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We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.
A brief review is presented of several models used to describe dynamic polarization of carbon nanostructures by charged particles moving in a broad range of incident velocities. For low-energy excitations of graphene we use the polarization function for its π electron bands in the Dirac cone approximations within a dielectric response approach that includes the transverse optical phonons in a polar substrate. For high-energy excitations by fast electrons we use a two-dimensional hydrodynamic model for the π and σ electron systems in the sp{sup 2} bonded carbon with various geometrical shapes. In particular, we use second quantization of the hydrodynamic model to show that large numbers of plasmons may be excited by moderately fast electrons in a C{sub 60} molecule. Results of the theoretical modeling are compared with several experiments.
We investigate the effects of strong magnetic fields (SMF) on the properties of neutron stars that have hyperons in their composition. The matter is described by a hadronic model in which a parameterized and derivative coupling between hadrons and mesons is considered. We study the magnetic effects on the equation of state (EoS) from Landau quantization, assuming a density dependent static magnetic field that reaches 10{sup 19} G in the center of the star. The Tolman- Oppenheimer-Volkoff (TOV) equations are solved in order to show the dependence of the massradius relation and population of hyperon stars on the central magnetic field and on different hyperon coupling schemes.
The de Broglie relation is a consequence of Planck-Einstein's energy quantization plus Lorentz invariance in describing any system of interaction. Once interaction results in a stable minimum energy configuration, the system, including low dimensional structures and devices, transforms into a particle, without further interactions. However any attempt to make observation of the particle, the interaction causes the entity to revert back to the realm of quantum mechanics. Certain steps may be described by the use of constitutive equations obtained by the use of RPA, Random Phase Approximation, resembling classical descriptions such as refractive index, deformation potentials, effective mass and others. All interactions are quantum mechanical, even appear to be classical.
White noise of dissipationless microwave radio frequency superconducting quantum interference device (RF-SQUID) multiplexers has been experimentally studied to evaluate their readout performance for transition edge sensor (TES) photon counters ranging from near infrared to gamma ray. The characterization has been carried out at 4 K, first to avoid the low-frequency fluctuations present at around 0.1 K, and second, for a feasibility study of readout operation at 4 K for extended applications. To increase the resonant Q at 4 K and maintain low noise SQUID operation, multiplexer chips consisting of niobium nitride (NbN)-based coplanar-waveguide resonators and niobium (Nb)-based RF-SQUIDs have been developed. This hybrid multiplexer exhibited 1 × 10{sup 4} ≤ Q ≤ 2 × 10{sup 4} and the square root of spectral density of current noise referred to the SQUID input √S{sub I} = 31 pA/√Hz. The former and the latter are factor-of-five and seven improvements from our previous results on Nb-based resonators, respectively. Two-directional readout on the complex plane of the transmission component of scattering matrix S{sub 21} enables us to distinguish the flux noise from noise originating from other sources, such as the cryogenic high electron mobility transistor (HEMT) amplifier. Systematic noise measurements with various microwave readout powers P{sub MR} make it possible to distinguish the contribution of noise sources within the system as follows: (1) The achieved √S{sub I} is dominated by the Nyquist noise from a resistor at 4 K in parallel to the SQUID input coil which is present to prevent microwave leakage to the TES. (2) The next dominant source is either the HEMT-amplifier noise (for small values of P{sub MR}) or the quantization noise due to the resolution of 300-K electronics (for large values of P{sub MR}). By a decrease of these noise levels to a degree that is achievable by current technology, we predict that the microwave RF-SQUID multiplexer can exhibit √S{sub I} ≤ 5 pA/√Hz, i.e., close to √S{sub I} of state-of-the-art DC-SQUID-based multiplexers.
We discuss the quantization of linearized gravity on globally hyperbolic, asymptotically flat, vacuum spacetimes, and the construction of distinguished states which are both of Hadamard form and invariant under the action of all bulk isometries. The procedure, we follow, consists of looking for a realization of the observables of the theory as a sub-algebra of an auxiliary, non-dynamical algebra constructed on future null infinity ℱ⁺. The applicability of this scheme is tantamount to proving that a solution of the equations of motion for linearized gravity can be extended smoothly to ℱ⁺. This has been claimed to be possible provided that a suitable gauge fixing condition, first written by Geroch and Xanthopoulos [“Asymptotic simplicity is stable,” J. Math. Phys. 19, 714 (1978)], is imposed. We review its definition critically, showing that there exists a previously unnoticed obstruction in its implementation leading us to introducing the concept of radiative observables. These constitute an algebra for which a Hadamard state induced from null infinity and invariant under the action of all spacetime isometries exists and it is explicitly constructed.
We overview a new type of supersymmetric quantum mechanics models based on the worldline realizations of the supergroup SU(2|1). Our main focus is on the models associated with the chiral multiplets (2,4,2). Considering two nonequivalent deformations of the standard N = 4, d = 1 superspace, we define the relevant chiral superfields and construct their SU(2|1) invariant actions. We give off- and on-shell descriptions of these models and perform their quantization. The basic peculiarities of such models and interrelations between them are briefly discussed.
The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.
We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space D = SU(m, 1)/U(m), with the method of coherent state quantization. In the commutative limit, we obtain the standard manifold. We also consider a quantum field theory model on the noncommutative manifold.
In this study, we address the electronic properties of conducting films constituted of an array of randomly distributed few layer graphene patches and investigate on their most salient galvanometric features in the moderate and extreme disordered limit. We demonstrate that, in annealed devices, the ambipolar behaviour and the onset of Landau level quantization in high magnetic field constitute robust hallmarks of few-layer graphene films. In the strong disorder limit, however, the magneto-transport properties are best described by a variable-range hopping behaviour. A large negative magneto-conductance is observed at the charge neutrality point, in consistency with localized transport regime.
We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting, nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.
A theoretical study of time-dependent dynamical Jahn-Teller effect in an impurity center in a solid is presented. We are considering the relaxation of excited states in the E⊗e-problem through the conical intersection of the potential energy. A strict quantum-mechanical treatment of vibronic interactions with both the main Jahn-Teller active vibration and the nontotally symmetric phonons causing the energy loss is given. The applied method enables us to calculate the time-dependence of the distribution function of the basic configurational coordinate. We have performed a series of numerical calculations allowing us, among other relaxation features, to visualise the details of the relaxation through the conical intersection. In particular, we elucidate how the Slonczewski quantization of the states in the conical intersection affects the relaxation.
Results of molecular quantum electrodynamics calculations of discriminatory interactions between two chiral molecules undergoing resonance energy transfer, van der Waals dispersion, and optical binding are presented. A characteristic feature of the theory is that the radiation field is quantized with signals consequently propagating between centres at the speed of light. In order to correctly describe optically active chromophores, it is necessary to include magnetic as well as electric dipole coupling terms in the time-dependent perturbation theory computations. Recent work investigating the effect of an absorptive and dispersive chiral medium on the rate of migration of energy will also be discussed.
Resonances are temporarily bound states which lie in the continuum part of the Hamiltonian. If the electronic coordinates of the Hamiltonian are scaled (“dilated”) by a complex parameter, η = αe{sup iθ} (α, θ real), then its complex eigenvalues represent the scattering states (resonant and non-resonant) while the eigenvalues corresponding to the bound states and the ionization and the excitation thresholds remain real and unmodified. These make the study of these transient species amenable to the bound state methods. We developed a quadratically convergent multiconfigurational self-consistent field method (MCSCF), a well-established bound-state technique, combined with a dilated Hamiltonian to investigate resonances. This is made possible by the adoption of a second quantization algebra suitable for a set of “complex conjugate biorthonormal” spin orbitals and a modified step-length constraining algorithm to control the walk on the complex energy hypersurface while searching for the stationary point using a multidimensional Newton-Raphson scheme. We present our computational results for the {sup 2}PBe{sup −} shape resonances using two different computationally efficient methods that utilize complex scaled MCSCF (i.e., CMCSCF). These two methods are to straightforwardly use CMCSCF energy differences and to obtain energy differences using an approximation to the complex multiconfigurational electron propagator. It is found that, differing from previous computational studies by others, there are actually two {sup 2}PBe{sup −} shape resonances very close in energy. In addition, N{sub 2} resonances are examined using one of these methods.
We use the framework of quantum field theory to obtain by deformation the Moyal-Weyl spacetime. This idea is extracted from recent progress in deformation theory concerning the emergence of the quantum plane of the Landau-quantization. The quantum field theoretical emerging spacetime is not equal to the standard Moyal-Weyl plane, but terms resembling relativistic corrections occur.
The idea that black holes (BHs) result in highly excited states representing both the “hydrogen atom” and the “quasi-thermal emission” in quantum gravity is today an intuitive but general conviction. In this paper it will be shown that such an intuitive picture is more than a picture. In fact, we will discuss a model of quantum BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. The model is completely consistent with existing results in the literature, starting from the celebrated result of Bekenstein on the area quantization.
We review recent developments in the treatment of spherically symmetric black holes in loop quantum gravity. In particular, we discuss an exact solution to the quantum constraints that represents a black hole and is free of singularities. We show that new observables that are not present in the classical theory arise in the quantum theory. We also discuss Hawking radiation by considering the quantization of a scalar field on the quantum spacetime.
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.