFT) and linear response time-dependent DFT......In this thesis, ab initio quantum-mechanical calculations are used to study the properties of plasmons in nanostructures that involve atomic length-scales. The plasmon is an electronic excitation that corresponds to oscillations in the electron charge density in metals, often visualized as water...... are applied to calculate the properties of plasmons in nanostructures in different dimensions. In order to identify and visualize localized plasmon modes, a method for calculating plasmon eigenmodes within the ab initio framework has been developed. In the studied materials, quantum mechanical effects...
The operator tensor formulation of quantum theory.
Hardy, Lucien
2012-07-28
In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
The initial value problem in Lagrangian drift kinetic theory
Burby, J. W.
2016-06-01
> Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, `renormalized' variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space Lagrangian instead of the usual `field particle' Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional formulations, does not support the troublesome rapidly varying modes.
Kinetic derivation of generalized phase space Chern-Simons theory
Hayata, Tomoya
2016-01-01
We study a kinetic theory in $2d$ phase space when all abelian Berry curvatures are nonzero. We derive the complete form of the Poisson brackets, and calculate transports induced by Berry curvatures. Then we construct the low-energy effective theory to reproduce the transports. Such an effective theory is given by the Chern-Simons theory in $1+2d$ dimensions. Some implications of the Chern-Simons theory are also discussed.
Quantum Theories of Self-Localization
Bernstein, Lisa Joan
In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.
Gao, Jiali; Major, Dan T; Fan, Yao; Lin, Yen-Lin; Ma, Shuhua; Wong, Kin-Yiu
2008-01-01
A method for incorporating quantum mechanics into enzyme kinetics modeling is presented. Three aspects are emphasized: 1) combined quantum mechanical and molecular mechanical methods are used to represent the potential energy surface for modeling bond forming and breaking processes, 2) instantaneous normal mode analyses are used to incorporate quantum vibrational free energies to the classical potential of mean force, and 3) multidimensional tunneling methods are used to estimate quantum effects on the reaction coordinate motion. Centroid path integral simulations are described to make quantum corrections to the classical potential of mean force. In this method, the nuclear quantum vibrational and tunneling contributions are not separable. An integrated centroid path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method along with a bisection sampling procedure was summarized, which provides an accurate, easily convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. In the ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT), these three aspects of quantum mechanical effects can be individually treated, providing useful insights into the mechanism of enzymatic reactions. These methods are illustrated by applications to a model process in the gas phase, the decarboxylation reaction of N-methyl picolinate in water, and the proton abstraction and reprotonation process catalyzed by alanine racemase. These examples show that the incorporation of quantum mechanical effects is essential for enzyme kinetics simulations.
A mathematical theory for deterministic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, Gerard ' t [Institute for Theoretical Physics, Utrecht University (Netherlands); Spinoza Institute, Postbox 80.195, 3508 TD Utrecht (Netherlands)
2007-05-15
Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.
String Field Theory from Quantum Gravity
Crane, Louis
2012-01-01
Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) ...
Bohmian mechanics and quantum theory an appraisal
Goldstein, Sheldon; Cushing, James T
1996-01-01
We are often told that quantum phenomena demand radical revisions of our scientific world view and that no physical theory describing well defined objects, such as particles described by their positions, evolving in a well defined way, let alone deterministically, can account for such phenomena. The great majority of physicists continue to subscribe to this view, despite the fact that just such a deterministic theory, accounting for all of the phe nomena of nonrelativistic quantum mechanics, was proposed by David Bohm more than four decades ago and has arguably been around almost since the inception of quantum mechanics itself. Our purpose in asking colleagues to write the essays for this volume has not been to produce a Festschrift in honor of David Bohm (worthy an undertaking as that would have been) or to gather together a collection of papers simply stating uncritically Bohm's views on quantum mechanics. The central theme around which the essays in this volume are arranged is David Bohm's vers...
General principles of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Bogolubov, N.N.; Logunov, A.A. (AN SSSR, Moscow (USSR) Moskovskij Gosudarstvennyj Univ., Moscow (USSR)); Oksak, A.I. (Institute for High Energy Physics, Moscow (USSR)); Todorov, I.T. (Bylgarska Akademiya na Naukite, Sofia (Bulgaria) Bulgarian Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria))
1990-01-01
This major volume provides a account of general quantum field theory, with an emphasis on model-independent methods. The important aspects of the development of the subject are described in detail and are shown to have promising links with many branches of modern mathematics and theoretical physics, such as random fields (probability), statistical physics, and elemantary particles. The material is presented in a thorough, systematic way and the mathematical methods of quantum field theory are also given. The text is self-contained and contains numerous exercises. Topics of independent interest are given in appendices. The book also contains a large bibliography. (author). 1181 refs. Includes index of notation and subject index; includes 1181 refs.
Quantum holonomy theory and Hilbert space representations
Energy Technology Data Exchange (ETDEWEB)
Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)
2016-11-15
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Quantum measure theory and its interpretation
Sorkin, R D
1997-01-01
The paper proposes a realistic, spacetime interpretation of quantum theory in which reality constitutes a *single* history obeying a "law of motion" which makes definite, but incomplete, predictions about its behavior. We associate a "quantum measure" |S| to the set S of histories, and point out that |S| ful- fills a sum rule generalizing that of classical probability theory. We inter- pret |S| as a "propensity", making this precise by stating a criterion for |S|=0 to imply "preclusion" (meaning that the true history will not lie in S). The criterion involves triads of correlated events, and in application to electron-electron scattering, for example, it yields definite predictions about the electron trajectories themselves, independently of any measuring devices which might or might not be present. (So we can give an objective account of measurements.) Two unfinished aspects of the interpretation involve conditonal preclusion (which apparently requires coarse-graining for its formulation) and the need to "lo...
The Global Approach to Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Folacci, Antoine; Jensen, Bruce [Faculte des Sciences, Universite de Corse (France); Department of Mathematics, University of Southampton (United Kingdom)
2003-12-12
Thanks to its impressive success in the second half of the 20th century, both in high-energy physics and in critical phenomena, quantum field theory has enjoyed an abundant literature. We therefore greet yet another book on this subject with caution: what can a monograph on quantum field theory bring now that is new, either conceptually or pedagogically? But when it is written by a physicist such as Bryce DeWitt, who has made his own contribution to the collection of field theory books with The Global Approach to Quantum Field Theory, all suspicion is naturally abandoned. DeWitt has made a formidable contribution to various areas of physics: general relativity, the interpretation of quantum mechanics, and most of all the quantization of non-Abelian gauge theories and quantum gravity. In addition, his pedagogical publications, especially the Les Houches schools of 1963 and 1983, have had a great impact on quantum field theory. We must begin by alerting the potential readers of this book that it cannot be compared to any other book in the field. This uniqueness applies to both the scientific content and the way the ideas are presented. For DeWitt, a central concept of field theory is that of 'space of histories'. For a field varphi{sup i} defined on a given spacetime M, the set of all varphi{sup i}(x) for all x in all charts of M defines its history. It is the space Phi of all possible histories (dynamically allowed or not) of the fields defined on M which is called the 'pace of histories' by DeWitt. If only bosonic fields are considered, the space of histories is an infinite-dimensional manifold and if fermionic fields are also present, it must be viewed as an infinite-dimensional supermanifold. The fields can then be regarded as coordinates on these structures, and the geometrical notions of differentiation, metric, connections, measure, as well as the geodesics which can be defined on it, are of fundamental importance in the development of the
No extension of quantum theory can have improved predictive power.
Colbeck, Roger; Renner, Renato
2011-08-02
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography.
Modeling in applied sciences a kinetic theory approach
Pulvirenti, Mario
2000-01-01
Modeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process Topics and Features * Integrated modeling perspective utilized in all chapters * Fluid dynamics of reacting gases * Self-contained introduction to kinetic models * Becker–Doring equations * Nonlinear kinetic models with chemical reactions * Kinet...
A principle of relativity for quantum theory
Zaopo, Marco
2012-01-01
In non relativistic physics it is assumed that both chronological ordering and causal ordering of events (telling wether there exists a causal relationship between two events or not) are absolute, observer independent properties. In relativistic physics on the other hand chronological ordering depends on the observer who assigns space-time coordinates to physical events and only causal ordering is regarded as an observer independent property. In this paper it is shown that quantum theory can be considered as a physical theory in which causal (as well as chronological) ordering of probabilistic events happening in experiments may be regarded as an observer dependent property.
The general principles of quantum theory
Temple, George
2014-01-01
Published in 1934, this monograph was one of the first introductory accounts of the principles which form the physical basis of the Quantum Theory, considered as a branch of mathematics. The exposition is restricted to a discussion of general principles and does not attempt detailed application to the wide domain of atomic physics, although a number of special problems are considered in elucidation of the principles. The necessary fundamental mathematical methods - the theory of linear operators and of matrics - are developed in the first chapter so this could introduce anyone to the new theor
Quantum Field Theory Without Divergence A
Chen Sow Hsin
2002-01-01
We anew explain the meaning of negative energies in the relativistic theory. On the basis we present two new conjectures. According to the conjectures, particles have two sorts of existing forms which are symmetric. From this we present a new Lagrangian density and a new quantization method for QED. That the energy of the vacuum state is equal to zero is naturally obtained. From this we can easily determine the cosmological constant according to experiments, and it is possible to correct nonperturbational methods which depend on the energy of the ground state in quantum field theory.
Topological quantum field theory: 20 years later
DEFF Research Database (Denmark)
Reshetikhin, Nicolai
2008-01-01
This article is an overview of the developments in topological quantum ﬁeld theory, and, in particular on the progress in the Chern–Simons theory.......This article is an overview of the developments in topological quantum ﬁeld theory, and, in particular on the progress in the Chern–Simons theory....
On space of integrable quantum field theories
Smirnov, F. A.; Zamolodchikov, A. B.
2017-02-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Quantum symmetries in supersymmetric Toda theories
Penati, S; Penati, Silvia; Zanon, Daniela
1992-01-01
: We consider two--dimensional supersymmetric Toda theories based on the Lie superalgebras $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ which admit a fermionic set of simple roots and a fermionic untwisted affine extension. In particular, we concentrate on two simple examples, the $B(1,1)$ and $A(1,1)$ theories. Both in the conformal and massive case we address the issue of quantum integrability by constructing the first non trivial conserved currents and proving their conservation to all--loop orders. While the $D(n+1,n)$ and $B(n,n)$ systems are genuine $N=1$ supersymmetric theories, the $A(n,n)$ models possess a global $N=2$ supersymmetry. In the conformal case, we show that the $A(n,n)$ stress--energy tensor, uniquely determined by the holomorphicity condition, has vanishing central charge and it corresponds to the stress--energy tensor of the associated topological theory. (Invited talk at the International Workshop ``String theory, quantum gravity and the unification of the fundamental interactions'', Roma, Septem...
High-temperature quantum kinetic effect in silicon nanosandwiches
Bagraev, N. T.; Grigoryev, V. Yu.; Klyachkin, L. E.; Malyarenko, A. M.; Mashkov, V. A.; Romanov, V. V.; Rul, N. I.
2017-01-01
The negative-U impurity stripes confining the edge channels of semiconductor quantum wells are shown to allow the effective cooling inside in the process of the spin-dependent transport, with the reduction of the electron-electron interaction. The aforesaid promotes also the creation of composite bosons and fermions by the capture of single magnetic flux quanta on the edge channels under the conditions of low sheet density of carriers, thus opening new opportunities for the registration of the quantum kinetic phenomena in weak magnetic fields at high-temperatures up to the room temperature. As a certain version noted above we present the first findings of the high temperature de Haas-van Alphen, 300 K, quantum Hall, 77 K, effects as well as quantum conductance staircase in the silicon sandwich structure that represents the ultra-narrow, 2 nm, p-type quantum well (Si-QW) confined by the delta barriers heavily doped with boron on the n-type Si (100) surface.
Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
Wiese, U -J
2013-01-01
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should al...
Matching the Unmatchable. Complexity Theory and Quantum Theory
Maldonado, Carlos Eduardo
2016-01-01
This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground for filling up such gap. Indeed, most works on complexity at large focus on the macroscopic world, leaving behind the importance of the microscopic world. This paper specifies what both worlds consist of, and argues that a solid account of the world, i.e. complexity, must necessarily take into account both dimensions of reality.
A Quantum Version of Wigner's Transition State Theory
Schubert, R.; Waalkens, H.; Wiggins, S.
2009-01-01
A quantum version of a recent realization of Wigner's transition state theory in phase space is presented. The theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the transition state to any desired order in (h) over bar. This leads to an explicit algor
A Quantum Version of Wigner’s Transition State Theory
Schubert, R.; Waalkens, H.; Wiggins, S.
2009-01-01
A quantum version of a recent realization of Wigner’s transition state theory in phase space is presented. The theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the transition state to any desired order in ħ. This leads to an explicit algorithm to com
String theory, quantum phase transitions, and the emergent Fermi liquid.
Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad
2009-07-24
A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.
Kinetic theory the nature of gases and of heat
Brush, Stephen G
1965-01-01
Kinetic Theory, Volume I: The Nature of Gases and of Heat covers the developments in area of kinetic theory, statistical mechanics, and thermodynamics. This book is organized into two parts encompassing 11 chapters. The book starts with an overview of the history of atomism, the caloric theory, the conservation of energy, the virial theorem, and atomic magnitudes. The second part deals first with the delineation of observed phenomena of motions through the repulsion theory. This part also considers other forces of nature, including fire and heat, with emphasis on the nature of motion of these
BOOK REVIEW: Kinetic Theory of Granular Gases
Trizac, Emmanuel
2005-11-01
Granular gases are composed of macroscopic bodies kept in motion by an external energy source such as a violent shaking. The behaviour of such systems is quantitatively different from that of ordinary molecular gases: due to the size of the constituents, external fields have a stronger effect on the dynamics and, more importantly, the kinetic energy of the gas is no longer a conserved quantity. The key role of the inelasticity of collisions has been correctly appreciated for about fifteen years, and the ensuing consequences in terms of phase behaviour or transport properties studied in an increasing and now vast body of literature. The purpose of this book is to help the newcomer to the field in acquiring the essential theoretical tools together with some numerical techniques. As emphasized by the authors—who were among the pioneers in the domain— the content could be covered in a one semester course for advanced undergraduates, or it could be incorporated in a more general course dealing with the statistical mechanics of dissipative systems. The book is self-contained, clear, and avoids mathematical complications. In order to elucidate the main physical ideas, heuristic points of views are sometimes preferred to a more rigorous route that would lead to a longer discussion. The 28 chapters are short; they offer exercises and worked examples, solved at the end of the book. Each part is supplemented with a relevant foreword and a useful summary including take-home messages. The editorial work is of good quality, with very few typographical errors. In spite of the title, kinetic theory stricto sensu is not the crux of the matter covered. The authors discuss the consequences of the molecular chaos assumption both at the individual particle level and in terms of collective behaviour. The first part of the book addresses the mechanics of grain collisions. It is emphasized that considering the coefficient of restitution ɛ —a central quantity governing the
Retarded versus time-nonlocal quantum kinetic equations
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Spicka, V.; Lipavsky, P. [Institute of Physics, Academy of Sciences, Praha (Czech Republic)
2000-07-01
The finite duration of the collisions in Fermionic systems as expressed by the retardation time in the non-Markovian Levinson equation is discussed in the quasiclassical limit. The separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates and (iii) of the single-particle energy, (iv) collision delay and (v) related non-local corrections to the scattering integral. In this way we transform the Levison equation into the Landau-Silin equation extended by the non-local corrections known from the theory of dense gases. The derived kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other. (authors)
On space of integrable quantum field theories
Smirnov, F A
2016-01-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields $X_s$, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars $X_s$ are built from the components of the associated conserved currents in a universal way. The first of these scalars, $X_1$, coincides with the composite field $(T{\\bar T})$ built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by $X_1$ are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations $X_s$ are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit...
On space of integrable quantum field theories
Directory of Open Access Journals (Sweden)
F.A. Smirnov
2017-02-01
Full Text Available We study deformations of 2D Integrable Quantum Field Theories (IQFT which preserve integrability (the existence of infinitely many local integrals of motion. The IQFT are understood as “effective field theories”, with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (TT¯ built from the components of the energy–momentum tensor. The deformations of quantum field theories generated by X1 are “solvable” in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Formalism locality in quantum theory and quantum gravity
Hardy, Lucien
2008-01-01
We expect a theory of Quantum Gravity to be both probabilistic and have indefinite causal structure. Indefinite causal structure poses particular problems for theory formulation since many of the core ideas used in the usual approaches to theory construction depend on having definite causal structure. For example, the notion of a state across space evolving in time requires that we have some definite causal structure so we can define a state on a space-like hypersurface. We will see that many of these problems are mitigated if we are able to formulate the theory in a "formalism local" (or F-local) fashion. A formulation of a physical theory is said to be F-local if, in making predictions for any given arbitrary space-time region, we need only refer to mathematical objects pertaining to that region. This is a desirable property both on the grounds of efficiency and since, if we have indefinite causal structure, it is not clear how to select some other space-time region on which our calculations may depend. The...
A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information
Plotnitsky, Arkady
2015-01-01
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be be addressed as well in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation for the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall, however, also consider Heisenberg's derivation of quantum mechanics, which inspired Dirac. I argue that Heisenberg's and Dirac's work alike was guided by their adherence to and confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by G. M. D' Ariano and his coworkers on the principles of quantum information theory, which extends quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equation from these principles alone...
Scattering theory for open quantum systems
Energy Technology Data Exchange (ETDEWEB)
Behrndt, Jussi [Technische Univ. Berlin (Germany). Inst. fuer Mathematik; Malamud, Mark M. [Donetsk National University (Ukraine). Dept. of Mathematics; Neidhardt, Hagen [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany)
2006-07-01
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator A{sub D} in a Hilbert space H is used to describe an open quantum system. In this case the minimal self-adjoint dilation K of A{sub D} can be regarded as the Hamiltonian of a closed system which contains the open system {l_brace}A{sub D},h{r_brace}, but since K is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {l_brace}A({mu}){r_brace} of maximal dissipative operators depending on energy {mu}, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schroedinger-Poisson systems. (orig.)
Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
Bahns, D; Fredenhagen, Klaus; Piacitelli, G
2003-01-01
We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the S-matrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences of coordinates q_j - q_k are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function of q_j - q_k by its expectation value in optimally localized states, while leaving the mean coordinates (q_1 + ... + q_n)/n invariant. The resulting procedure is to a large extent unique, and is invariant under translations and rotations, but violates Lorentz invariance. Indeed, optimal localization refers to a specific Lorentz frame, where the electric and magnetic parts of the commutator of the coordinates have to coincide*). Employing an adiabatic switching, we show...
Quantum field theory on brane backgrounds
Flachi, A
2001-01-01
stabilize the radius and simultaneously solving the hierarchy problem, unless the brane tensions are fine tuned to a high degree. The development of higher dimensional quantum field theories is reviewed from the older Kaluza-Klein theory to the new brane models, emphasising their relevance in modern particle physics. The issue of spontaneous symmetry breaking in the Randall-Sundrum model is considered. The role of the coupling between bulk fields and the curvature is investigated and a model in favour of bulk symmetry breaking is presented. The lowest order quantum corrections arising from a quantized scalar field in the Randall-Sundrum spacetime are computed. A careful discussion of the boundary conditions as well as the renormalization is provided. The massless case is also discussed and a proof of the vanishing of the conformal anomaly in this model is given. An analysis of the self-consistency is presented and the radius stabilization problem studied. It is shown that quantum effects may provide a stabili...
Quantum field theories of extended objects
Friedan, Daniel
2016-01-01
First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The fields live on the spaces E of relative integral (n-1)-cycles in M -- the integral (n-1)-currents of given boundary. Each E is a complete metric space geometrically analogous to a Riemann surface $\\Sigma$. For example, if $M=S^d$, $\\Sigma = S^2$. The quantum fields on E are to be mapped to observables in a 2d CFT on $\\Sigma$. The correlation functions on E are to be given by the 2d correlation functions on $\\Sigma$. The goal is to construct a CFT of extended objects in d=2n dimensions for every 2d CFT, and eventually a non-conformal QFT of extended objects for every non-conformal 2d QFT, so that all the technology of 2d QFT can be applied to the construction and analysis of quantum field theories of extended objects. The project depends crucially on settling some mathematical q...
Effective potential kinetic theory for strongly coupled plasmas
Baalrud, Scott D.; Daligault, Jérôme
2016-11-01
The effective potential theory (EPT) is a recently proposed method for extending traditional plasma kinetic and transport theory into the strongly coupled regime. Validation from experiments and molecular dynamics simulations have shown it to be accurate up to the onset of liquid-like correlation parameters (corresponding to Γ ≃ 10-50 for the one-component plasma, depending on the process of interest). Here, this theory is briefly reviewed along with comparisons between the theory and molecular dynamics simulations for self-diffusivity and viscosity of the one-component plasma. A number of new results are also provided, including calculations of friction coefficients, energy exchange rates, stopping power, and mobility. The theory is also cast in the Landau and Fokker-Planck kinetic forms, which may prove useful for enabling efficient kinetic computations.
Measurement theory in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Okamura, Kazuya, E-mail: okamura@math.cm.is.nagoya-u.ac.jp; Ozawa, Masanao, E-mail: ozawa@is.nagoya-u.ac.jp [Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya 464-8601 (Japan)
2016-01-15
In this paper, we aim to establish foundations of measurement theory in local quantum physics. For this purpose, we discuss a representation theory of completely positive (CP) instruments on arbitrary von Neumann algebras. We introduce a condition called the normal extension property (NEP) and establish a one-to-one correspondence between CP instruments with the NEP and statistical equivalence classes of measuring processes. We show that every CP instrument on an atomic von Neumann algebra has the NEP, extending the well-known result for type I factors. Moreover, we show that every CP instrument on an injective von Neumann algebra is approximated by CP instruments with the NEP. The concept of posterior states is also discussed to show that the NEP is equivalent to the existence of a strongly measurable family of posterior states for every normal state. Two examples of CP instruments without the NEP are obtained from this result. It is thus concluded that in local quantum physics not every CP instrument represents a measuring process, but in most of physically relevant cases every CP instrument can be realized by a measuring process within arbitrary error limits, as every approximately finite dimensional von Neumann algebra on a separable Hilbert space is injective. To conclude the paper, the concept of local measurement in algebraic quantum field theory is examined in our framework. In the setting of the Doplicher-Haag-Roberts and Doplicher-Roberts theory describing local excitations, we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a CP instrument with the NEP, provided that the split property holds for the net of local algebras.
Wave operator theory of quantum dynamics
Durand, Philippe; Paidarová, Ivana
1998-09-01
An energy-dependent wave operator theory of quantum dynamics is derived for time-independent and time-dependent Hamiltonians. Relationships between Green's functions, wave operators, and effective Hamiltonians are investigated. Analytical properties of these quantities are especially relevant for studying resonances. A derivation of the relationship between the Green's functions and the (t,t') method of Peskin and Moiseyev [J. Chem. Phys. 99, 4590 (1993)] is presented. The observable quantities can be derived from the wave operators determined with the use of efficient iterative procedures. As in the theory of Bloch operators for bound states, the theory is based on a partition of the full Hilbert space into three subspaces: the model space, an intermediate space, and the outer space. On the basis of this partition an alternative definition of active spaces currently considered in large scale calculations is suggested. A numerical illustration is presented for several model systems and for the Stark effect in the hydrogen atom.
Linear Transformation Theory of Quantum Field Operators and Its Applications
Institute of Scientific and Technical Information of China (English)
MA Lei
2003-01-01
We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.
Quantum: information theory: technological challenge; Computacion Cuantica: un reto tecnologico
Energy Technology Data Exchange (ETDEWEB)
Calixto, M.
2001-07-01
The new Quantum Information Theory augurs powerful machines that obey the entangled logic of the subatomic world. Parallelism, entanglement, teleportation, no-cloning and quantum cryptography are typical peculiarities of this novel way of understanding computation. (Author) 24 refs.
Structural aspects of quantum field theory and noncommutative geometry
Grensing, Gerhard
2013-01-01
This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation. The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a r...
Quantum kinetics and thermalization in a particle bath model.
Alamoudi, S M; Boyanovsky, D; de Vega, H J
1999-07-01
We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.
Multichannel quantum defect theory for polar molecules
Elfimov, Sergei V.; Dorofeev, Dmitrii L.; Zon, Boris A.
2014-02-01
Our work is devoted to developing a general approach for nonpenetrating Rydberg states of polar molecules. We propose a method to estimate the accuracy of calculation of their wave functions and quantum defects. Basing on this method we estimate the accuracy of Born-Oppenheimer (BO) and inverse Born-Oppenheimer (IBO) approximations for these states. This estimation enables us to determine the space and energy regions where BO and IBO approximations are valid. It depends on the interplay between l coupling (due to dipole potential of the core) and l uncoupling (due to rotation the core). Next we consider the intermediate region where both BO and IBO are not valid. For this intermediate region we propose a modification of Fano's multichannel quantum defect theory to match BO and IBO wave functions and show that it gives more reliable results. They are demonstrated on the example of SO molecule.
Preference reversal in quantum decision theory
Yukalov, V I
2015-01-01
We consider the psychological effect of preference reversal and show that it finds a natural explanation in the frame of quantum decision theory. When people choose between lotteries with non-negative payoffs, they prefer a more certain lottery because of uncertainty aversion. But when people evaluate lottery prices, e.g. for selling to others the right to play them, they do this more rationally, being less subject to behavioral biases. This difference can be explained by the presence of the attraction factors entering the expression of quantum probabilities. Only the existence of attraction factors can explain why, considering two lotteries with close utility factors, a decision maker prefers one of them when choosing, but evaluates higher the other one when pricing. We derive a general quantitative criterion for the preference reversal to occur that relates the utilities of the two lotteries to the attraction factors under choosing versus pricing and test successfully its application on experiments by Tvers...
Relativistic kinetic theory with applications in astrophysics and cosmology
Vereshchagin, Gregory V
2017-01-01
Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neut...
[The kinetic theory of the aging of living systems].
Viktorov, A A; Kholodnov, V A
2013-01-01
Kinetic theory of aging of living systems is proposed. Theory is based on the concept of continuous adaptation of biological system (BS) from its birth to changing conditions of environment (ENV). Adaptation rate as rate of risk of destructions accumulation in BS is studied as competition between two simultaneous processes: BS destruction and recombination of damages defined by kinetics of autocatalytic chemical reactions. Kinetic theory assumes critical phenomenon: failure of adaptation when intensity of ENV impact becomes higher some critical level. Choice of parameters of kinetic mathematical model and accounting dependence of ENV impact intensity on time allows describing the following results observed in medical practice: child mortality, depletion of adaptive reserves, slowing the rate of aging of long-living persons, damped harmonic oscillations of biological response at pulse toxic intervention and to estimate risks of disease and death.
Geometry, topology and quantum field theory (fundamental theories of physics)
Bandyopadhyay, P.
2013-01-01
This monograph deals with the geometrical and topological aspects related to quantum field theory with special reference to the electroweak theory and skyrmions. This book is unique in its emphasis on the topological aspects of a fermion manifested through chiral anomaly which is responsible for the generation of mass. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. These geometrical and topological features help us to consider a massive fermion as a skyrmion and for a composite state we can realise the internal symmetry of hadrons from reflection group. Also, an overview of noncommutative geometry has been presented and it is observed that the manifold M 4 x Z2 has its relevance in the description of a massive fermion as skyrmion when the discrete space is considered as the internal space and the symmetry breaking gives rise to chiral anomaly leading to topological features.
A Simple Theory of Quantum Gravity
Horndeski, Gregory W
2015-01-01
A novel theory of Quantum Gravity is presented in which the real gravitons manifest themselves as holes in space. In general, these holes propagate at the speed of light through an expanding universe with boundary denoted by U, which is comprised of pulsating cells. These holes can form bound and semi-bound states. The geometry of U is non-Euclidean on a small scale, but there are indications that it can become Euclidean on a large scale. The motions of elementary particles through U are governed by probability 4 and 7-vectors, which are related to the momentum vectors in Minkowski space. The connection of this theory to Newtonian gravity is discussed, and an expression for the gravitational redshift of photons is derived which relates the redshift to the probability that a photon absorbs a virtual graviton. The theory also provides a possible explanation of dark matter and dark energy as gravitational phenomena, which do not require the introduction of any new particles. A quantum cosmology is presented in w...
The Global Approach to Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Fulling, S A [Texas A and M University (United States)
2006-05-21
Parts I and II develop the basic classical and quantum kinematics of fields and other dynamical systems. The presentation is conducted in the utmost generality, allowing for dynamical quantities that may be anticommuting (supernumbers) and theories subject to the most general possible gauge symmetry. The basic ingredients are action functionals and the Peierls bracket, a manifestly covariant replacement for the Poisson bracket and equal-time commutation relations. For DeWitt the logical progression is Peierls bracket {yields} Schwinger action principle {yields} Feynman functional integral although he points out that the historical development was in the opposite order. It must be pointed out that the Peierls-Schwinger-DeWitt approach, despite some advantages over initial-value formulations, has some troubles of its own. In particular, it has never completely escaped from the arena of scattering theory, the paradigm of conventional particle physics. One is naturally led to study matrix elements between an 'in-vacuum' and an 'out-vacuum' though such concepts are murky in situations, such as big bangs and black holes, where the ambient geometry is not asymptotically static in the far past and future. The newest material in the treatise appears in two chapters in part II devoted to the interpretation of quantum theory, incorporating some unpublished work of David Deutsch on the meaning of probability in physics. Parts III through V apply the formalism in depth to successively more difficult classes of systems: quantum mechanics, linear (free) fields, and interacting fields. DeWitt's characteristic tools of effective actions, heat kernels, and ghost fields are developed. Chapters 26 and 31 outline new approaches developed in collaboration with DeWitt's recent students C Molina-Paris and C Y Wang, respectively. The most of parts VI and VII consist of special topics, such as anomalies, particle creation by external fields, Unruh acceleration
Quantum Theory of Reactive Scattering in Phase Space
Goussev, A.; Schubert, R.; Waalkens, H.; Wiggins, S.; Nicolaides, CA; Brandas, E
2010-01-01
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of Poincare-Birkhoff normal form theory and the perspective of dynamical systems theory. Over the past 10 years the classical normal form theory has provided a met
Theory and simulations of quantum glass forming liquids.
Markland, Thomas E; Morrone, Joseph A; Miyazaki, Kunimasa; Berne, B J; Reichman, David R; Rabani, Eran
2012-02-21
A comprehensive microscopic dynamical theory is presented for the description of quantum fluids as they transform into glasses. The theory is based on a quantum extension of mode-coupling theory. Novel effects are predicted, such as reentrant behavior of dynamical relaxation times. These predictions are supported by path integral ring polymer molecular dynamics simulations. The simulations provide detailed insight into the factors that govern slow dynamics in glassy quantum fluids. Connection to other recent work on both quantum glasses as well as quantum optimization problems is presented.
Quantum theory from first principles an informational approach
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-01-01
Quantum theory is the soul of theoretical physics. It is not just a theory of specific physical systems, but rather a new framework with universal applicability. This book shows how we can reconstruct the theory from six information-theoretical principles, by rebuilding the quantum rules from the bottom up. Step by step, the reader will learn how to master the counterintuitive aspects of the quantum world, and how to efficiently reconstruct quantum information protocols from first principles. Using intuitive graphical notation to represent equations, and with shorter and more efficient derivations, the theory can be understood and assimilated with exceptional ease. Offering a radically new perspective on the field, the book contains an efficient course of quantum theory and quantum information for undergraduates. The book is aimed at researchers, professionals, and students in physics, computer science and philosophy, as well as the curious outsider seeking a deeper understanding of the theory.
AP Theory IV: Intrinsic Topological Quantum Langlands Theory
Winkelnkemper, H E
2010-01-01
Without using any moduli, sheaves, stacks, nor any analytic, nor category-type arguments, we exhibit an analogue to Geometric Langlands Theory in an entirely model-independent, non-perturbative,purely smooth topological context in Artin Presentation Theory. A basic initial feature is that AP Theory, as a whole, is already, ab initio, a universal canonical 2D sigma-model, targeting smooth, compact, simply-connected 4-manifolds with a connected boundary, and its topological Planckian quantum starting point, as well as its cone-like, infinitely-generated at each stage, graded group of homology-preserving, but topology-changing transitions/interactions, exhibit the most general qualitative S-duality. We first point out the numerous mathematically rigorous, model-free, (i.e., intrinsic), topological AP analogues with the heuristic Kapustin-Witten version of Geometric Langlands theory, as well as the crucial differences between the two theories. The latter have to exist since AP Theory deals, a priori, essentially ...
Hydrodynamization and transient modes of expanding plasma in kinetic theory
Heller, Michal P; Spalinski, Michal
2016-01-01
We study the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation. Our studies uncover qualitative similarities to the results on hydrodynamization in strongly coupled gauge theories. In particular, we demonstrate that the gradient expansion in this model has vanishing radius of convergence. The asymptotic character of the hydrodynamic gradient expansion is crucial for the recently discovered applicability of hydrodynamics at large gradients. Furthermore, the analysis of the resurgent properties of the series provides, quite remarkably, indication for the existence of a novel transient, damped oscillatory mode of expanding plasmas in kinetic theory.
Quantum Electrodynamics Theory of Laser Assisted Recombination
Institute of Scientific and Technical Information of China (English)
敖淑艳; 程太旺; 李晓峰; 潘守甫; 傅盘铭
2003-01-01
Using a formal scattering theoretical approach, we develop a nonperturbative quantum electrodynamics theory to describe laser assisted recombination (LAR), in which an electron initially in the quantized Volkov state recombines with an ion and emits a high-energy photon with frequency defined by energy conservation laws.The transition probability is expressed as an analytic closed form and the spectrum of LAR reflects mainly the properties of general Bessel functions. For the case of a fast electron the LAR spectrum is confined in a well-defined range, while for a slow electron, the LAR spectrum exhibits a double-plateau structure.
Measuring orbital interaction using quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Rissler, Joerg [Fachbereich Physik, Philipps-Universitaet Marburg, AG Vielteilchentheorie, Renthof 6, D-35032 Marburg (Germany)], E-mail: rissler@staff.uni-marburg.de; Noack, Reinhard M. [Fachbereich Physik, Philipps-Universitaet Marburg, AG Vielteilchentheorie, Renthof 6, D-35032 Marburg (Germany); White, Steven R. [Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575 (United States)
2006-04-21
Quantum information theory gives rise to a straightforward definition of the interaction of electrons I {sub p,q} in two orbitals p,q for a given many-body wave function. A convenient way to calculate the von Neumann entropies needed is presented in this work, and the orbital interaction I {sub p,q} is successfully tested for different types of chemical bonds. As an example of an application of I {sub p,q} beyond the interpretation of wave functions, I {sub p,q} is then used to investigate the ordering problem in the density-matrix renormalization group.
Quantum theory of the solid state
Callaway, Joseph
1991-01-01
This new edition presents a comprehensive, up-to-date survey of the concepts and methods in contemporary condensed matter physics, emphasizing topics that can be treated by quantum mechanical methods. The book features tutorial discussions of a number of current research topics.Also included are updated treatments of topics that have developed significantly within the past several years, such as superconductivity, magnetic impurities in metals, methods for electronic structure calculations, magnetic ordering in insulators and metals, and linear response theory. Advanced level graduate students
Open quantum systems and Random Matrix Theory
Mulhall, Declan
2014-01-01
A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the $\\Delta_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and $\\Delta_3(L)$ statistic exhibit the signatures of missed levels.
Open quantum systems and random matrix theory
Mulhall, Declan
2015-01-01
A simple model for open quantum systems is analyzed with random matrix theory. The system is coupled to the continuum in a minimal way. In this paper the effect on the level statistics of opening the system is seen. In particular the Δ3(L ) statistic, the width distribution and the level spacing are examined as a function of the strength of this coupling. The emergence of a super-radiant transition is observed. The level spacing and Δ3(L ) statistics exhibit the signatures of missed levels or intruder levels as the super-radiant state is formed.
Modified Enskog Kinetic Theory for Strongly Coupled Plasmas
Baalrud, Scott D
2015-01-01
Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S.~D.~Baalrud and J.~Daligault, Phys.~Rev.~Lett.~{\\bf 110}, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling ($\\Gamma \\gtrsim 30$). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.
Modified Enskog kinetic theory for strongly coupled plasmas.
Baalrud, Scott D; Daligault, Jérôme
2015-06-01
Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling (Γ≳30). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.
Quantum Theory and Probability Theory: Their Relationship and Origin in Symmetry
Directory of Open Access Journals (Sweden)
Philip Goyal
2011-04-01
Full Text Available Quantum theory is a probabilistic calculus that enables the calculation of the probabilities of the possible outcomes of a measurement performed on a physical system. But what is the relationship between this probabilistic calculus and probability theory itself? Is quantum theory compatible with probability theory? If so, does it extend or generalize probability theory? In this paper, we answer these questions, and precisely determine the relationship between quantum theory and probability theory, by explicitly deriving both theories from first principles. In both cases, the derivation depends upon identifying and harnessing the appropriate symmetries that are operative in each domain. We prove, for example, that quantum theory is compatible with probability theory by explicitly deriving quantum theory on the assumption that probability theory is generally valid.
Implementation of quantum game theory simulations using Python
Madrid S., A.
2013-05-01
This paper provides some examples about quantum games simulated in Python's programming language. The quantum games have been developed with the Sympy Python library, which permits solving quantum problems in a symbolic form. The application of these methods of quantum mechanics to game theory gives us more possibility to achieve results not possible before. To illustrate the results of these methods, in particular, there have been simulated the quantum battle of the sexes, the prisoner's dilemma and card games. These solutions are able to exceed the classic bottle neck and obtain optimal quantum strategies. In this form, python demonstrated that is possible to do more advanced and complicated quantum games algorithms.
Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities
Aerts, Diederik
2012-01-01
In this paper we present 'Quantum Model Theory' (QMod), a theory we developed to model entities that entail the typical quantum effects of 'contextuality, 'superposition', 'interference', 'entanglement' and 'emergence'. This aim of QMod is to put forward a theoretical framework that has the technical power of standard quantum mechanics, namely it makes explicitly use of the standard complex Hilbert space and its quantum mechanical calculus, but is also more general than standard quantum mechanics, in the sense that it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement. In this sense, QMod is a generalization of quantum mechanics, similar to how the general relativity manifold mathematical formalism is a generalization of special relativity and classical physics. We prove by means of a representation theorem that QMod can be used for any entity entailing the typical quantum effects mentioned above. Some examples of application of QMod in concept theory and macroscopic...
Gravitational Decoherence, Alternative Quantum Theories and Semiclassical Gravity
Hu, B L
2014-01-01
In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity; 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not; 3) Gravitational Decoherence: Derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schr\\"odinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.
Positive Cosmological Constant and Quantum Theory
Directory of Open Access Journals (Sweden)
Felix M. Lev
2010-11-01
Full Text Available We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but that the de Sitter (dS algebra as the symmetry algebra is more relevant than the Poincare or anti de Sitter ones. The physical interpretation of irreducible representations (IRs of the dS algebra is considerably different from that for the other two algebras. One IR of the dS algebra splits into independent IRs for a particle and its antiparticle only when Poincare approximation works with a high accuracy. Only in this case additive quantum numbers such as electric, baryon and lepton charges are conserved, while at early stages of the Universe they could not be conserved. Another property of IRs of the dS algebra is that only fermions can be elementary and there can be no neutral elementary particles. The cosmological repulsion is a simple kinematical consequence of dS symmetry on quantum level when quasiclassical approximation is valid. Therefore the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for explaining this phenomenon (in agreement with a similar conclusion by Bianchi and Rovelli.
Quantum Field Theories and Prime Numbers Spectrum
Menezes, G
2012-01-01
The Riemann hypothesis states that all nontrivial zeros of the zeta function lie on the critical line $\\Re(s)=1/2$. Hilbert and P\\'olya suggested a possible approach to prove it, based on spectral theory. Within this context, some authors formulated the question: is there a quantum mechanical system related to the sequence of prime numbers? In this Letter we assume that there is a class of hypothetical physical systems described by self-adjoint operators with countable infinite number of degrees of freedom with spectra given by the sequence of primes numbers. We prove a no-go theorem. We show that the generating functional of connected Schwinger functions of such theories cannot be constructed.
Probabilities and Signalling in Quantum Field Theory
Dickinson, Robert; Millington, Peter
2016-01-01
We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anti-commutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anti-commutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.
Random Matrix Theory and Quantum Chromodynamics
Akemann, Gernot
2016-01-01
These notes are based on the lectures delivered at the Les Houches Summer School in July 2015. They are addressed at a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part is devoted to the solution of the chiral Gaussian Unitary Ensemble in the presence of characteristic polynomials, using orthogonal polynomial techniques. This includes all eigenvalue density correlation functions, smallest eigenvalue distributions and their microscopic limit at the origin. These quantities are relevant for the description of the Dirac operator spectrum in Quantum Chromodynamics with three colours in four Euclidean space-time dimensions. In the second part these two theories are related based on symmetries, and the random matrix approximation is explained. In the last part recent developments are covered including the effect of finite chemical potential and finite space-time lattice spacing, and their corresponding orthogonal polynomials. We also give some ...
Quantum field theory and critical phenomena
Zinn-Justin, Jean
1996-01-01
Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions except gravity, but also for the understanding of second-order phase transitions in statistical mechanics. This advanced text is based on graduate courses and summer schools given by the author over a number of years. It approaches the subject in terms of path and functional intergrals, adopting a Euclidean metric and using the language of partition and correlation functions. Renormalization and the renormalization group are examined, as are critical phenomena and the role of instantons. Changes for this edition 1. Extensive revision to eliminate a few bugs that had survived the second edition and (mainly) to improve the pedagogical presentation, as a result of experience gathered by lecturing. 2. Additional new topics; holomorphic or coherent state path integral; functional integral and representation of the field theory S-matrix in the holomorphic formalis; non-relativistic li...
Quantum field theory on projective modules
Gayral, V; Krajewski, T; Wulkenhaar, R
2006-01-01
We propose a general formulation of perturbative quantum field theory on (finitely generated) projective modules over noncommutative algebras. This is the analogue of scalar field theories with non-trivial topology in the noncommutative realm. We treat in detail the case of Heisenberg modules over noncommutative tori and show how these models can be understood as large rectangular pxq matrix models, in the limit p/q->theta, where theta is a possibly irrational number. We find out that the modele is highly sensitive to the number-theoretical aspect of theta and suffers from an UV/IR-mixing. We give a way to cure the entanglement and prove one-loop renormalizability.
Scalar Quantum Field Theory on Fractals
Kar, Arnab
2011-01-01
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale invariant scalar field theories, by imitating Wiener's construction of the measure on the space of functions of one variable. These are Gaussian measures, except for one example of a non-Gaussian fixed point for the Ising model on a fractal. In the continuum limits what we construct have correlation functions that vary as a power of distance. In most cases this is a positive power (as for the Wiener measure) but we also find a few examples with negative exponent. In all cases the exponent is an irrational number, which depends on the particular subdivision scheme used. This suggests that the continuum limits corresponds to quantum field theories (random fields) on spaces of fractional dimension.
Quantum field theories on categories fibered in groupoids
Benini, Marco
2016-01-01
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first examples of homotopical quantum field theories resembling some aspects of gauge theories.
The black hole information problem beyond quantum theory
Mueller, Markus P; Dahlsten, Oscar C O
2012-01-01
The origin of black hole entropy and the black hole information problem provide important clues for trying to piece together a quantum theory of gravity. Thus far, discussions on this topic have mostly assumed that in a consistent theory of gravity and quantum mechanics, quantum theory will be unmodified. Here, we examine the black hole information problem in the context of generalisations of quantum theory. In particular, we examine black holes in the setting of generalised probabilistic theories, in which quantum theory and classical probability theory are special cases. We compute the time it takes information to escape a black hole, assuming that information is preserved. We find that under some very general assumptions, the arguments of Page (that information should escape the black hole after half the Hawking photons have been emitted), and the black-hole mirror result of Hayden and Preskill (that information can escape quickly) need to be modified. The modification is determined entirely by what we cal...
Elements of quantum computing history, theories and engineering applications
Akama, Seiki
2015-01-01
A quantum computer is a computer based on a computational model which uses quantum mechanics, which is a subfield of physics to study phenomena at the micro level. There has been a growing interest on quantum computing in the 1990's, and some quantum computers at the experimental level were recently implemented. Quantum computers enable super-speed computation, and can solve some important problems whose solutions were regarded impossible or intractable with traditional computers. This book provides a quick introduction to quantum computing for readers who have no backgrounds of both theory of computation and quantum mechanics. “Elements of Quantum Computing” presents the history, theories, and engineering applications of quantum computing. The book is suitable to computer scientists, physicist, and software engineers.
Nonequilibrium fermion production in quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Pruschke, Jens
2010-06-16
The creation of matter in the early universe or in relativistic heavy-ion collisions is inevitable connected to nonequilibrium physics. One of the key challenges is the explanation of the corresponding thermalization process following nonequilibrium instabilities. The role of fermionic quantum fields in such scenarios is discussed in the literature by using approximations of field theories which neglect important quantum corrections. This thesis goes beyond such approximations. A quantum field theory where scalar bosons interact with Dirac fermions via a Yukawa coupling is analyzed in the 2PI effective action formalism. The chosen approximation allows for a correct description of the dynamics including nonequilibrium instabilities. In particular, fermion-boson loop corrections allow to study the interaction of fermions with large boson fluctuations. The applied initial conditions generate nonequilibrium instabilities like parametric resonance or spinodal instabilities. The equations of motion for correlation functions are solved numerically and major characteristics of the fermion dynamics are described by analytical solutions. New mechanisms for the production of fermions are found. Simulations in the case of spinodal instability show that unstable boson fluctuations induce exponentially growing fermion modes with approximately the same growth rate. If the unstable regime lasts long enough a thermalization of the infrared part of the fermion occupation number occurs on time scales much shorter than the time scale on which bosonic quantum fields thermalize. Fermions acquire an excess of occupation in the ultraviolet regime compared to a Fermi-Dirac statistic characterized by a power-law with exponent two. The fermion production mechanism via parametric resonance is found to be most efficient after the instability ends. Quantum corrections then provide a very efficient particle creation mechanism which is interpreted as an amplification of decay processes. The ratio
The initial value problem in Lagrangian drift kinetic theory
Burby, J W
2015-01-01
Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low-orders. These unphysical modes, which may be rapidly oscillating, damped, or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem (Vlasov-Poisson for electrostatics, Vlasov-Darwin or Vlasov-Maxwell for electromagnetics.) In short, the system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, "renormalized" variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase space Lagrangian instead of the usual "field+particle" Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dime...
Snow avalanche friction relation based on extended kinetic theory
Rauter, Matthias; Fischer, Jan-Thomas; Fellin, Wolfgang; Kofler, Andreas
2016-11-01
Rheological models for granular materials play an important role in the numerical simulation of dry dense snow avalanches. This article describes the application of a physically based model from the field of kinetic theory to snow avalanche simulations. The fundamental structure of the so-called extended kinetic theory is outlined and the decisive model behavior for avalanches is identified. A simplified relation, covering the basic features of the extended kinetic theory, is developed and implemented into an operational avalanche simulation software. To test the obtained friction relation, simulation results are compared to velocity and runout observations of avalanches, recorded from different field tests. As reference we utilize a classic phenomenological friction relation, which is commonly applied for hazard estimation. The quantitative comparison is based on the combination of normalized residuals of different observation variables in order to take into account the quality of the simulations in various regards. It is demonstrated that the extended kinetic theory provides a physically based explanation for the structure of phenomenological friction relations. The friction relation derived with the help of the extended kinetic theory shows advantages to the classic phenomenological friction, in particular when different events and various observation variables are investigated.
Topos quantum theory reduced by context-selection functors
Nakayama, Kunji
2016-12-01
In this paper we deal with quantum theories on presheaves and sheaves on context categories consisting of commutative von Neumann algebras of bounded operators on a Hilbert space. Our aim is first to reduce presheaf-based topos quantum theory via sheafification and then to import quantum probabilities to the reduced sheaf quantum theory. The first is done by means of a functor that selects some expedient contexts. Note that since the functor defines a Grothendieck topology on the category consisting of all contexts, it induces a sheaf topos on which we construct a downsized quantum theory. We also show that the sheaf quantum theory can be replaced by a more manageable presheaf quantum theory. Quantum probabilities are imported by means of a Grothendieck topology that is defined on a category consisting of probabilities and that enables to regard them as intuitionistic truth-values. From these topologies, we construct another Grothendieck topology that is defined on the product of the context category and the probability category. It reflects the selection of contexts and the identification of probabilities with truth-values. We construct a quantum theory equipped with quantum probabilities as truth-values on the sheaf topos induced by the Grothendieck topology.
Dissipative time-dependent quantum transport theory.
Zhang, Yu; Yam, Chi Yung; Chen, GuanHua
2013-04-28
A dissipative time-dependent quantum transport theory is developed to treat the transient current through molecular or nanoscopic devices in presence of electron-phonon interaction. The dissipation via phonon is taken into account by introducing a self-energy for the electron-phonon coupling in addition to the self-energy caused by the electrodes. Based on this, a numerical method is proposed. For practical implementation, the lowest order expansion is employed for the weak electron-phonon coupling case and the wide-band limit approximation is adopted for device and electrodes coupling. The corresponding hierarchical equation of motion is derived, which leads to an efficient and accurate time-dependent treatment of inelastic effect on transport for the weak electron-phonon interaction. The resulting method is applied to a one-level model system and a gold wire described by tight-binding model to demonstrate its validity and the importance of electron-phonon interaction for the quantum transport. As it is based on the effective single-electron model, the method can be readily extended to time-dependent density functional theory.
The $\\hbar$ Expansion in Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Quantum Decision Theory in Simple Risky Choices.
Favre, Maroussia; Wittwer, Amrei; Heinimann, Hans Rudolf; Yukalov, Vyacheslav I; Sornette, Didier
2016-01-01
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker's choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains.
Quantum decision theory in simple risky choices
Favre, M; Heinimann, H R; Yukalov, V I; Sornette, D
2016-01-01
Quantum decision theory (QDT) is a novel theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker's choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) results, and find that our results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. We examine gender differences in our sample in order to illustrate how QDT can be used to differentiate between ...
Quantum theory of the generalised uncertainty principle
Bruneton, Jean-Philippe; Larena, Julien
2017-04-01
We extend significantly previous works on the Hilbert space representations of the generalized uncertainty principle (GUP) in 3 + 1 dimensions of the form [X_i,P_j] = i F_{ij} where F_{ij} = f({{P}}^2) δ _{ij} + g({{P}}^2) P_i P_j for any functions f. However, we restrict our study to the case of commuting X's. We focus in particular on the symmetries of the theory, and the minimal length that emerge in some cases. We first show that, at the algebraic level, there exists an unambiguous mapping between the GUP with a deformed quantum algebra and a quadratic Hamiltonian into a standard, Heisenberg algebra of operators and an aquadratic Hamiltonian, provided the boost sector of the symmetries is modified accordingly. The theory can also be mapped to a completely standard Quantum Mechanics with standard symmetries, but with momentum dependent position operators. Next, we investigate the Hilbert space representations of these algebraically equivalent models, and focus specifically on whether they exhibit a minimal length. We carry the functional analysis of the various operators involved, and show that the appearance of a minimal length critically depends on the relationship between the generators of translations and the physical momenta. In particular, because this relationship is preserved by the algebraic mapping presented in this paper, when a minimal length is present in the standard GUP, it is also present in the corresponding Aquadratic Hamiltonian formulation, despite the perfectly standard algebra of this model. In general, a minimal length requires bounded generators of translations, i.e. a specific kind of quantization of space, and this depends on the precise shape of the function f defined previously. This result provides an elegant and unambiguous classification of which universal quantum gravity corrections lead to the emergence of a minimal length.
The future (and past) of quantum theory after the Higgs boson: a quantum-informational viewpoint.
Plotnitsky, Arkady
2016-05-28
Taking as its point of departure the discovery of the Higgs boson, this article considers quantum theory, including quantum field theory, which predicted the Higgs boson, through the combined perspective of quantum information theory and the idea of technology, while also adopting anon-realistinterpretation, in 'the spirit of Copenhagen', of quantum theory and quantum phenomena themselves. The article argues that the 'events' in question in fundamental physics, such as the discovery of the Higgs boson (a particularly complex and dramatic, but not essentially different, case), are made possible by the joint workings of three technologies: experimental technology, mathematical technology and, more recently, digital computer technology. The article will consider the role of and the relationships among these technologies, focusing on experimental and mathematical technologies, in quantum mechanics (QM), quantum field theory (QFT) and finite-dimensional quantum theory, with which quantum information theory has been primarily concerned thus far. It will do so, in part, by reassessing the history of quantum theory, beginning with Heisenberg's discovery of QM, in quantum-informational and technological terms. This history, the article argues, is defined by the discoveries of increasingly complex configurations of observed phenomena and the emergence of the increasingly complex mathematical formalism accounting for these phenomena, culminating in the standard model of elementary-particle physics, defining the current state of QFT.
Generalized fluid theory including non-Maxwellian kinetic effects
Izacard, Olivier
2016-01-01
The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasma come mainly from the use of very CPU-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize t...
EDITORIAL: Focus on Quantum Information and Many-Body Theory
Eisert, Jens; Plenio, Martin B.
2010-02-01
Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac
Algebraic formulation of quantum theory, particle identity and entanglement
Govindarajan, T. R.
2016-08-01
Quantum theory as formulated in conventional framework using statevectors in Hilbert spaces misses the statistical nature of the underlying quantum physics. Formulation using operators 𝒞∗ algebra and density matrices appropriately captures this feature in addition leading to the correct formulation of particle identity. In this framework, Hilbert space is an emergent concept. Problems related to anomalies and quantum epistemology are discussed.
Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference
Leifer, M S
2011-01-01
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Classical probability theory is independent of causal structure, whereas the conventional quantum formalism requires causal structure to be fixed in advance. In this paper, we develop the formalism of quantum conditional states, which unifies the description of experiments involving two systems at a single time with the description of those involving a single system at two times. The analogies between quantum theory and classical probability theory are expressed succinctly within the formalism and it unifies the mathematical description of distinct concepts, such as ensemble preparation procedures, measurements, and quantum dynamics. We introduce a quantum generalization of Bayes' theorem and the associated notion of Bayesian conditioning. Conditioning a quantum state on a classical variable is the correct rule for updating quantum states in light of classical data...
Quantum field theory in curved spacetime and black hole thermodynamics
Wald, Robert M
1994-01-01
In this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth. This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum f...
Quantum correlations beyond entanglement and their role in quantum information theory
Streltsov, Alexander
2015-01-01
Quantum correlations are not restricted to the well known entanglement investigated in Bell-type experiments. Other forms of correlations, for example quantum discord, have recently been shown to play an important role in several aspects of quantum information theory. First experiments also support these findings. This book is an introduction into this up-and-coming research field and its likely impact on quantum technology. After giving a general introduction to the concept of quantum correlations and their role in quantum information theory, the author describes a number of pertinent results and their implications.
Kinetic theory of exciton-exciton annihilation.
May, Volkhard
2014-02-07
Weakly excited states of dye aggregates and supramolecular complexes can be characterized by single or two exciton states. Stronger excitation results in the presence of multiple excited molecules, and complex processes of internal energy transfer dynamics take place. The direct consideration of all excited states is limited to systems with a few molecules only. Therefore, an approach is used based on transition operators among the molecular states of interest and resulting in a dynamic theory for excitation energy transfer in strongly excited molecular systems. As a first application of this theory a detailed description of exciton-exciton annihilation is given. The obtained novel nonlinear theory is related to the standard description. Possible further approximation schemes in the offered theoretical framework are discussed.
Quantum Gravity from the Point of View of Locally Covariant Quantum Field Theory
Brunetti, Romeo; Fredenhagen, Klaus; Rejzner, Katarzyna
2016-08-01
We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.
The Einstein-Vlasov System/Kinetic Theory
Directory of Open Access Journals (Sweden)
Andréasson Håkan
2005-01-01
Full Text Available The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einsteins equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e. to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.
General System theory, Like-Quantum Semantics and Fuzzy Sets
Licata, Ignazio
2006-01-01
It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics . In conclusion we propose an example of formal quantum coherence.
What information theory can tell us about quantum reality
Adami, C
1998-01-01
An investigation of Einstein's ``physical'' reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schroedinger-cat paradoxes. Quantum reality, the picture based on unitarily evolving wavefunctions, is complete, but appears incomplete from the observer's point of view for fundamental reasons arising from the quantum information theory of measurement. Physical reality, the picture based on classically accessible observables is, in the worst case of EPR experiments, unrelated to the quantum reality it purports to reflect. Thus, quantum information theory implies that only correlations, not the correlata, are physically accessible: the mantra of the Ithaca interpretation of quantum mechanics.
Quantum gravity from descriptive set theory
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S
2004-03-01
We start from Hilbert's criticism of the axioms of classical geometry and the possibility of abandoning the Archimedean axiom. Subsequently we proceed to the physical possibility of a fundamental limitation on the smallest length connected to certain singular points in spacetime and below which measurements become meaningless, Finally we arrive at the conclusion that maximising the Hawking-Bekenstein informational content of spacetime makes the existence of a transfinite geometry for physical 'spacetime' not only plausible but probably inevitable. The main part of the paper is then concerned with a proposal for a mathematical description of a transfinite, non-Archimedean geometry using descriptive set theory. Nevertheless, and despite all abstract mathematics, we remain quite close to similar lines of investigation initiated by physicists like A. Wheeler, D. Finkelstein and G. 'tHooft. In particular we introduce a logarithmic gauge transformation linking classical gravity with the electro weak via a version of informational entropy. That way we may claim to have accomplished an important step towards a general theory of quantum gravity using {epsilon}{sup ({infinity}}{sup )} and complexity theory and finding that {alpha}{sub G}=(2){sup {alpha}}{sup -bar{sub ew-1}} congruent with (1.7)(10){sup 38} where {alpha}{sub G} is the dimensionless Newton gravity constant, and {alpha}{sub ew}{approx_equal}128 is the fine structure constant at the electro weak scale.
Continuum regularization of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
CDT-a entropic theory of quantum gravity
DEFF Research Database (Denmark)
Ambjørn, Jan; Görlich, A.; Jurkiewicz, J.
2010-01-01
High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Lattice (hep-lat)......High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Lattice (hep-lat)...
Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces
Wulkenhaar, R.
I give an introduction to Euclidean quantum field theory from the point of view of statistical physics, with emphasis both on Feynman graphs and on the Wilson-Polchinski approach to renormalisation. In the second part I discuss attempts to renormalise quantum field theories on noncommutative spaces.
There, and Back Again Quantum Theory and Global Optimisation
Audenaert, K M R
2004-01-01
We consider a problem in quantum theory that can be formulated as an optimisation problem and present a global optimisation algorithm for solving it, the foundation of which relies in turn on a theorem from quantum theory. To wit, we consider the maximal output purity $\
Objections to Handel's quantum theory of 1/f noise
Nieuwenhuizen, Th.M.; Frenkel, D.; Kampen, N.G. van
1987-01-01
A quantum theory of quantum 1/f noise was proposed by Handel in 1975. It relates 1/f noise in currents to infrared divergences in cross sections due to, e.g., soft-photon emission. We state a number of objections to this theory. Many of the points we raise have been raised before, but have not appea
Superconformal quantum field theories in string. Gauge theory dualities
Energy Technology Data Exchange (ETDEWEB)
Wiegandt, Konstantin
2012-08-14
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
Quantum optical effective-medium theory and transformation quantum optics for metamaterials
DEFF Research Database (Denmark)
Wubs, Martijn; Amooghorban, Ehsan; Zhang, Jingjing
2016-01-01
While typically designed to manipulate classical light, metamaterials have many potential applications for quantum optics as well. We argue why a quantum optical effective-medium theory is needed. We present such a theory for layered metamaterials that is valid for light propagation in all spatial...... directions, thereby generalizing earlier work for one-dimensional propagation. In contrast to classical effective-medium theory there is an additional effective parameter that describes quantum noise. Our results for metamaterials are based on a rather general Lagrangian theory for the quantum...
Lectures on algebraic quantum field theory and operator algebras
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Berlin Univ. (Germany). Institut fuer Theoretische Physik. E-mail: schroer@cbpf.br
2001-04-01
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)
Two Quantum Effects In The Theory Of Gravitation
Robinson, S P
2005-01-01
We will discuss two methods by which the formalism of quantum field theory can be included in calculating the physical effects of gravitation. In the first of these, the consequences of treating general relativity as an effective quantum field theory will be examined. The primary result will be the calculation of the first-order quantum gravity corrections to the β functions of arbitrary Yang-Mills theories. These corrections will effect the high-energy phenomenology of such theories, including the details of coupling constant unification. Following this, we will address the question of how to form effective quantum field theories in classical gravitational backgrounds. We follow the prescription that effective theories should provide a description of experimentally accessible degrees of freedom with all other degrees of freedom integrated out of the theory. We will show that this prescription appears to fail for a scalar field in a black hole background because of an anomaly generated in general cov...
Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.
Gao, J
2016-01-01
Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.
Frahm, K M; Shepelyansky, D L; Fleckinger, Robert; Frahm, Klaus M.; Shepelyansky, Dima L.
2004-01-01
We determine the universal law for fidelity decay in quantum computations of complex dynamics in presence of internal static imperfections in a quantum computer. Our approach is based on random matrix theory applied to quantum computations in presence of imperfections. The theoretical predictions are tested and confirmed in extensive numerical simulations of a quantum algorithm for quantum chaos in the dynamical tent map with up to 18 qubits. The theory developed determines the time scales for reliable quantum computations in absence of the quantum error correction codes. These time scales are related to the Heisenberg time, the Thouless time, and the decay time given by Fermi's golden rule which are well known in the context of mesoscopic systems. The comparison is presented for static imperfection effects and random errors in quantum gates. A new convenient method for the quantum computation of the coarse-grained Wigner function is also proposed.
Preference reversal in quantum decision theory.
Yukalov, Vyacheslav I; Sornette, Didier
2015-01-01
We consider the psychological effect of preference reversal and show that it finds a natural explanation in the frame of quantum decision theory. When people choose between lotteries with non-negative payoffs, they prefer a more certain lottery because of uncertainty aversion. But when people evaluate lottery prices, e.g., for selling to others the right to play them, they do this more rationally, being less subject to behavioral biases. This difference can be explained by the presence of the attraction factors entering the expression of quantum probabilities. Only the existence of attraction factors can explain why, considering two lotteries with close utility factors, a decision maker prefers one of them when choosing, but evaluates higher the other one when pricing. We derive a general quantitative criterion for the preference reversal to occur that relates the utilities of the two lotteries to the attraction factors under choosing vs. pricing and test successfully its application on experiments by Tversky et al. We also show that the planning paradox can be treated as a kind of preference reversal.
Protected gates for topological quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Beverland, Michael E.; Pastawski, Fernando; Preskill, John [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125 (United States); Buerschaper, Oliver [Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin (Germany); Koenig, Robert [Institute for Advanced Study and Zentrum Mathematik, Technische Universität München, 85748 Garching (Germany); Sijher, Sumit [Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
2016-02-15
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Eu, Byung Chan
2016-01-01
This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respe...
Quantitative study of kinetic ballooning mode theory in simple geometry
Aleynikova, Ksenia; Zocco, Alessandro
2017-09-01
The theory of kinetic ballooning modes (KBMs) in a magnetically confined toroidal plasma is studied analytically and numerically by means of gyrokinetic simulations. A physics-based ordering for β (the ratio of kinetic to magnetic plasma pressure) with small asymptotic parameters is found. This allows us to derive several simplified limits of previously known theories. We introduce a variational approach which provides explicit dispersion relations in terms of integrals of quadratic forms constructed from numerical eigenfunctions. It is found that, for large pressure gradients, the growth rate and frequencies computed by gyrokinetic codes show excellent agreement with those evaluated by using a diamagnetic modification of ideal magnetohydrodynamic if geometric drifts are kept consistent with the equilibrium pressure gradient. For moderate pressure gradients, a new finite-β formulation of the KBM theory is proposed. Also in this case, a good agreement between numerical simulations and analytical theory is found.
Heating of metals at a free surface by laser irradiation - an electron kinetic theory approach
Energy Technology Data Exchange (ETDEWEB)
Yilbas, B.S.
1986-05-01
Application of Fourier theory to heat conduction due to laser irradiation at high power intensities (i.e. 10/sup 10/ W/m/sup 2/) gives errors of the order of 30 per cent at the upper end of the temperature rise time. This is caused by the assumptions made in the Fourier theory, since the heat flux through a given plane depends on the electron energy distribution through the material. On the scale of distance required to examine the problem, the material can no longer be considered as being a homogeneous continuum and when the power intensities of interest are concerned, the higher order terms in the heat transfer equation become important. Therefore, the problem requires to be examined in the quantum field. Application of electron kinetic theory to the problem enhances the solution within an accuracy greater than 90 per cent. The present theory introduces a new model for the conduction mechanism.
Classical geometry from the quantum Liouville theory
Hadasz, L; Piatek, M; Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin
2005-01-01
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Classical geometry from the quantum Liouville theory
Energy Technology Data Exchange (ETDEWEB)
Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl
2005-09-26
Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.
Quasiparticle excitations in relativistic quantum field theory
Arteaga, Daniel
2008-01-01
We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.
Radiation reaction in quantum field theory
Higuchi, Atsushi
2002-11-01
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant α and in the small ħ approximation. We show that it disagrees with the result obtained using the Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. However, the discrepancy is much smaller than the Compton wavelength of the particle. We also point out that the electromagnetic correction to the potential has no classical limit.
Quantum field theory lectures of Sidney Coleman
Derbes, David; Griffiths, David; Hill, Brian; Sohn, Richard; Ting, Yuan-Sen
2017-01-01
Sidney Coleman was a physicist's physicist. He is largely unknown outside of the theoretical physics community, and known only by reputation to the younger generation. He was an unusually effective teacher, famed for his wit, his insight and his encyclopedic knowledge of the field to which he made many important contributions. There are many first-rate quantum field theory books (the ancient Bjorken and Drell, the more modern Itzykson and Zuber, the now-standard Peskin and Schroder, and the recent Zee), but the immediacy of Prof. Coleman's approach and his ability to present an argument simply without sacrificing rigor makes his book easy to read and ideal for the student. Part of the motivation in producing this book is to pass on the work of this outstanding physicist to later generations, a record of his teaching that he was too busy to leave himself.
Quantum graphs and random-matrix theory
Pluhař, Z.; Weidenmüller, H. A.
2015-07-01
For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit (BGS) conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that the generating function for every (P,Q) correlation function for both closed and open graphs coincides with the corresponding expression of random-matrix theory. We show that the classical Perron-Frobenius operator is bistochastic and possesses a single eigenvalue +1. In the quantum case that implies the existence of a zero (or massless) mode of the effective action. That mode causes universal fluctuation properties. Avoiding the saddle-point approximation we show that for graphs that are classically mixing (i.e. for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap) and that do not carry a special class of bound states, the zero mode dominates in the limit of infinite graph size.
A state-dependent noncontextuality inequality in algebraic quantum theory
Kitajima, Yuichiro
2017-08-01
The noncontextuality condition states that a value of any observable is independent of which other compatible observable is measured jointly with it. Klyachko, Can, Binicioğlu, and Shumovsky have introduced an inequality which holds if there is a noncontextual hidden variable theory. It is called KCBS inequality, which is state-dependent. Its violation shows a contradiction between predictions of quantum theory and noncontextual hidden variable theories. In the present paper, it is shown that there is a state which does not violate KCBS inequality in the case of quantum mechanics of finite degrees of freedom, and that any normal state violates it in the case of algebraic quantum field theory. It is a difference between quantum mechanics of finite degrees of freedom and algebraic quantum field theory from a point of view of KCBS inequality.
Quantum Field Theory on Pseudo-Complex Spacetime
Schuller, F P; Grimm, T W; Schuller, Frederic P.; Wohlfarth, Mattias N.R.; Grimm, Thomas W.
2003-01-01
The pseudo-complex Poincare group encodes both a universal speed and a maximal acceleration, which can be viewed as the kinematics of Born-Infeld electrodynamics. The irreducible representations of this group are constructed, providing the particle spectrum of a relativistic quantum theory that also respects a maximal acceleration. One finds that each standard relativistic particle is associated with a 'pseudo'-partner of equal spin but generically different mass. These pseudo-partners act as Pauli-Villars regulators for the other member of the doublet, as is found from the explicit construction of quantum field theory on pseudo-complex spacetime. Conversely, a Pauli-Villars regularised quantum field theory on real spacetime possesses a field phase space with integrable pseudo-complex structure, which gives rise to a quantum field theory on pseudo-complex spacetime. This equivalence between (i) maximal acceleration kinematics, (ii) pseudo-complex quantum field theory, and (iii) Pauli-Villars regularisation ri...
Quantum theory of chemical reaction rates
Energy Technology Data Exchange (ETDEWEB)
Miller, W.H. [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry]|[Lawrence Berkeley Lab., CA (United States). Chemical Sciences Div.
1994-10-01
If one wishes to describe a chemical reaction at the most detailed level possible, i.e., its state-to-state differential scattering cross section, then it is necessary to solve the Schroedinger equation to obtain the S-matrix as a function of total energy E and total angular momentum J, in terms of which the cross sections can be calculated as given by equation (1) in the paper. All other physically observable attributes of the reaction can be derived from the cross sections. Often, in fact, one is primarily interested in the least detailed quantity which characterizes the reaction, namely its thermal rate constant, which is obtained by integrating Eq. (1) over all scattering angles, summing over all product quantum states, and Boltzmann-averaging over all initial quantum states of reactants. With the proper weighting factors, all of these averages are conveniently contained in the cumulative reaction probability (CRP), which is defined by equation (2) and in terms of which the thermal rate constant is given by equation (3). Thus, having carried out a full state-to-state scattering calculation to obtain the S-matrix, one can obtain the CRP from Eq. (2), and then rate constant from Eq. (3), but this seems like ``overkill``; i.e., if one only wants the rate constant, it would clearly be desirable to have a theory that allows one to calculate it, or the CRP, more directly than via Eq. (2), yet also correctly, i.e., without inherent approximations. Such a theory is the subject of this paper.
Building a Hydrodynamics Code with Kinetic Theory
Sagert, Irina; Colbry, Dirk; Pickett, Rodney; Strother, Terrance
2013-01-01
We report on the development of a test-particle based kinetic Monte Carlo code for large systems and its application to simulate matter in the continuum regime. Our code combines advantages of the Direct Simulation Monte Carlo and the Point-of-Closest-Approach methods to solve the collision integral of the Boltzmann equation. With that, we achieve a high spatial accuracy in simulations while maintaining computational feasibility when applying a large number of test-particles. The hybrid setup of our approach allows us to study systems which move in and out of the hydrodynamic regime, with low and high particle densities. To demonstrate our code's ability to reproduce hydrodynamic behavior we perform shock wave simulations and focus here on the Sedov blast wave test. The blast wave problem describes the evolution of a spherical expanding shock front and is an important verification problem for codes which are applied in astrophysical simulation, especially for approaches which aim to study core-collapse supern...
Cui, Ping
The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO
Quantum kinetics of ultracold fermions coupled to an optical resonator
Piazza, Francesco; Strack, Philipp
2014-10-01
We study the far-from-equilibrium statistical mechanics of periodically driven fermionic atoms in a lossy optical resonator. We show that the interplay of the Fermi surface with cavity losses leads to subnatural cavity linewidth narrowing, squeezed light, and nonthermal quantum statistics of the atoms. Adapting the Keldysh approach, we set up and solve a quantum kinetic Boltzmann equation in a systematic 1/N expansion with N the number of atoms. In the strict thermodynamic limit N ,V→∞,N/V=const. we find that the atoms (fermions or bosons) remain immune against cavity-induced heating or cooling. At next-to-leading order in 1/N, we find a "one-way thermalization" of the atoms determined by cavity decay. In absence of an equilibrium fluctuation-dissipation relation, the long-time limit Δt →∞ does not commute with the thermodynamic limit N →∞, such that for the physically relevant case of large but finite N, the dynamics ultimately becomes strongly coupled, especially close to the superradiance phase transition.
Automated Transition State Theory Calculations for High-Throughput Kinetics.
Bhoorasingh, Pierre L; Slakman, Belinda L; Seyedzadeh Khanshan, Fariba; Cain, Jason Y; West, Richard Henry
2017-08-18
A scarcity of known chemical kinetic parameters leads to the use of many reaction rate estimates, which are not always sufficiently accurate, in the construction of detailed kinetic models. To reduce the reliance on these estimates and improve the accuracy of predictive kinetic models, we have developed a high-throughput, fully automated, reaction rate calculation method, AutoTST. The algorithm integrates automated saddle-point geometry search methods and a canonical transition state theory kinetics calculator. The automatically calculated reaction rates compare favorably to existing estimated rates. Comparison against high level theoretical calculations show the new automated method performs better than rate estimates when the estimate is made by a poor analogy. The method will improve by accounting for internal rotor contributions and by improving methods to determine molecular symmetry.
Quantum and concept combination, entangled measurements, and prototype theory.
Aerts, Diederik
2014-01-01
We analyze the meaning of the violation of the marginal probability law for situations of correlation measurements where entanglement is identified. We show that for quantum theory applied to the cognitive realm such a violation does not lead to the type of problems commonly believed to occur in situations of quantum theory applied to the physical realm. We briefly situate our quantum approach for modeling concepts and their combinations with respect to the notions of "extension" and "intension" in theories of meaning, and in existing concept theories.
Analyzing Students’ Level of Understanding on Kinetic Theory of Gases
Nurhuda, T.; Rusdiana, D.; Setiawan, W.
2017-02-01
The purpose of this research is to analysis students’ level of understanding on gas kinetic theory. The method used is descriptive analytic with 32 students at the 11th grade of one high school in Bandung city as a sample. The sample was taken using random sampling technique. Data collection tool used is an essay test with 23 questions. The instrument was used to identify students’ level of understanding and was judged by four expert judges before it was employed, from 27 questions become to 23 questions, for data collection. Questions used are the conceptual understanding including the competence to explain, extrapolate, translate and interpret. Kinetic theory of gases section that was tested includes ideal gas law, kinetic molecular theory and equipartition of energy. The result shows from 0-4 level of understanding, 19% of the students have partial understanding on the 3th level and 81% of them have partial understanding with a specific misconception on 2th level. For the future research, it is suggested to overcome these conceptual understanding with an Interactive Lecture Demonstrations teaching model and coupled with some teaching materials based on multi-visualization because kinetic theory of gases is a microscopic concept.
Kinetic theory and turbulent discontinuities. [shock tube flow
Johnson, J. A., III; I, L.; Li, Y.; Ramaian, R.; Santigo, J. P.
1981-01-01
Shock tube discontinuities were used to test and extend a kinetic theory of turbulence. In shock wave and contact surface fluctuations, coherent phenomena were found which provide new support for the microscopic nonempirical approach to turbulent systems, especially those with boundary layer-like instabilities.
Linear kinetic theory and particle transport in stochastic mixtures
Energy Technology Data Exchange (ETDEWEB)
Pomraning, G.C. [Univ. of California, Los Angeles, CA (United States)
1995-12-31
We consider the formulation of linear transport and kinetic theory describing energy and particle flow in a random mixture of two or more immiscible materials. Following an introduction, we summarize early and fundamental work in this area, and we conclude with a brief discussion of recent results.
Adiabatic quantum computation and quantum annealing theory and practice
McGeoch, Catherine C
2014-01-01
Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'''' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a nov
Low-Energy Effective Theories of Quantum Link and Quantum Spin Models
Schlittgen, B
2001-01-01
Quantum spin and quantum link models provide an unconventional regularization of field theory in which classical fields arise via dimensional reduction of discrete variables. This D-theory regularization leads to the same continuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state path integral techniques. We illustrate our method for the $(2+1)$-d Heisenberg quantum spin model which is the D-theory regularization of the 2-d O(3) model. Similarly, we prove that in the continuum limit a $(2+1)$-d quantum spin model with $SU(N)_L\\times SU(N)_R\\times U(1)_{L=R}$ symmetry is equivalent to the 2-d principal chiral model. Finally, we show that $(4+1)$-d SU(N) quantum link models reduce to ordinary 4-d Yang-Mills theory.
Pilot-wave approaches to quantum field theory
Struyve, Ward
2011-01-01
The purpose of this paper is to present an overview of recent work on pilot-wave approaches to quantum field theory. In such approaches, systems are not only described by their wave function, as in standard quantum theory, but also by some additional variables. In the non-relativistic pilot-wave theory of de Broglie and Bohm those variables are particle positions. In the context of quantum field theory, there are two natural choices, namely particle positions and fields. The incorporation of those variables makes it possible to provide an objective description of nature in which rather ambiguous notions such as `measurement' and `observer' play no fundamental role. As such, the theory is free of the conceptual difficulties, such as the measurement problem, that plague standard quantum theory.
Limited Holism and Real-Vector-Space Quantum Theory
Hardy, Lucien
2010-01-01
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by "bilocal tomography": the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic.
Limited Holism and Real-Vector-Space Quantum Theory
Hardy, Lucien; Wootters, William K.
2012-03-01
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by "bilocal tomography": the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic.
Quantum groups and quantum field theory III. Renormalisation
Brouder, C; Brouder, Christian; Schmitt, William
2002-01-01
The Hopf algebra of renormalisation in quantum field theory is described at a general level. The products of fields at a point are assumed to form a bialgebra B and renormalisation endows T(T(B)^+), the double tensor algebra of B, with the structure of a noncommutative bialgebra. When the bialgebra B is commutative, renormalisation turns S(S(B)^+), the double symmetric algebra of B, into a commutative bialgebra. The usual Hopf algebra of renormalisation is recovered when the elements of $T^1(B)$ are not renormalised, i.e. when Feynman diagrams containing one single vertex are not renormalised. When B is the Hopf algebra of a commutative group, a homomorphism is established between the bialgebra S(S(B)^+) and the Faa di Bruno bialgebra of composition of series. The relation with the Connes-Moscovici Hopf algebra of diffeomorphisms is given. Finally, the bialgebra S(S(B)^+) is shown to give the same results as the standard renormalisation procedure for the scalar field.
Entanglement negativity in quantum field theory.
Calabrese, Pasquale; Cardy, John; Tonni, Erik
2012-09-28
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem [formula: see text], and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln//ρ(A)(T(2))//. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))] for the case of two adjacent intervals of lengths ℓ(1), ℓ(2) in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
Gravitational Quantum Foam and Supersymmetric Gauge Theories
Maeda, T; Noma, Y; Tamakoshi, T; Maeda, Takashi; Nakatsu, Toshio; Noma, Yui; Tamakoshi, Takeshi
2005-01-01
We study K\\"{a}hler gravity on local SU(N) geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of an infinite number of gravitational quanta. We count these quanta in a relative manner by measuring a deviation of the local geometry from a singular Calabi-Yau threefold, that is a A_{N-1} singularity fibred over \\mathbb{P}^1. With such a regularization prescription, the number of the gravitational quanta becomes finite and turns to be the perturbative prepotential for five-dimensional \\mathcal{N}=1 supersymmetric SU(N) Yang-Mills. These quanta are labelled by lattice points in a certain convex polyhedron on \\mathbb{R}^3. The polyhedron becomes obtainable from a plane partition which is the ground state of a statistical model of random plane partition that describes the exact partition function for the gauge theory. Each gravitational quantum of the local geometry is shown...
Reflections on Topological Quantum Field Theory
Picken, R F
1997-01-01
(Talk presented at the XVth Workshop on Geometric Methods in Physics, Quantizations, Deformations and Coherent States, in Bialowieza, Poland, July 1-7, 1996.) The aim of this article is to introduce some basic notions of Topological Quantum Field Theory (TQFT) and to consider a modification of TQFT, applicable to embedded manifolds. After an introduction based around a simple example (Section 1) the notion of a d-dimensional TQFT is defined in category-theoretical terms, as a certain type of functor from a category of d-dimensional cobordisms to the category of vector spaces (Section 2). A construction due to Turaev, an operator-valued invariant of tangles, is discussed in Section 3. It bears a strong resemblance to 1-dimensional TQFTs, but carries much richer structure due to the fact that the 1-dimensional manifolds involved are embedded in a 3-dimensional space. This leads us, in Section 4, to propose a class of TQFT-like theories, appropriate to embedded, rather than pure, manifolds.
Consistent chiral kinetic theory in Weyl materials: chiral magnetic plasmons
Gorbar, E V; Shovkovy, I A; Sukhachov, P O
2016-01-01
We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern--Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. T...
Kinetic theory and quasilinear theories of jet dynamics
Bouchet, F; Tangarife, T
2016-01-01
We review progress that has been made to constructa theory for the jet formation and maintenance in planetary atmospheres. The theory is built in the regime where velocityfluctuations around the base jet are very small compared to the zonaljet velocity itself. Such situations are frequent in many naturaljets, for instance in the atmosphere of outer planets, the most prominentexample being probably Jupiter's troposphere jets. As discussed inother chapters of this book, fluctuations close to Jupiter zonaljets are smaller than the zonal jets themselves. In such a regime, it is natural and often justified to treat the non-zonalpart of the dynamics with a quasi-linear approximation: at leadingorder the dynamics of the non-zonal flow is described by theequation linearized close to the quasi-stationary zonal jets. The theory, based on a multi-scale method called stochastic averaging, share similarities with Stochastic Structural Stability Theory (S3T) and with second order closure(CE2), also discussed in other chapt...
Lütkenhaus, N.; Shields, A. J.
2009-04-01
work done to date relates to point-to-point links. Another recent advance has been the development of trusted networks for QKD. This is important for further increasing the range of the technology, and for overcoming denial-of-service attacks on an individual link. It is interesting to see that the optimization of QKD devices differs for point-to-point and network applications. Network operation is essential for widespread adoption of the technology, as it can dramatically reduce the deployment costs and allow connection flexibility. Also important is the multiplexing of the quantum signals with conventional network traffic. For the future, quantum repeaters should be developed for longer range links. On the theoretical side, different approaches to security proofs have recently started to converge, offering several paradigms of the same basic idea. Our improved theoretical understanding places more stringent demands on the QKD devices. We are aware by now that finite size effects in key generation arise not only from parameter estimation. It will not be possible to generate a key from just a few hundred received signals. It is a stimulating challenge for the theory of security proofs to develop lean proof strategies that work with finite signal block sizes. As QKD advances to a real-world cryptographic solution, side channel attacks must be carefully analysed. Theoretical security proofs for QKD schemes are so far based on physical models of these devices. It is in the nature of models that any real implementation will deviate from this model, creating a potential weakness for an eavesdropper to exploit. There are two solutions to this problem: the traditional path of refining the models to reduce the deviations, or the radically different approach of device-independent security proofs, in which none or only a few well controlled assumptions about the devices are made. Clearly, it is desirable to find security proofs that require only minimal or fairly general model
Institute of Scientific and Technical Information of China (English)
QIAN Shang-Wu; GU Zhi-Yu
2003-01-01
This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of m≥3 nodes.
Group Field Theory and Loop Quantum Gravity
Oriti, Daniele
The following sections are included: * GFT from LQG Perspective: The Underlying Ideas * GFT Kinematics: Hilbert Space and Observables * The Quantum Dynamics * The Continuum Limit of Quantum Geometry in GFT * Extracting Effective Continuum Physics from GFTs * Conclusions * References
Theory of an optomechanical quantum heat engine
2014-08-12
generation of quantum interfaces between light and mechani - cal systems with broad potential for applications in quantum technology. One example is the... quantum heat engine. This heat engine is based on an Otto cycle between a cold photonic reservoirand a hot phononic reservoir [K. Zhang, F. Bariani, and...efficiency of the engine and (ii) perform an investigation of the quantum thermodynamics underlying this scheme. In particular, we analyze the
Foundations of quantum theory from classical concepts to operator algebras
Landsman, Klaas
2017-01-01
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.
Perturbative Quantum Field Theory in the String-Inspired Formalism
Schubert, C
2001-01-01
We review the status and present range of applications of the ``string-inspired'' approach to perturbative quantum field theory. This formalism offers the possibility of computing effective actions and S-matrix elements in a way which is similar in spirit to string perturbation theory, and bypasses much of the apparatus of standard second-quantized field theory. Its development was initiated by Bern and Kosower, originally with the aim of simplifying the calculation of scattering amplitudes in quantum chromodynamics and quantum gravity. We give a short account of the original derivation of the Bern-Kosower rules from string theory. Strassler's alternative approach in terms of first-quantized particle path integrals is then used to generalize the formalism to more general field theories, and, in the abelian case, also to higher loop orders. A considerable number of sample calculations are presented in detail, with an emphasis on quantum electrodynamics.
Quantum theory and the role of mind in nature
Stapp, Henry P
2001-01-01
Orthodox Copenhagen quantum theory renounces the quest to understand the reality in which we are imbedded, and settles for practical rules describing connections between our observations. Many physicist have regarded this renunciation of our effort to describe nature herself as premature, and John von Neumann reformulated quantum theory as a theory of an evolving objective universe interacting with human consciousness. This interaction is associated both in Copenhagen quantum theory and in von Neumann quantum theory with a sudden change that brings the objective physical state of a system in line with a subjectively felt psychical reality. The objective physical state is thereby converted from a material substrate to an informational and dispositional substrate that carries both the information incorporated into it by the psychical realities, and certain dispositions for the occurrence of future psychical realities. The present work examines and proposes solutions to two problems that have appeared to block t...
Andreev, Pavel A
2014-01-01
We discuss complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider contribution of the annihilation interaction in the quantum hydrodynamic equations and in spectrum of waves in magnetized electron-positron plasmas. We consider propagation of waves parallel and perpendicular to an external magnetic field. We also consider oblique propagation of longitudinal waves. We derive set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory for the linear wave behavior in absence of external fields. We calculate contribution of the Darwin...
Rodríguez, Juan I; Ayers, Paul W; Götz, Andreas W; Castillo-Alvarado, F L
2009-07-14
A new approach for computing the atom-in-molecule [quantum theory of atoms in molecule (QTAIM)] energies in Kohn-Sham density-functional theory is presented and tested by computing QTAIM energies for a set of representative molecules. In the new approach, the contribution for the correlation-kinetic energy (T(c)) is computed using the density-functional theory virial relation. Based on our calculations, it is shown that the conventional approach where atomic energies are computed using only the noninteracting part of the kinetic energy might be in error by hundreds of kJ/mol.
Diffusion, quantum theory, and radically elementary mathematics (MN-47)
Faris, William G
2014-01-01
Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein''s work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book''s inspiration is Princeton University mathematics professor Edward Nelson''s influential work in
Quantum theory of the solid state part B
Callaway, Joseph
1974-01-01
Quantum Theory of the Solid State, Part B describes the concepts and methods of the central problems of the quantum theory of solids. This book discusses the developed machinery applied to impurities, disordered systems, effects of external fields, transport phenomena, and superconductivity. The representation theory, low field diamagnetic susceptibility, electron-phonon interaction, and Landau theory of fermi liquids are also deliberated. This text concludes with an introduction to many-body theory and some applications. This publication is a suitable textbook for students who have completed
Quantum resource theories in the single-shot regime
Gour, Gilad
2017-06-01
One of the main goals of any resource theory such as entanglement, quantum thermodynamics, quantum coherence, and asymmetry, is to find necessary and sufficient conditions that determine whether one resource can be converted to another by the set of free operations. Here we find such conditions for a large class of quantum resource theories which we call affine resource theories. Affine resource theories include the resource theories of athermality, asymmetry, and coherence, but not entanglement. Remarkably, the necessary and sufficient conditions can be expressed as a family of inequalities between resource monotones (quantifiers) that are given in terms of the conditional min-entropy. The set of free operations is taken to be (1) the maximal set (i.e., consists of all resource nongenerating quantum channels) or (2) the self-dual set of free operations (i.e., consists of all resource nongenerating maps for which the dual map is also resource nongenerating). As an example, we apply our results to quantum thermodynamics with Gibbs preserving operations, and several other affine resource theories. Finally, we discuss the applications of these results to resource theories that are not affine and, along the way, provide the necessary and sufficient conditions that a quantum resource theory consists of a resource destroying map.
The quantum theory of nonlinear optics
Drummond, Peter D
2014-01-01
Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamic...
Non perturbative methods in two dimensional quantum field theory
Abdalla, Elcio; Rothe, Klaus D
1991-01-01
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
The Development of Elementary Quantum Theory from 1900 to 1927
Capellmann, Herbert
2016-01-01
Planck's introduction of the quantum of action in 1900 was followed by 25 years of trial and error in quest of the understanding of the quantum world; different ideas and directions had to be pursued until the path leading to the elementary quantum theory was discovered. Radical changes away from traditional perceptions about natural phenomena were necessary, the entire system of basic concepts in classical physics had to be abandoned and replaced by a new mode of thought. Continuity and determinism of classical laws were no longer applicable on the quantum scale, where dynamical behaviour proceeds by discontinuous and statistical quantum transitions. Albert Einstein laid the essential foundations for the new concept; Max Born made the decisive step further leading to the breakthrough in 1925. The development of the ideas, which eventually resulted in the elementary quantum theory in 1925/26, will be described, relying on original publications and letters written during that period in time by the major contri...
Kinetic theory and long range correlations in moderately dense gases
Energy Technology Data Exchange (ETDEWEB)
Petrosky, T.; Prigogine, I. [Univ. of Texas, Austin, TX (United States)
1997-01-01
The complex spectral representation of the Liouville operator is applied to moderately dense gases interacting through hard-core potentials in arbitrary d-dimensional spaces. It is shown that Markovian kinetic equations exist for all d. This provides an answer to the long standing question do kinetic equations exist in two dimensional systems. The non-Markovian effects, such as the long-time tails for arbitrary n-mode coupling, are estimated by superposition of the Markovian evolutions in each subspace as introduced in our spectral decomposition. The long-time tail effects invalidate the traditional kinetic theory based on a truncation of BBGKY hierarchy for d < 4, as well as the Green-Kubo formalism, as there appear contributions of order t{sup -1}, t{sup -{1/2}},... coming from multiple mode-mode couplings even for d = 3.
Aquilanti, Vincenzo; Coutinho, Nayara Dantas; Carvalho-Silva, Valter Henrique
2017-03-01
This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature. This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.
The structure of states and maps in quantum theory
Indian Academy of Sciences (India)
Sudhavathani Simon; S P Rajagopalan; R Simon
2009-09-01
The structure of statistical state spaces in the classical and quantum theories are compared in an interesting and novel manner. Quantum state spaces and maps on them have rich convex structures arising from the superposition principle and consequent entanglement. Communication channels (physical processes) in the quantum scheme of things are in one-to-one correspondence with completely positive maps. Positive maps which are not completely positive do not correspond to physical processes. Nevertheless they prove to be invaluable mathematical tools in establishing or witnessing entanglement of mixed states. We consider some of the recent developments in our understanding of the convex structure of states and maps in quantum theory, particularly in the context of quantum information theory.
Entropy in quantum information theory - Communication and cryptography
DEFF Research Database (Denmark)
Majenz, Christian
to density matrices, the von Neumann entropy behaves dierently. The latter does not, for example, have the monotonicity property that the latter possesses: When adding another quantum system, the entropy can decrease. A long-standing open question is, whether there are quantum analogues of unconstrained non......Entropies have been immensely useful in information theory. In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. The rst one concerns the von Neumann entropy. While a direct generalization of the Shannon entropy...... in quantum Shannon theory. While immensely more entanglement-consuming, the variant of port based teleportation is interesting for applications like instantaneous non-local computation and attacks on quantum position-based cryptography. Port based teleportation cannot be implemented perfectly...
Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory
Dolce, Donatello
2016-01-01
In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In thi...
Haag's Theorem and Parameterized Quantum Field Theory
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Quantum game theory and open access publishing
Hanauske, Matthias; Bernius, Steffen; Dugall, Berndt
2007-08-01
The digital revolution of the information age and in particular the sweeping changes of scientific communication brought about by computing and novel communication technology, potentiate global, high grade scientific information for free. The arXiv, for example, is the leading scientific communication platform, mainly for mathematics and physics, where everyone in the world has free access on. While in some scientific disciplines the open access way is successfully realized, other disciplines (e.g. humanities and social sciences) dwell on the traditional path, even though many scientists belonging to these communities approve the open access principle. In this paper we try to explain these different publication patterns by using a game theoretical approach. Based on the assumption, that the main goal of scientists is the maximization of their reputation, we model different possible game settings, namely a zero sum game, the prisoners’ dilemma case and a version of the stag hunt game, that show the dilemma of scientists belonging to “non-open access communities”. From an individual perspective, they have no incentive to deviate from the Nash equilibrium of traditional publishing. By extending the model using the quantum game theory approach it can be shown, that if the strength of entanglement exceeds a certain value, the scientists will overcome the dilemma and terminate to publish only traditionally in all three settings.
Finiteness of cominuscule quantum K-theory
Buch, Anders; Mihalcea, Leonardo C; Perrin, Nicolas
2010-01-01
The product of two Schubert classes in the quantum K-theory ring of a homogeneous space X = G/P is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on X. We show that if X is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to X that take the marked points to general Schubert varieties and whose domains are reducible curves of genus zero. We show that all such varieties have rational singularities, and that boundary Gromov-Witten varieties defined by two Schubert varieties are either empty or unirational. We also prove a relative Kleiman-Bertini theorem for rational singularities, which is of independent interest. A key result is that when X is cominuscule, all boundary Gromov-Witten varieties defined by three single points in X are rationally connected.
Generalized fluid theory including non-Maxwellian kinetic effects
Izacard, Olivier
2017-04-01
The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker-Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function (e.g. the INMDF (Izacard, O. 2016b Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas. Phys. Plasmas 23, 082504) that stands for interpreted non-Maxwellian distribution function). One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. The results
On the embedding of quantum field theory on curved spacetimes into loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Stottmeister, Alexander
2015-07-15
The main theme of this thesis is an investigation into possible connections between loop quantum gravity and quantum field theory on curved spacetimes: On the one hand, we aim for the formulation of a general framework that allows for a derivation of quantum field theory on curved spacetimes in a semi-classical limit. On the other hand, we discuss representation-theoretical aspects of loop quantum gravity and quantum field theory on curved spacetimes as both of the latter presumably influence each other in the aforesaid semi-classical limit. Regarding the first point, we investigate the possible implementation of the Born-Oppenheimer approximation in the sense of space-adiabatic perturbation theory in models of loop quantum gravity-type. In the course of this, we argue for the need of a Weyl quantisation and an associated symbolic calculus for loop quantum gravity, which we then successfully define, at least to a certain extent. The compactness of the Lie groups, which models a la loop quantum gravity are based on, turns out to be a main obstacle to a fully satisfactory definition of a Weyl quantisation. Finally, we apply our findings to some toy models of linear scalar quantum fields on quantum cosmological spacetimes and discuss the implementation of space-adiabatic perturbation theory therein. In view of the second point, we start with a discussion of the microlocal spectrum condition for quantum fields on curved spacetimes and how it might be translated to a background-independent Hamiltonian quantum theory of gravity, like loop quantum gravity. The relevance of this lies in the fact that the microlocal spectrum condition selects a class of physically relevant states of the quantum matter fields and is, therefore, expected to play an important role in the aforesaid semi-classical limit of gravity-matter systems. Following this, we switch our perspective and analyse the representation theory of loop quantum gravity. We find some intriguing relations between the
Motivating quantum field theory: the boosted particle in a box
Vutha, Amar C
2013-01-01
It is a maxim often stated, yet rarely illustrated, that the combination of special relativity and quantum mechanics necessarily leads to quantum field theory. An elementary illustration is provided, using the familiar particle in a box, boosted to relativistic speeds. It is shown that quantum fluctuations of momentum lead to energy fluctuations, that are inexplicable without a framework that endows the vacuum with dynamical degrees of freedom and allows particle creation/annihilation.
Feynman integral and perturbation theory in quantum tomography
Fedorov, Aleksey
2013-11-01
We present a definition for tomographic Feynman path integral as representation for quantum tomograms via Feynman path integral in the phase space. The proposed representation is the potential basis for investigation of Path Integral Monte Carlo numerical methods with quantum tomograms. Tomographic Feynman path integral is a representation of solution of initial problem for evolution equation for tomograms. The perturbation theory for quantum tomograms is constructed.
Quantum information theory of the Bell-state quantum eraser
Glick, Jennifer R.; Adami, Christoph
2017-01-01
Quantum systems can display particle- or wavelike properties, depending on the type of measurement that is performed on them. The Bell-state quantum eraser is an experiment that brings the duality to the forefront, as a single measurement can retroactively be made to measure particlelike or wavelike properties (or anything in between). Here we develop a unitary information-theoretic description of this and several related quantum measurement situations that sheds light on the trade-off between the quantum and classical features of the measurement. In particular, we show that both the coherence of the quantum state and the classical information obtained from it can be described using only quantum-information-theoretic tools and that those two measures satisfy an equality on account of the chain rule for entropies. The coherence information and the which-path information have simple interpretations in terms of state preparation and state determination and suggest ways to account for the relationship between the classical and the quantum world.
Generalized fluid theory including non-Maxwellian kinetic effects
Izacard, Olivier
2016-01-01
The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasma come mainly from the use of very CPU-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker-Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function (e.g., the INMDF [O. Izacard, Phys. Plasmas 23, 082504 (2016)]). One of the main dif...
The Gaussian radial basis function method for plasma kinetic theory
Energy Technology Data Exchange (ETDEWEB)
Hirvijoki, E., E-mail: eero.hirvijoki@chalmers.se [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden); Candy, J.; Belli, E. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Embréus, O. [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden)
2015-10-30
Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas. - Highlights: • A radically new method to address the velocity space discretization of the non-linear kinetic equation of plasmas. • Elegant and physically intuitive, flexible and mesh-free. • Demonstration of numerical solution of both 2-D and 3-D non-linear Fokker–Planck relaxation problem.
Quantum theory of the optical and electronic properties of semiconductors
Haug, Hartmut
2009-01-01
This invaluable textbook presents the basic elements needed to understand and research into semiconductor physics. It deals with elementary excitations in bulk and low-dimensional semiconductors, including quantum wells, quantum wires and quantum dots. The basic principles underlying optical nonlinearities are developed, including excitonic and many-body plasma effects. Fundamentals of optical bistability, semiconductor lasers, femtosecond excitation, the optical Stark effect, the semiconductor photon echo, magneto-optic effects, as well as bulk and quantum-confined Franz-Keldysh effects, are covered. The material is presented in sufficient detail for graduate students and researchers with a general background in quantum mechanics.This fifth edition includes an additional chapter on 'Quantum Optical Effects' where the theory of quantum optical effects in semiconductors is detailed. Besides deriving the 'semiconductor luminescence equations' and the expression for the stationary luminescence spectrum, the resu...
Probing the kinetics of quantum dot-based proteolytic sensors.
Díaz, Sebastián A; Malonoski, Anthony P; Susumu, Kimihiro; Hofele, Romina V; Oh, Eunkeu; Medintz, Igor L
2015-09-01
As an enzyme superfamily, proteases are rivaled only by kinases in terms of their abundance within the human genome. Two ratiometric quantum dot (QD) Förster resonance energy transfer-based sensors designed to monitor the activity of the proteolytic enzymes collagenase and elastase are investigated here. Given the unique material constraints of these sensing constructs, assays are realized utilizing excess enzyme and fixed substrate in progress curve format to yield enzyme specificity or k cat/K m ratios. The range of k cat/Km values derived is 0.5-1.1 mM(-1) s(-1) for the collagenase sensor and 3.7-4.2 mM(-1) s(-1) for the elastase sensor. Of greater interest is the observation that the elastase sensor can be well represented by the Michaelis-Menten model while the collagenase sensor cannot. The latter demonstrates increased specificity at higher peptide substrate/QD loading values and an apparent QD-caused reversible inhibition as the reaction progresses. Understanding the detailed kinetic mechanisms that underpin these types of sensors will be important especially for their further quantitative utilization.
Noncommunting observables in quantum detection and estimation theory
Helstrom, C. W.
1971-01-01
In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.
Quantum mechanical generalization of the balistic electron wind theory
Lacina, A.
1980-06-01
The Fiks' quasiclassical theory of the electron wind force is quantum mechanically generalized. Within the framework of this generalization the space dependence of the electron wind force is calculated in the vicinity of an interface between two media. It is found that quantum corrections may be comparable with or even greater than corresponding quasiclassical values.
Can quantum theory and special relativity peacefully coexist?
Seevinck, M.P.
2010-01-01
This white paper aims to identify an open problem in 'Quantum Physics and the Nature of Reality' --namely whether quantum theory and special relativity are formally compatible--, to indicate what the underlying issues are, and put forward ideas about how the problem might be addressed.
Can quantum theory and special relativity peacefully coexist?
Seevinck, M.P.
2010-01-01
This white paper aims to identify an open problem in ‘Quantum Physics and the Nature of Reality’—namely whether quantum theory and special relativity are formally compatible—, to indicate what the underlying issues are, and put forward ideas about how the problem might be addressed.
Tales of the quantum understanding physics' most fundamental theory
Hobson, Art
2016-01-01
This is a book about the quanta that make up our universe--the highly unified bundles of energy of which everything is made. It explains wave-particle duality, randomness, quantum states, non-locality, Schrodinger's cat, quantum jumps, and more, in everyday language for non-scientists and scientists who wish to fathom science's most fundamental theory.
From Scalar Field Theories to Supersymmetric Quantum Mechanics
Bazeia, D
2016-01-01
In this work we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here we unveil an interesting novelty, showing that the same scalar field model may describe distinct quantum mechanical problems.
Can quantum theory and special relativity peacefully coexist?
Seevinck, M.P.
This white paper aims to identify an open problem in ‘Quantum Physics and the Nature of Reality’—namely whether quantum theory and special relativity are formally compatible—, to indicate what the underlying issues are, and put forward ideas about how the problem might be addressed.
Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory
Bandyopadhyay, Somshubhro; Banik, Manik; Bhattacharya, Some Sankar; Ghosh, Sibasish; Kar, Guruprasad; Mukherjee, Amit; Roy, Arup
2016-12-01
We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism comparable to that in quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.
Three myths about time reversal in quantum theory
Roberts, Bryan W
2016-01-01
Many have suggested that the transformation standardly referred to as 'time reversal' in quantum theory is not deserving of the name. I argue on the contrary that the standard definition is perfectly appropriate, and is indeed forced by basic considerations about the nature of time in the quantum formalism.
Reciprocal Ontological Models Show Indeterminism Comparable to Quantum Theory
Bandyopadhyay, Somshubhro; Banik, Manik; Bhattacharya, Some Sankar; Ghosh, Sibasish; Kar, Guruprasad; Mukherjee, Amit; Roy, Arup
2017-02-01
We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism comparable to that in quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.
Can quantum theory and special relativity peacefully coexist?
Seevinck, M.P.
2010-01-01
This white paper aims to identify an open problem in 'Quantum Physics and the Nature of Reality' --namely whether quantum theory and special relativity are formally compatible--, to indicate what the underlying issues are, and put forward ideas about how the problem might be addressed.
[The concepts of quantum theory can be introduced into psychophysiology].
Shuĭkin, N N
1998-01-01
There are some ideas in the quantum mechanics, which may be assimilated by psychophysiology. The concept of interference alternatives, advanced by Richard Feynman, may extend the subject matter of the notion of need. The quantum theory assumes virtual transitions. The idea of the physical virtual process may be the rational basis for subjective reality.
Coherent chemical kinetics as quantum walks. I. Reaction operators for radical pairs.
Chia, A; Tan, K C; Pawela, Ł; Kurzyński, P; Paterek, T; Kaszlikowski, D
2016-03-01
Classical chemical kinetics uses rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, in other words, a reaction that contains only incoherent transitions. A prominent example of a reaction containing coherent transitions is the radical-pair model. The kinetics of such reactions is defined by the so-called reaction operator that determines the radical-pair state as a function of intermediate transition rates. We argue that the well-known concept of quantum walks from quantum information theory is a natural and apt framework for describing multisite chemical reactions. By composing Kraus maps that act only on two sites at a time, we show how the quantum-walk formalism can be applied to derive a reaction operator for the standard avian radical-pair reaction. Our reaction operator predicts the same recombination dephasing rate as the conventional Haberkorn model, which is consistent with recent experiments [K. Maeda et al., J. Chem. Phys. 139, 234309 (2013)], in contrast to previous work by Jones and Hore [J. A. Jones and P. J. Hore, Chem. Phys. Lett. 488, 90 (2010)]. The standard radical-pair reaction has conventionally been described by either a normalized density operator incorporating both the radical pair and reaction products or a trace-decreasing density operator that considers only the radical pair. We demonstrate a density operator that is both normalized and refers only to radical-pair states. Generalizations to include additional dephasing processes and an arbitrary number of sites are also discussed.
Quantum theory and human perception of the macro-world.
Aerts, Diederik
2014-01-01
We investigate the question of 'why customary macroscopic entities appear to us humans as they do, i.e., as bounded entities occupying space and persisting through time', starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new 'conceptual quantum interpretation', including a highly detailed reformulation of the question to confront the new insights and views that arise with the foregoing analysis. At the end of the final section, a nuanced answer is given that can be summarized as follows. The specific and very classical perception of human seeing-light as a geometric theory-and human touching-only ruled by Pauli's exclusion principle-plays a role in our perception of macroscopic entities as ontologically stable entities in space. To ascertain quantum behavior in such macroscopic entities, we will need measuring apparatuses capable of its detection. Future experimental research will have to show if sharp quantum effects-as they occur in smaller entities-appear to be ontological aspects of customary macroscopic entities. It remains a possibility that standard quantum theory is an incomplete theory, and hence incapable of coping ultimately with separated entities, meaning that a more general theory will be needed.
Quantum Theory and Human Perception of the Macro-World
Directory of Open Access Journals (Sweden)
Diederik eAerts
2014-06-01
Full Text Available We investigate the question of 'why customary macroscopic entities appear to us humans as they do, i.e. as bounded entities occupying space and persisting through time', starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new `conceptual quantum interpretation', including a highly detailed reformulation of the question to confront the new insights and views that arise with the foregoing analysis. At the end of the final section, a nuanced answer is given that can be summarized as follows. The specific and very classical perception of human seeing -- light as a geometric theory -- and human touching -- only ruled by Pauli's exclusion principle -- plays a role in our perception of macroscopic entities as ontologically stable objects in space. To ascertain quantum behavior in such macroscopic entities, we will need measuring apparatuses capable of its detection. Future experimental research will have to show if sharp quantum effects -- as they occur in smaller entities -- appear to be ontological aspects of customary macroscopic entities. It remains a possibility that standard quantum theory is an incomplete theory, and hence incapable of coping with separated entities, meaning that a more general
Quantum Theory of Hyperfine Structure Transitions in Diatomic Molecules.
Klempt, E.; And Others
1979-01-01
Described is an advanced undergraduate laboratory experiment in which radio-frequency transitions between molecular hyperfine structure states may be observed. Aspects of the quantum theory applied to the analysis of this physical system, are discussed. (Authors/BT)
Statistical approach to quantum field theory an introduction
Wipf, Andreas
2013-01-01
Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems w...
CPT/Lorentz Invariance Violation and Quantum Field Theory
Arias, P; Gamboa-Rios, J; López-Sarrion, J; Méndez, F; Arias, Paola; Das, Ashok; Gamboa, Jorge; Lopez-Sarrion, Justo; Mendez, Fernando
2006-01-01
Analogies between the noncommutative harmonic oscillator and noncommutative fields are analyzed. Following this analogy we construct examples of quantum fields theories with explicit CPT and Lorentz symmetry breaking. Some applications to baryogenesis and neutrino oscillation are also discussed
Theory of quantum fluctuations and the Onsager relations
Energy Technology Data Exchange (ETDEWEB)
Goderis, D.; Verbeure, A.; Vets, P. (Universiteit Leuven (Belgium))
1989-09-01
A microscopic model is constructed within the theory of normal fluctuations for quantum systems, yielding an irreversible dynamics satisfying the Onsager relations. The property of return to equilibrium and the principle of minimal entropy production are proved.
Quantum Yang-Mills theory: an overview of a programme
Milsted, Ashley
2016-01-01
We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\\mathbb{Z}/2\\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. ...
Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
Tanasa, Adrian
2010-01-01
We briefly review the r\\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative Grosse-Wulkenhaar model.