Showing papers on "Quantization (physics) published in 1998"

Strong interactions of single atoms and photons in cavity QED

Abstract: An important development in modern physics is the emerging capability for investigations of dynamical processes for open quantum systems in a regime of strong coupling for which individual quanta play a decisive role. Of particular significance in this context is research in cavity quantum electrodynamics which explores quantum dynamical processes for individual atoms strongly coupled to the electromagnetic field of a resonator. An overview of the research activities in the Quantum Optics Group at Caltech is presented with an emphasis on strong coupling in cavity QED which enables exploration of a new regime of nonlinear optics with single atoms and photons.

Quantum Transport and Dissipation

Abstract: Theory of Coherent Transport. Quantization of Transport. Single-Electron Tunneling. Dissipative Quantum Systems. Driven Quantum Systems. Chaos, Coherence, and Dissipation. Indexes.

Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics

Abstract: A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers-Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional current- and charge-density operator fields in order to take into account the noise associated with the dissipation in the medium. It is shown that the equal-time commutation relations between the fundamental electromagnetic fields $\hat E$ and $\hat B$ and the potentials $\hat A$ and $\hat \phi$ in the Coulomb gauge can be expressed in terms of the Green tensor of the classical problem. From the Green tensors for bulk material and an inhomogeneous medium consisting of two bulk dielectrics with a common planar interface it is explicitly proven that the well-known equal-time commutation relations of QED are preserved.

The Applicability of Mathematics as a Philosophical Problem

Abstract: The semantic applicability of mathematics - Frege's achievements the descriptive applicability of mathematics mathematics, analogies and discovery in physics Pythagorean analogies in physics formalisms and formalist reasoning in quantum mechanics formalist reasoning - the mystery of quantization appendix - a "nonphysical" derivation of quantum mechanics appendix - nucleon-pion scattering appendix -nonrelativistic Schroedinger equation with spin.

Quantization of Lie bialgebras, V

Abstract: This paper is a continuation of "Quantization of Lie bialgebras I-IV". The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting of the formal deformation theory and give interesting examples of such algebras. In particular, we construct a quantum vertex operator algebra from a rational, trigonometric, or elliptic R-matrix, which is a quantum deformation of the affine vertex operator algebra. The simplest vertex operator in this algebra is the quantum current of Reshetikhin and Semenov-Tian-Shansky.

Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity

Abstract: We study the phase space structure and the quantization of a pointlike particle in (2 + 1)-dimensional gravity. By adding boundary terms to the first-order Einstein-Hilbert action, and removing all redundant gauge degrees of freedom, we arrive at a reduced action for a gravitating particle in 2 + 1 dimensions, which is invariant under Lorentz transformations and a group of generalized translations. The momentum space of the particle turns out to be the group manifold SL(2). Its position coordinates have non-vanishing Poisson brackets, resulting in a non-commutative quantum spacetime. We use the representation theory of SL(2) to investigate its structure. We find a discretization of time, and some semi-discrete structure of space. An uncertainty relation forbids a fully localized particle. The quantum dynamics is described by a discretized Klein-Gordon equation.

Quantum theory of geometry: III. Non-commutativity of Riemannian structures

Abstract: The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures - such as triad and area operators - exhibit a non-commutativity. At first sight, this feature is surprising because it implies that the framework does not admit a triad representation. To better understand this property and to reconcile it with intuition, we analyse its origin in detail. In particular, a careful study of the underlying phase space is made and the feature is traced back to the classical theory; there is no anomaly associated with quantization. We also indicate why the uncertainties associated with this non-commutativity become negligible in the semiclassical regime.

Relativistic Quantum Mechanics: With Applications in Condensed Matter and Atomic Physics

Abstract: This graduate text introduces relativistic quantum theory, emphasising its important applications in condensed matter physics. Basic theory, including special relativity, angular momentum and particles of spin zero are first reprised. The text then goes on to discuss the Dirac equation, symmetries and operators, and free particles. Physical consequences of solutions including hole theory and Klein's paradox are considered. Several model problems are solved. Important applications of quantum theory to condensed matter physics then follow. Relevant theory for the one electron atom is explored. The theory is then developed to describe the quantum mechanics of many electron systems, including Hartree-Fock and density functional methods. Scattering theory, band structures, magneto-optical effects and superconductivity are among other significant topics discussed. Many exercises and an extensive reference list are included. This clear account of relativistic quantum theory will be valuable to graduate students and researchers working in condensed matter physics and quantum physics.

Quantum Dynamics of an Excess Proton in Water Using an Extended Empirical Valence-Bond Hamiltonian

Abstract: The classical and quantum dynamics of an excess proton in water is studied by molecular dynamics simulations. The electronic structure of the system is described by an extended multistate valence-bond Hamiltonian that allows for the breaking and formation of O−H+ bonds. The proton quantum character is treated by means of an effective (path-integral) proton-transfer surface. Whereas classical simulations predict that the hydrated proton appears in a mixture of and structures, inclusion of proton quantization leads to the prevalence of . The proton-transfer mechanism can be described mostly as the translocation of a transient structure across the water hydrogen-bond network. The computed lifetime of a particular is close to 2 ps, a value compatible with experimental estimates.

Quantization of an interacting spin - 3 / 2 field and the Delta isobar

Abstract: Quantization of the free and interacting Rarita-Schwinger field is considered using the Hamiltonian path-integral formulation. The particular interaction we study in detail is the $\ensuremath{\pi}N\ensuremath{\Delta}$ coupling used in the phenomenology of the pion-nucleon and nucleon-nucleon systems. Within the Dirac constraint analysis, we show that there is an excess of degrees of freedom in the model, as well as the inconsistency related to the Johnson-Sudarshan-Velo-Zwanzinger problem. It is further suggested that couplings invariant under the gauge transformation of the Rarita-Schwinger field are generally free from these inconsistencies. We then construct and briefly analyze some lowest in derivatives gauge-invariant $\ensuremath{\pi}N\ensuremath{\Delta}$ couplings.

QED commutation relations for inhomogeneous Kramers-Kronig dielectrics

Abstract: Recently a quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium has been developed and applied to a system consisting of two infinite half-spaces with a common planar interface (H.T. Dung, L. Kn\"oll, and D.-G. Welsch, Phys. Rev. A 57, 3931 (1998)). Here we show that the scheme, which is based on the classical Green-tensor integral representation of the electromagnetic field, applies to any inhomogeneous medium. For this purpose we prove that the fundamental equal-time commutation relations of QED are preserved for an arbitrarily space-dependent, Kramers-Kronig consistent permittivity. Further, an extension of the quantization scheme to linear media with bounded regions of amplification is given, and the problem of anisotropic media is briefly addressed.

Decoherence, chaos, quantum-classical correspondence, and the algorithmic arrow of time

Abstract: The environment – external or internal degrees of freedom coupled to the system – can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous destruction of superpositions leads to environment-induced superselection (einselection). Here I investigate it in the context of quantum chaos (i.e., quantum dynamics of systems which are classically chaotic). I show that the evolution of a chaotic macroscopic (but, ultimately, quantum) system is not just difficult to predict (requiring an accuracy exponentially increasing with time) but quickly ceases to be deterministic in principle as a result of the Heisenberg indeterminacy (which limits the resolution available in the initial conditions). This happens after a time t which is only logarithmic in the Planck constant. A definitely macroscopic (if somewhat outrageous) example is afforded by various components of the solar system which are chaotic, with the Lyapunov timescales ranging from a bit more than a month (Hyperion) to millions of years (planetary system as a whole). On the timescale t the initial minimum uncertainty wavepackets corresponding to celestial bodies would be smeared over distances of the order of radii of their orbits into "Schrodinger cat – like" states, and the concept of a trajectory would cease to apply. In reality, such paradoxical states are eliminated by decoherence which helps restore quantum-classical correspondence. The price for the recovery of classicality is the loss of predictability: In the classical limit (associated with effective decoherence, and not just with the smallness of ) the rate of increase of the von Neumann entropy of the decohering system is independent of the strength of the coupling to the environment, and equal to the sum of the positive Lyapunov exponents. Algorithmic aspects of entropy production are briefly explored to illustrate the effect of decoherence from the point of view of the observer. We show that "decoherence strikes twice", introducing unpredictability into the system and extracting quantum coherence from the observers memory, where it enters as a price for the classicality of his records.

Adiabatic Charge Pumping in Almost Open Dots

Abstract: We consider adiabatic charge transport through an almost open quantum dot. We show that the charge transmitted in one cycle is quantized in the limit of vanishing temperature and one-electron mean level spacing in the dot. The explicit analytic expression for the pumped charge at finite temperature is obtained for spinless electrons. The pumped charge is produced by both nondissipative and dissipative currents. The former give a quantized contribution to the transferred charge, whereas the latter are responsible for the corrections to charge quantization which are expressed through the conductance of the system.

Instantaneous spreading and Einstein causality in quantum theory

Abstract: In nonrelativistic quantum mechanics the wave-function of a free particle which initially is in a finite volume immediately spreads to infinity. In a nonrelativistic theory this is of no concern, but we show that the same instantaneous spreading can occur in relativistic quantum theory and that transition probabilities in widely separated systems may instantaneously become nonzero. We discuss how this affects Einstein causality.

Classical Euclidean general relativity from ``left-handed area = right-handed area"

Abstract: A classical continuum theory corresponding to Barrett and Crane's model of Euclidean quantum gravity is presented. The fields in this classical theory are those of SO(4) BF theory, a simple topological theory of an so(4) valued 2-form field, $B^{IJ}_{\m }$, and an so(4) connection. The left handed (self-dual) and right handed (anti-self-dual) components of $B$ define a left handed and a, generally distinct, right handed area for each spacetime 2-surface. The theory being presented is obtained by adding to the BF action a Lagrange multiplier term that enforces the constraint that the left handed and the right handed areas be equal. It is shown that Euclidean general relativity (GR) forms a sector of the resulting theory. The remaining three sectors of the theory are also characterized and it is shown that, except in special cases, GR canonical initial data is sufficient to specify the GR sector as well as a specific solution within this sector. Finally, the path integral quantization of the theory is discussed at a formal level and a hueristic argument is given suggesting that in the semiclassical limit the path integral is dominated by solutions in one of the non-GR sectors, which would mean that the theory quantized in this way is not a quantization of GR.

Functional Tetrahedron Equation

Abstract: We describe a method for constructing classical integrable models in a (2+1)-dimensional discrete spacetime based on the functional tetrahedron equation, an equation that makes the symmetries of a model obvious in a local form. We construct a very general “block-matrix model,” find its algebraic-geometric solutions, and study its various particular cases. We also present a remarkably simple quantization scheme for one of those cases.

Non-Abelian Reduction in Deformation Quantization

Abstract: We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization Under assumptions of the classical Marsden–Weinstein Theorem we define a reduction of the algebra A with respect to the G-action The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization A similar statement within the framework of geometric quantization is known as the Guillemin–Sternberg conjecture (by now, completely proved)

Many-particle ground states and excitations in nanometer-size quantum structures

Abstract: Recent experiments, which study the electronic structure of self-organized InAs nanostructures, are summarized. The results from simultaneously performed far-infrared (FIR) and capacitance spectroscopy allow for a detailed investigation of both many-particle ground states and excitations in these three-dimensionally confined, few-electron systems. Experimental data from quantum dots, coupled dots and ring-like structures are presented and evaluated with respect to the contributions from quantization, electron–electron interaction and an external applied magnetic field to the energy spectrum.

DeDonder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory

Abstract: A quantization of field theory based on the DeDonder-Weyl covariant Hamiltonian formulation is discussed. A hypercomplex extension of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears as a result of quantization of Poisson brackets of differential forms put forward for the DeDonder-Weyl formulation earlier. The proposed covariant hypercomplex Schr\"odinger equation is shown to lead in the classical limit to the DeDonder-Weyl Hamilton-Jacobi equation and to obey the Ehrenfest principle in the sense that the DeDonder-Weyl canonical field equations are satisfied for the expectation values of properly chosen operators.

Self-consistent 2-D model for quantum effects in n-MOS transistors

Abstract: We present a self-consistent two-dimensional (2-D) model for carrier quantization effects in the channel of highly-doped n-MOSFET's. Quantization is taken into account inside a box region surrounding the inversion channel. The proposed approach extends previously proposed one-dimensional (1-D) schemes allowing one to estimate the quantum mechanical (QM) effects on the device current. Good convergence properties are achieved exploiting the effective intrinsic density concept. The simulator has been applied to MOS devices with different peak channel doping, resulting in an improved description of the device behavior.

Mesoscopic charge quantization

Abstract: We study the Coulomb blockade in a chaotic quantum dot connected to a lead by a single channel at nearly perfect transmission. We take into account quantum fluctuations of the dot charge and a finite level spacing for electron states within the dot. Mesoscopic fluctuations of thermodynamic and transport properties in the Coulomb blockade regime exist at any transmission coefficient. In contrast to the previous theories, we show that by virtue of these mesoscopic fluctuations, the Coulomb blockade is not destroyed completely even at perfect transmission. The oscillatory dependence of all the observable characteristics on the gate voltage is preserved, its period is still defined by the charge of a single electron. However, phases of those oscillations at perfect transmission are random; because of the randomness, the Coulomb blockade shows up not in the averages but in the correlation functions of the fluctuating observables (e.g., capacitance or tunneling conductance). This phenomenon may be called ``mesoscopic charge quantization.''