Showing papers on "Quantization (physics) published in 2005"

Introductory quantum optics

Abstract: This book provides an elementary introduction to the subject of quantum optics, the study of the quantum mechanical nature of light and its interaction with matter. The presentation is almost entirely concerned with the quantized electromagnetic field. Topics covered include single-mode field quantization in a cavity, quantization of multimode fields, quantum phase, coherent states, quasi-probability distribution in phase space, atom-field interactions, the Jaynes-Cummings model, quantum coherence theory, beam splitters and interferometers, dissipative interactions, nonclassical field states with squeezing etc., 'Schrodinger cat' states, tests of local realism with entangled photons from down-conversion, experimental realizations of cavity quantum electrodynamics, trapped ions, decoherence, and some applications to quantum information processing, particularly quantum cryptography. The book contains many homework problems and an extensive bibliography. This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first and second year graduate students.

Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers

Abstract: We report results of numerical simulations on multiple-soliton generation and soliton energy quantization in a soliton fiber ring laser passively mode locked by using the nonlinear polarization rotation technique. We found numerically that the formation of multiple solitons in the laser is caused by a peak-power-limiting effect of the laser cavity. It is also the same effect that suppresses the soliton pulse collapse, an intrinsic feature of solitons propagating in gain media, and makes the solitons stable in the laser. Furthermore, we show that the soliton energy quantization observed in the lasers is a natural consequence of the gain competition between the multiple solitons. Enlightened by the numerical result we speculate that multisoliton formation and soliton energy quantization observed in other types of soliton fiber lasers could have a similar mechanism.

Putting mechanics into quantum mechanics

Abstract: Nanoelectromechanical structures are starting to approach the ultimate quantum mechanical limits for detecting and exciting motion at the nanoscale. Nonclassical states of a mechanical resonator are also on the horizon.

Group field theory: An Overview

Abstract: We give a brief overview of the properties of a higher-dimensional generalization of matrix model which arise naturally in the context of a background approach to quantum gravity, the so-called group field theory. We show in which sense this theory provides a third quantization point-of-view on quantum gravity.

Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Abstract: and

How to model quantum plasmas

Abstract: Traditional plasma physics has mainly focused on regimes characterized by high temperatures and low densities, for which quantum-mechanical effects have virtually no impact. However, recent technological advances (particularly on miniaturized semiconductor devices and nanoscale objects) have made it possible to envisage practical applications of plasma physics where the quantum nature of the particles plays a crucial role. Here, I shall review different approaches to the modeling of quantum effects in electrostatic collisionless plasmas. The full kinetic model is provided by the Wigner equation, which is the quantum analog of the Vlasov equation. The Wigner formalism is particularly attractive, as it recasts quantum mechanics in the familiar classical phase space, although this comes at the cost of dealing with negative distribution functions. Equivalently, the Wigner model can be expressed in terms of $N$ one-particle Schr{o}dinger equations, coupled by Poisson's equation: this is the Hartree formalism, which is related to the `multi-stream' approach of classical plasma physics. In order to reduce the complexity of the above approaches, it is possible to develop a quantum fluid model by taking velocity-space moments of the Wigner equation. Finally, certain regimes at large excitation energies can be described by semiclassical kinetic models (Vlasov-Poisson), provided that the initial ground-state equilibrium is treated quantum-mechanically. The above models are validated and compared both in the linear and nonlinear regimes.

Quantum Consistency of the Superstring in AdS5 ? S5 Background

Abstract: Using arguments based on BRST cohomology, the pure spinor formalism for the superstring in an AdS5 ? S5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level.

Between classical and quantum

Abstract: The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it.

A modern introduction to quantum field theory

Abstract: 1. Introduction 2. Lorentz and Poincare symmetries in quantum field theory 3. Classical field theory 4. Quantization of free fields 5. Perturbation theory and Feynman diagrams 6. Cross sections and decay rates 7. Quantum electrodynamics 8. The low-energy limit of the electroweak theory 9. Path integral quantization 10. Non-Abelian gauge theories 11. Spontaneous symmetry breaking

Quantum correction in exact quantization rules

Abstract: An exact quantization rule for the Schrodinger equation is presented. In the exact quantization rule, in addition to Nπ, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the quantum correction is an invariant, independent of the number of nodes in the wave function. In those systems, the energy levels of all the bound states can be easily calculated from the exact quantization rule and the solution for the ground state, which can be obtained by solving the Riccati equation. With this new method, we re-calculate the energy levels for the one-dimensional systems with a finite square well, with the Morse potential, with the symmetric and asymmetric Rosen-Morse potentials, and with the first and the second Poschl-Teller potentials, for the harmonic oscillators both in one dimension and in three dimensions, and for the hydrogen atom.

Nanofiber-mediated radiative transfer between two distant atoms

Abstract: We study spontaneous emission from a pair of two-level atoms near a nanofiber. We demonstrate a substantial radiative exchange between distant atoms mediated by the guided modes of the nanofiber. The exchange is shown to lead to increased and decreased lifetimes of the subradiant and superradiant states, respectively. Our analysis is based on the full quantization of both the radiation and guided modes of the fiber in the framework of the Heisenberg-Langevin theory and the master equation formalism.

Fermions from half-BPS supergravity

Abstract: We discuss collective coordinate quantization of the half-BPS geometries of Lin, Lunin and Maldacena [1]. The LLM geometries are parameterized by a single function u on a plane. We treat this function as a collective coordinate. We arrive at the collective coordinate action as well as path integral measure by considering D3 branes in an arbitrary LLM geometry. The resulting functional integral is shown, using known methods ([2]), to be the classical limit of a functional integral for free fermions in a harmonic oscillator. The function u gets identified with the classical limit of the Wigner phase space distribution of the fermion theory which satisfies u*u = u. The calculation shows how configuration space of supergravity becomes a phase space (hence noncommutative) in the half-BPS sector. Our method sheds new light on counting supersymmetric configurations in supergravity.

Parent Field Theory and Unfolding in BRST First-Quantized Terms

Abstract: For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space–time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.

Classical And Quantum Dissipative Systems

Abstract: Phenomenological Equations of Motion for Dissipative Systems Lagrangian Hamiltonian and Hamilton-Jacobi Formulation of the Classical Dissipative Systems Noether's Theorem and Non-Noether Conservation Laws Dissipative Forces Derived from Many-Body Problems A Particle Coupled to a Field and the Damped Motion of a Central Particle Coupled to a Heat Bath Quantization of Dissipative Systems in General and of Explicitly Time-Dependent Hamiltonians in Particular Density Matrix and the Wigner Distribution Function for Damped Systems Path Integral Formulation of a Damped Harmonic Oscillator Quantization of the Motion of an Infinite Chain Heisenberg's Equations of Motion for a Particle Coupled to a Heat Bath Quantum Mechanical Models of Dissipative Systems and the Concept of Optical Potential.

Bell-type quantum field theories

Abstract: In his paper (1986 Beables for quantum field theory Phys. Rep. 137 49?54) John S Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |?|2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; we call such processes Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to 'second quantization'. As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field.

What is Renormalization

Abstract: "Preprint" of paper from 1989 that wasn't arxiv'ed at the time. Abstract: Our understanding of quantum field theories, and, in particular, of renomalization has changed radically in recent years; renormalization is no longer a deeply mysterious procedure for hiding embarrassing infinities. This talk is a non-technical presentation of modern attitudes towards renormalization, and their implications (both theoretical and experimental) for quantum theories of electromagnetic, strong, and weak interactions.

Stability of quantized control systems under dynamic bit assignment

Abstract: In recent years, there have been several papers characterizing the minimum number of quantization levels required to assure closed-loop stability. This minimum bit rate is usually achieved through time-varying quantization policies. Many networks, however, prefer a constant bit rate configuration, so it is useful to characterize the stability of quantized feedback systems under constant bit rate quantization. This note first derives a lower bound on the number of quantization levels required for closed-loop stability under constant bit rates. We then introduce a novel dynamic bit allocation policy that achieves this bound.

Lagrange structure and quantization

Abstract: A path-integral quantization method is proposed for dynamical systems whose clas- sical equations of motion do not necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the La- grangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d + 1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in d dimensions. As the topological sigma-model has a well defined action, it is path-integral quan- tized in the usual way that results in quantization of the original (not necessarily Lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quanti- zation scheme is exemplified by several models including the ones whose classical dynamics are not variational.

Higher derivative quantum gravity with Gauss-Bonnet term

Abstract: Higher derivative theory is one of the important models of quantum gravity, renormalizable and asymptotically free within the standard perturbative approach. We consider the $4\ensuremath{-}ϵ$ renormalization group for this theory, an approach which proved fruitful in $2\ensuremath{-}ϵ$ models. A consistent formulation in dimension $n=4\ensuremath{-}ϵ$ requires taking quantum effects of the topological term into account, hence we perform a calculation which is more general than the ones done before. In the special $n=4$ case we confirm a known result by Fradkin, Tseytlin, Avramidi, and Barvinsky, while contributions from a topological term do cancel. In the more general case of $4\ensuremath{-}ϵ$ renormalization group equations there is an extensive ambiguity related to gauge-fixing dependence. As a result, physical interpretation of these equations is not universal unless we treat $ϵ$ as a small parameter. In the sector of essential couplings one can find a number of new fixed points, but some of them have no analogs in the $n=4$ case.

Quantization of multiparticle auger rates in semiconductor quantum dots

Abstract: We have resolved single-exponential relaxation dynamics of the 2-, 3-, and 4-electron-hole pair states in nearly monodisperse cadmium selenide quantum dots with radii ranging from 1 to 4 nanometers. Comparison of the discrete relaxation constants measured for different multiple-pair states indicates that the carrier decay rate is cubic in carrier concentration, which is characteristic of an Auger process. We observe that in the quantum-confined regime, the Auger constant is strongly size-dependent and decreases with decreasing the quantum dot size as the radius cubed.

Genericness of a Big Bounce in Isotropic Loop Quantum Cosmology

Abstract: The absence of isotropic singularity in loop quantum cosmology can be understood in an effective classical description as the Universe exhibiting a big bounce. We show that with a scalar matter field, the big bounce is generic in the sense that it is independent of quantization ambiguities and the details of scalar field dynamics. The volume of the Universe at the bounce point is parametrized by a single parameter. It provides a minimum length scale which serves as a cutoff for computations of density perturbations thereby influencing their amplitudes.

Geometry Quantization from Supergravity: the case of "Bubbling AdS"

Abstract: We consider the moduli space of 1/2 BPS configurations of type IIB SUGRA found by Lin, Lunin and Maldacena ([1]), and quantize it directly from the supergravity action, around any point in the moduli space. This quantization is done using the Crnkovic-Witten-Zuckerman covariant method. We make some remarks on the applicability and validity of this general on-shell quantization method. We then obtain an expression for the symplectic form on the moduli space of LLM configurations, and show that it exactly coincides with the one expected from the dual fermion picture. This equivalence is shown for any shape and topology of the droplets and for any number of droplets. This work therefore generalizes the previous work ([2]) and resolves the puzzle encountered there.

Reflection Symmetries of q-Bernoulli Polynomials

Abstract: A large part of the theory of classical Bernoulli polynomials B n (x)’s follows from their reflection symmetry around x = 1/2: B n (1 − x) = (−1) n B n (x). This symmetry not only survives quantization but has two equivalent forms, classical and quantum, depending upon whether one reflects around 1/2 the classical x or quantum [x] q .

Quantum resolution of black hole singularities

Abstract: We study the classical and quantum theory of spherically symmetric spacetimes with scalar field coupling in general relativity. We utilize the canonical formalism of geometrodynamics adapted to the Painleve–Gullstrand coordinates, and present a new quantization of the resulting field theory. We give an explicit construction of operators that capture curvature properties of the spacetime and use these to show that the black hole curvature singularity is avoided in the quantum theory.

Three-dimensional loop quantum gravity: coupling to point particles

Abstract: We consider the coupling between three-dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian quantization generalizing loop quantum gravity techniques. We give a complete description of the kinematical Hilbert space of the coupled system. Finally, we define the physical Hilbert space of the system of self-gravitating massive spinning point particles using Rovelli's generalized projection operator which can be represented as a sum over spin-foam amplitudes. In addition we provide an explicit expression of the classical distance operator between two particles which is defined as an observable.

Quantum turbulence in condensate collisions: an application of the classical field method.

Abstract: We apply the classical field method to simulate the production of correlated atoms during the collision of two Bose-Einstein condensates. Our nonperturbative method includes the effect of quantum noise, and describes collisions of high density condensates with very large out-scattered fractions. Quantum correlation functions for the scattered atoms show that the correlation between pairs of atoms of opposite momentum is rather small. We also predict the existence of quantum turbulence in the field of the scattered atoms.

Simulating Nonequilibrium Quantum Fields with Stochastic Quantization Techniques

Abstract: We present lattice simulations of nonequilibrium quantum fields in Minkowskian space-time. Starting from a nonthermal initial state, the real-time quantum ensemble in (3 + 1) dimensions is constructed by a stochastic process in an additional (5th) "Langevin-time." For the example of a self-interacting scalar field, we show how to resolve apparent unstable Langevin dynamics and compare our quantum results with those obtained in classical field theory. Such a direct simulation method is crucial for our understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in strongly coupled quantum many-body systems.