Showing papers on "Quantization (physics) published in 1996"
TL;DR: This investigation of the excited levels of the atom-cavity system reveals nonlinear quantum features at extremely low field strengths.
Abstract: We have observed the Rabi oscillation of circular Rydberg atoms in the vacuum and in small coherent fields stored in a high Q cavity. The signal exhibits discrete Fourier components at frequencies proportional to the square root of successive integers. This provides direct evidence of field quantization in the cavity. The weights of the Fourier components yield the photon number distribution in the field. This investigation of the excited levels of the atom-cavity system reveals nonlinear quantum features at extremely low field strengths.
866 citations
TL;DR: The quantization law for the antisymmetric tensor field of $M$-theory contains a gravitational contribution not known previously as discussed by the authors, which greatly facilitates the analysis.
Abstract: The quantization law for the antisymmetric tensor field of $M$-theory contains a gravitational contribution not known previously. When it is included, the low energy effective action of $M$-theory, including one-loop and Chern-Simons contributions, is well-defined. The relation of $M$-theory to the $E_8\times E_8$ heterotic string greatly facilitates the analysis.
441 citations
TL;DR: The transport properties of high-quality quantum wires fabricated in GaAs-AlGaAs by using cleaved edge overgrowth are measured and several aspects of the data can be explained qualitatively using Luttinger liquid theory although there remain major inconsistencies with such an interpretation.
Abstract: We have measured the transport properties of high-quality quantum wires fabricated in GaAs-AlGaAs by using cleaved edge overgrowth. The low temperature conductance is quantized as the electron density in the wire is varied. While the values of the conductance plateaus are reproducible, they deviate from multiples of the universal value of ${2e}^{2}/h$ by as much as 25%. As the temperature or dc bias increases the conductance steps approach the universal value. Several aspects of the data can be explained qualitatively using Luttinger liquid theory although there remain major inconsistencies with such an interpretation.
328 citations
TL;DR: In this paper, a quantization scheme for the radiation field in dispersive and absorptive linear dielectrics is developed, which applies to both bulk material and multilayer dielectric structures.
Abstract: A quantization scheme for the radiation field in dispersive and absorptive linear dielectrics is developed, which applies to both bulk material and multilayer dielectric structures. Starting from the phenomenological Maxwell equations, where the properties of the dielectric are described by a permittivity consistent with the Kramers-Kronig relations, an expansion of the field operators is performed that is based on the Green function of the classical Maxwell equations and preserves the equal-time canonical field commutation relations. In particular, in frequency intervals with approximately vanishing absorption the concept of quantization through mode expansion for dispersive dielectrics is recognized. The theory further reveals that weak absorption gives rise to space-dependent mode operators that spatially evolve according to quantum Langevin equations in the space domain. To illustrate the applicability of the theory to inhomogeneous structures, the quantization of the radiation field in a dispersive and absorptive one-interface dielectric is performed. \textcopyright{} 1996 The American Physical Society.
294 citations
TL;DR: In this article, a self-interacting scalar field on a truncated sphere is described and quantized using the functional (path) integral approach, which possesses full symmetry with respect to the isometries of the sphere.
Abstract: We describe a self-interacting scalar field on a truncated sphere and perform the quantization using the functional (path) integral approach. The theory possesses full symmetry with respect to the isometries of the sphere. We explicitly show that the model is finite and that UV regularization automatically takes place.
263 citations
TL;DR: In this paper, the authors investigated the canonical commutation rules for gravitating quantized particles in a 2+1 dimensional world and found that these particles live on a space-time lattice.
Abstract: By investigating the canonical commutation rules for gravitating quantized particles in a 2+1 dimensional world it is found that these particles live on a space-time lattice. The space-time lattice points can be characterized by three integers. Various representations are possible, the details depending on the topology chosen for energy-momentum space. We find that an $S_2\times S_1$ topology yields a physically most interesting lattice within which first quantization of Dirac particles is possible. An $S_3$ topology also gives a lattice, but does not allow first quantized particles.
258 citations
TL;DR: In this article, the truncated 4-dimensional sphereS4 and the action of the self-interacting scalar field on it are constructed and path integral quantization is performed while simultaneously keeping theSO(5) symmetry and the finite number of degrees of freedom.
Abstract: The truncated 4-dimensional sphereS4 and the action of the self-interacting scalar field on it are constructed. The path integral quantization is performed while simultaneously keeping theSO(5) symmetry and the finite number of degrees of freedom. The usual field theory UV-divergences are manifestly absent.
175 citations
TL;DR: In this paper, a deformation of the observable algebra of quantum gravity is described, in which the loop algebra is extended to framed loops, and the spinor identities are extended to a set of relations which are governed by the Kauffman bracket.
148 citations
TL;DR: In this paper, a new D=2 nonrelativistic classical mechanics model is proposed, which is based on the Noether theorem of the (2+1)-Galilean symmetry algebra with two central charges: mass m and the coupling constant k of a Chern-Simons-like term.
Abstract: We consider a new D=2 nonrelativistic classical mechanics model providing via the Noether theorem the (2+1)-Galilean symmetry algebra with two central charges: mass m and the coupling constant k of a Chern-Simons-like term. In this way we provide the dynamical interpretation of the second central charge of the (2+1)-dimensional Galilean algebra. We discuss also the interpretation of k as describing the noncommutativity of D=2 space coordinates. The model is quantized in two ways: using the Ostrogradski-Dirac formalism for higher order Lagrangians with constraints and the Faddeev-Jackiw method which describes constrained systems and produces nonstandard symplectic structures. We show that our model describes the superposition of a free motion in noncommutative D=2 space as well as the "internal" oscillator modes. We add a suitably chosen class of velocity-dependent two-particle interactions, which is descrobed by local potentials in D=2 noncommutative space. We treat, in detail, the particular case of a harmonic oscillator and describe its quantization. It appears that the indefinite metric due to the third order time derivative term in the field equations, even in the presence of interactions, can be eliminated by the imposition of a subsidiary condition.
148 citations
Book•
01 Jul 1996TL;DR: A comprehensive and coherent introduction to modern quantum cosmology can be found in this paper, where the reader is led through Hamiltonian supergravity and canonical quantization and quantum amplitudes through to models of supersymmetric mini superspace and quantum wormholes.
Abstract: This volume provides a comprehensive and coherent introduction to modern quantum cosmology - the study of the universe as a whole according to the laws of quantum mechanics. In particular, it presents a useful survey of the many profound consequences of supersymmetry (supergravity) in quantum cosmology. After a general introduction to quantum cosmology, the reader is led through Hamiltonian supergravity and canonical quantization and quantum amplitudes through to models of supersymmetric mini superspace and quantum wormholes. The book is rounded off with a look at exciting further developments, including the possible finiteness of supergravity. Ample introductory material is included, ensuring this topical volume is well suited as a graduate text. Researchers in theoretical and mathematical physics, applied maths and cosmology will also find it of immediate interest.
140 citations
TL;DR: In this article, the spin Calogero-Moser model was quantized in the R-matrix formalism, and the quantum R-Matrix of the model was shown to be dynamical.
Abstract: We quantize the spin Calogero-Moser model in theR-matrix formalism. The quantumR-matrix of the model is dynamical. ThisR-matrix has already appeared in Gervais-Neveu's quantization of Toda field theory and in Felder's quantization of the Knizhnik-Zamolodchikov-Bernard equation.
TL;DR: In this article, the authors study the low energy effective theory describing the dynamics of D-particles and find evidence for the existence of non-BPS states whose mass grows like λ 1/3 over the BPS mass.
Abstract: We study the low energy effective theory describing the dynamics of D-particles. This corresponds to the quantum-mechanical system obtained by dimensional reduction of (9+1)-dimensional supersymmetric Yang-Mills theory to 0+1 dimensions and can be interpreted as the nonrelativistic limit of the Born-Infeld action. We study the system of two like-charged D-particles and find evidence for the existence of non-BPS states whose mass grows like λ1/3 over the BPS mass. We give a string interpretation of this phenomenon in terms of a linear potential generated by strings stretching from the two D-particles. Some comments on the possible relations to black hole entropy and elevendimensional supergravity are also given.
TL;DR: In this article, the authors used tunnel-current spectroscopy to map the quantum-mechanical energy levels of an electron confined in a semiconductor quantum well in a high magnetic field.
Abstract: QUALITATIVE insight into the properties of a quantum-mechanical system can be gained from the study of the relationship between the system's classical newtonian dynamics, and its quantum dynamics as described by the Schrodinger equation. The Bohr–Sommerfeld quantization scheme—which underlies the historically important Bohr model for hydrogen-like atoms—describes the relationship between the classical and quantum-mechanical regimes, but only for systems with stable, periodic or quasi-periodic orbits1. Only recently has progress been made in understanding the quantization of systems that exhibit non-periodic, chaotic motion. The spectra of quantized energy levels for such systems are irregular, and show fluctuations associated with unstable periodic orbits of the corresponding classical system1–3. These orbits appear as 'scars'—concentrations of probability amplitude—in the wavefunction of the system4. Although wavefunction scarring has been the subject of extensive theoretical investigation5–10, it has not hitherto been observed experimentally in a quantum system. Here we use tunnel-current spectroscopy to map the quantum-mechanical energy levels of an electron confined in a semiconductor quantum well in a high magnetic field10–13. We find clear experimental evidence for wavefunction scarring, in full agreement with theoretical predictions10.
TL;DR: In this paper, a solution to the quantization problem is presented in the novel approach of Zariski quantization of fields (observables, functions, in this case polynomials).
Abstract: Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After considering some impossibilities and pushing some analogies with field quantization, a solution to the quantization problem is presented in the novel approach of Zariski quantization of fields (observables, functions, in this case polynomials). This quantization is based on the factorization over ${\Bbb R}$ of polynomials in several real variables. We quantize the infinite-dimensional algebra of fields generated by the polynomials by defining a deformation of this algebra which is Abelian, associative and distributive. This procedure is then adapted to derivatives (needed for the Nambu brackets), which ensures the validity of the Fundamental Identity of Nambu Mechanics also at the quantum level. Our construction is in fact more general than the particular case considered here: it can be utilized for quite general defining identities and for much more general star-products.
TL;DR: A quantum theory for mesoscopic electric circuits in accord with the discreteness of electric charges is proposed and the Schrodinger equation for the quantum LC design and L design is solved exactly and a minimum uncertainty state is solved.
Abstract: A quantum theory for mesoscopic electric circuits in accord with the discreteness of electric charges is proposed. On the basis of the theory, the Schr\"odinger equation for the quantum LC design and L design is solved exactly. The uncertainty relation for electric charge and current is obtained and a minimum uncertainty state is solved. By introducing a gauge field, a formula for persistent current arising from magnetic flux is obtained. \textcopyright{} 1996 The American Physical Society.
Book•
01 Jan 1996
TL;DR: In this paper, Tonomura et al. showed that the superposition principle in macroscopic systems is equivalent to the Bohm-Aharonov effect in quantum physics.
Abstract: Part 1 Proceedings of 1st Symposium, S. Kamefuchi et al: gauge fields, electromagnetism and the Bohm-Aharonov effect, C.N. Yang non-local phenomena and the Aharonov-Bohm effect, Y. Aharonov electron holography, Aharonov-Bohm effect and flux quantization, A. Tonomura et al the superposition principle in macroscopic systems, A.J. Leggett and other papers. Part 2 Proceedings of 2nd Symposium, M. Namiki et al: quantum measurements in neutron interferometry, H. Rauch the two-photon polarization correlation of metastable hydrogen as test between quantum mechanics and local realistic theories, H. Kleinpoppen proof of the Aharonov-Bohm effect with completely shielded magnetic field, A. Tonomura et al fractional quantum statistics in two-dimensional systems, Y.-S. Wu and other papers. Part 3 Proceedings of 3rd Symposium, S. Kobayashi et al: optical manifestations of Berry's topological phases - Aharonov-Bohm-like effects in a simple model, R.Y. Chiao high precision determination of and quantum electrodynamics for nonrelativistic systems, T. Kinoshita observations on conductance quantization and dephasing in mesoscale systems, A. Stern et al quantum ballistic electron transport and conductance quantization in a constricted two-dimensional electron gas, B.J. van Wees and other papers. Part 4 Proceedings of 4th Symposium, M. Tsukada et al: reflections on the development of theoretical physics, C.N. Yang the effect of dissipation on tunnelling, A.J. Leggett quantum diffusion in metals, J. Kondo tunnelling phenomena in nuclear physics, R.A. Broglia et al and other papers.
TL;DR: In this article, the exact WKB method and micro-local analysis techniques were used to obtain a complete description of the scattering matrix when the energy is very close to a unique, quadratic maximum of the potential.
Abstract: We study the well-known problem of 1-d quantum scattering by a potential barrier in the semiclassical limit. Using the so-called exact WKB method and semiclassical microlocal analysis techniques, we get a very precise and complete description of the scattering matrix, in particular when the energy is very close to a unique, quadratic maximum of the potential. In our one-dimensional setting, we also recover the Bohr-Sommerfeld quantization condition for the resonances generated by such a maximum.
TL;DR: In this article, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory.
Abstract: Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this article, the authors re-examine the quantization of this mid-superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization.
Abstract: It is well‐known that the Einstein‐Rosen solutions to the 3+1‐ dimensional vacuum Einstein’s equations are in one to one correspondence with solutions of 2+1‐dimensional general relativity coupled to axi‐symmetric, zero rest mass scalar fields. We first re‐examine the quantization of this midi‐superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization. We then use the resulting quantum theory to analyze several conceptual and technical issues of quantum gravity.
TL;DR: It is found that Coulomb self-consistent interactions reduce the amplitude of the echo, and it is shown that quantum effects allow for the appearance of linear echoes.
Abstract: Echo phenomena occurring in various physical systems are investigated, and analytical results are checked against computer experiments. It is found that Coulomb self-consistent interactions reduce the amplitude of the echo. Proof is given of the possibility of refocusing an initially localized packet by periodically kicking the particles, and the relation between this behavior and chaotic diffusion is discussed. Quantum echoes are investigated via simulations of the Wigner equation in the case of an anharmonic oscillator. It is shown that quantum effects allow for the appearance of linear echoes. The reversibility properties of classical and quantum many-particle systems are discussed. @S1063-651X~96!09206-9#
TL;DR: In this paper, the Hall effect has been shown to be similar to the wave-like character of both photons and electrons, but unlike photons, electrons are also charged, and thus experience the Lorentz force in a magnetic field.
Abstract: PHOTONS and electrons, despite their very different nature, show many similarities in their behaviour. Several photonic counterparts of established electronic phenomena—such as photonic energy bands1, weak localization2–4, and the quantization of5 (and fluctuations in6–8) optical transmission—have now been observed. These similarities originate in the wave-like character of both photons and electrons. But unlike photons, electrons are also charged, and thus experience the Lorentz force in a magnetic field. This force leads to the well known Hall effect, in which the application of a magnetic field to an electron-transporting medium generates a new current (or voltage) perpendicular to the direction of both the original current and the applied magnetic field. Despite the absence of photonic charge, one of us has predicted9 that the propagation of light through a disordered, scattering medium should be similarly affected by a magnetic field, although the origin of the effect is very different. Here we report the experimental confirmation of this phenomenon.
TL;DR: Conditions for rotating particle detectors to respond in a variety of bounded spacetimes are derived and the results are compared with the folklore that particle detectors do not respond in the vacuum state appropriate to their motion.
Abstract: We derive conditions for rotating particle detectors to respond in a variety of bounded spacetimes and compare the results with the folklore that particle detectors do not respond in the vacuum state appropriate to their motion. Applications involving possible violations of the second law of thermodynamics are briefly addressed.
TL;DR: In this paper, the authors revisited the quantization of matter-coupled, two-dimensional dilaton gravity and discussed two avenues for consistent quantization: modification of the constraints, and BRST quantization.
TL;DR: In this paper, the energy band spectra, eigenfunctions, and quantum Poincar\'e sections of a free particle moving in a two-dimensional channel bounded by a periodically varying (ripple) wall and a flat wall were obtained.
Abstract: We obtain the energy band spectra, eigenfunctions, and quantum Poincar\'e sections of a free particle moving in a two-dimensional channel bounded by a periodically varying (ripple) wall and a flat wall. Classical Poincar\'e sections show a generic transition from regular to chaotic motion as the size of the ripple is increased. The energy band structure is obtained for two representative geometries corresponding to a wide and a narrow channel. The comparison of numerical results with the level-splitting predictions of low-order quantum degenerate perturbation theory elucidate some aspects of the classical-quantum correspondence. For larger ripple amplitudes the conduction bands for narrow channels become flat and nearly equidistant at low energies. Quantum-classical correspondence is discussed with the aid of quantum Poincar\'e (Husimi) plots.
TL;DR: The vacuum energy of a scalar field in a spherically symmetric background field is considered and the renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function.
Abstract: The vacuum energy of a scalar field in a spherically symmetric background field is considered. It is expressed through the Jost function of the corresponding scattering problem. The renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function. The method is demonstrated in a simple explicit example. {copyright} {ital 1996 The American Physical Society.}
TL;DR: It is shown that conductance quantization is influenced by the geometry of the microconstriction, that is, its length and the shape of its transverse cross section, which leads to a steplike decrease of the conductance upon increasing the strength of the applied magnetic field.
Abstract: The transport properties of three-dimensional quantum microconstrictions in field-free conditions and under the influence of magnetic fields of arbitrary strengths and directions are studied via a generalized Buttiker model @Phys. Rev. B 41, 7906 ~1990!#. It is shown that conductance quantization is influenced by the geometry of the microconstriction ~that is, its length and the shape of its transverse cross section !. In a weak longitudinal magnetic field, when r c@d, where r c is the cyclotron radius and d the effective transverse size of the narrowing of the microconstriction, the conductance exhibits Aharonov-Bohm-type behavior. This behavior transforms in the strong-field limit, r c!d, into Shubnikov-de Haas oscillations with a superimposed Aharonov-Bohm fine structure. The dependence of the Aharonov-Bohm-type features on the length of the microconstriction and on temperature are demonstrated. Transverse magnetic fields lead to depopulation of the magnetoelectric subbands, resulting in a steplike decrease of the conductance upon increasing the strength of the applied magnetic field.
TL;DR: An independent oscillator model is derived, sufficiently realistic to encompass essentially all linear physical optics, and is able to explain why a typical linear environment for the electromagnetic field will effectively render the former classically distinct, but leave the latter fully quantum mechanical.
Abstract: We study environmentally induced decoherence of an electromagnetic field in a homogeneous, linear, dielectric medium. We derive an independent oscillator model for such an environment, which is sufficiently realistic to encompass essentially all linear physical optics. Applying the ``predictability sieve'' to the quantum field, and introducing the concept of a ``quantum halo,'' we recover the familiar dichotomy between background field configurations and photon excitations around them. We are then able to explain why a typical linear environment for the electromagnetic field will effectively render the former classically distinct, but leave the latter fully quantum mechanical. Finally, we suggest how and why quantum matter fields should suffer a very different form of decoherence. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this paper, the concept of quantum state is given in terms of classical probability for position in squeezed and rotated classical reference frames in phase space, and the positive probability density of the harmonic oscillator position is obtained by solving a new eigenvalue equation of standard quantum mechanics instead of the Schrodinger equation.
Abstract: The concept of quantum state is given in terms of classical probability for position in squeezed and rotated classical reference frames in phase space. Stationary states and energy levels of the quantum system are obtained in a classical formulation of quantum mechanics. The positive probability density of the harmonic oscillator position is obtained by solving a new eigenvalue equation of standard quantum mechanics instead of the Schrodinger equation. The orthogonality and completeness relations are found for the eigendistributions.
TL;DR: In this article, the role of the equivalence principle in the context of nonrelativistic quantum mechanics and matter wave interferometry, especially atom beam interferometers, is discussed.
Abstract: The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.